DETAILED ACTION
Notice of Pre-AIA or AIA Status
The present application, filed on or after March 16, 2013, is being examined under the first inventor to file provisions of the AIA .
Specification
The disclosure is objected to because of the following informalities: In page 6, line 1 of the specification description, the sentence “To arrive at an quantum optimal control method, the original time-dependent problem…” should read “To arrive at a quantum optimal control method…” Appropriate correction is required.
Drawings
The drawings are objected to because figures 3B, 4A, 4B, 5E, 5F, 5G, and 6F are not clear to view. Corrected drawing sheets in compliance with 37 CFR 1.121(d) are required in reply to the Office action to avoid abandonment of the application. Any amended replacement drawing sheet should include all of the figures appearing on the immediate prior version of the sheet, even if only one figure is being amended. The figure or figure number of an amended drawing should not be labeled as “amended.” If a drawing figure is to be canceled, the appropriate figure must be removed from the replacement sheet, and where necessary, the remaining figures must be renumbered and appropriate changes made to the brief description of the several views of the drawings for consistency. Additional replacement sheets may be necessary to show the renumbering of the remaining figures. Each drawing sheet submitted after the filing date of an application must be labeled in the top margin as either “Replacement Sheet” or “New Sheet” pursuant to 37 CFR 1.121(d). If the changes are not accepted by the examiner, the applicant will be notified and informed of any required corrective action in the next Office action. The objection to the drawings will not be held in abeyance.
Information Disclosure Statement
The information disclosure statement (IDS) submitted on March 6, 2024, was considered by the examiner. The submission is in compliance with the provisions of 37 CFR 1.97.
Claim Rejections - 35 USC § 112
The following is a quotation of 35 U.S.C. 112(b):
(b) CONCLUSION.—The specification shall conclude with one or more claims particularly pointing out and distinctly claiming the subject matter which the inventor or a joint inventor regards as the invention.
The following is a quotation of 35 U.S.C. 112 (pre-AIA ), second paragraph:
The specification shall conclude with one or more claims particularly pointing out and distinctly claiming the subject matter which the applicant regards as his invention.
Claims 7 and 16 are rejected under 35 U.S.C. 112(b) , where claims 7 and 16 recite the limitation "… wherein the Floquet problem is multi-tonal”, and it is not clear what is defined as a Floquet problem. Therefore, there is insufficient antecedent basis for this limitation in the claim. Appropriate correction is required.
Claim Rejections - 35 USC § 101
35 U.S.C. 101 reads as follows:
Whoever invents or discovers any new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof, may obtain a patent therefore, subject to the conditions and requirements of this title.
Claims 1-18 are rejected under 35 U.S.C. 101 because the claimed invention is directed to an abstract idea (math concept or mental process) without significantly more.
Claim 1:
Regarding claim 1, in step 1 of the 101-analysis set forth in MPEP 2106, the claim recites “1. A method comprising: (a) modeling a quantum mechanical process having one or more time-dependent parameters; (b) constructing a Fourier representation of the time-dependent parameters to determine one or more fundamental frequencies; (c) forming a time-independent Hamiltonian from quantum-mechanical operators derived from the fundamental frequencies; (d) solving, in closed form, a time-independent Schrödinger equation that includes the Hamiltonian; (e) forming an electromagnetic pulse according to the closed-form solution, wherein the electromagnetic pulse optimizes a cost function of the time-dependent parameters; and (f) applying the electromagnetic pulse to the quantum mechanical process, thereby altering at least one observable property of the quantum mechanical process,” and a method is one of the four statutory categories of invention.
In step 2A prong 1 of the 101-analysis set forth in the MPEP 2106, the examiner has determined that the following limitations recite a process that, under the broadest reasonable interpretation, covers a math concept but for recitation of generic computer components:
1. A method comprising: (a) modeling a quantum mechanical process having one or more time-dependent parameters; (This recites a mathematical relationship, mathematical formula or equation, or mathematical calculation, see in specification pages 11-12 stating “
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”, see MPEP 2106.04(a)(2), subsection I),
(b) constructing a Fourier representation of the time-dependent parameters to determine one or more fundamental frequencies; (This recites a mathematical relationship, mathematical formula or equation, or mathematical calculation, see in US PG Pub. US20250077928A1 paragraph [0021] from the specification stating “To arrive at an quantum optimal control method, the original time-dependent problem is represented as a Floquet Hamiltonian. This can be done by first parameterizing the control(s) using a Fourier representation with potentially several fundamental frequencies (i.e., as a multi-tone Floquet problem), and then promoting the control-drive degrees of freedom to a quantum-mechanical operator representation. These steps remove the explicit time-dependence of the Schrödinger equation associated with the original control problem”, and see figure 5D
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, see MPEP 2106.04(a)(2), subsection I),
(c) forming a time-independent Hamiltonian from quantum-mechanical operators derived from the fundamental frequencies; (This recites a mathematical relationship, mathematical formula or equation, or mathematical calculation, see in page 6, lines 1-9, or US PG Pub. US20250077928A1 paragraph [0021] from the specification stating “This can be done by first parameterizing the control(s) using a Fourier representation with potentially several fundamental frequencies (i.e., as a multi-tone Floquet problem), … These steps remove the explicit time-dependence of the Schrödinger equation associated with the original control problem, defining a new, time independent differential equation that can be solved by diagonalizing the Floquet Hamiltonian in an expanded Hilbert space”, see MPEP 2106.04(a)(2), subsection I),
(d) solving, in closed form, a time-independent Schrödinger equation that includes the Hamiltonian; (This recites a mathematical relationship, mathematical formula or equation, or mathematical calculation, see in page 6, lines 1-9, or US PG Pub. US20250077928A1paragraph [0021] from the specification stating “This can be done by first parameterizing the control(s) using a Fourier representation with potentially several fundamental frequencies (i.e., as a multi-tone Floquet problem), … These steps remove the explicit time-dependence of the Schrödinger equation associated with the original control problem, defining a new, time independent differential equation that can be solved by diagonalizing the Floquet Hamiltonian in an expanded Hilbert space”, see MPEP 2106.04(a)(2), subsection I),
If claim limitations, under their broadest reasonable interpretation, cover performance of the limitations as a math concept but for the recitation of generic computer components, then it falls within the math concept grouping of abstract ideas. Accordingly, the claim “recites” an abstract idea.
In step 2A prong 2 of the 101-analysis set forth in MPEP 2106, the examiner has determined that the following additional elements do not integrate this judicial exception into a practical application:
(e) forming an electromagnetic pulse according to the closed-form solution, wherein the electromagnetic pulse optimizes a cost function of the time-dependent parameters; (In step 2A, prong 2, this recites mere instructions to apply an exception using generic computer – see MPEP 2106.05(f)),
and (f) applying the electromagnetic pulse to the quantum mechanical process, thereby altering at least one observable property of the quantum mechanical process, (In step 2A, prong 2, this recites mere instructions to apply an exception using generic computer – see MPEP 2106.05(f)),
Since the claim as a whole, looking at the additional elements individually and in combination, does not contain any other additional elements that are indicative of integration into a practical application, the claim is “directed” to an abstract idea.
In step 2B of the 101-analysis set forth in the 2019 PEG, the examiner has determined that the claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception.
As discussed above, additional elements v and vi recite mere instructions to apply the judicial exception using generic computer components, which are not indicative of significantly more. Considering the additional elements individually and in combination, and the claim as a whole, the additional elements do not provide significantly more than the abstract idea. Therefore, the claim is not patent eligible.
Claim 2:
Regarding claim 2, it is dependent upon claim 1, and thereby incorporates the limitations of, and corresponding analysis applied to claim 1. Further, claim 2 recites the following additional element:
The method of claim 1, wherein the quantum mechanical process comprises a single-qubit gate for fluxonium qubits, (In step 2A, prong 2, this is considered mere instructions to apply an exception using generic computer, see figure 7A for details – see MPEP 2106.05(f)), (In step 2B, this is also considered mere instructions to apply an exception using generic computer – see MPEP 2106.05(f)),
Since the claim does not recite additional elements that either integrate the judicial exception into a practical application, nor provide significantly more than the judicial exception, the claim is not patent eligible.
Claim 3:
Regarding claim 3, it is dependent upon claim 1, and thereby incorporates the limitations of, and corresponding analysis applied to claim 1. Further, claim 3 recites the following additional element:
The method according to claim 1, wherein the quantum mechanical process comprises a microwave two-qubit controlled-Z gate for transmon qubits, (In step 2A, prong 2, this is considered mere instructions to apply an exception using generic computer – see MPEP 2106.05(f)), (In step 2B, this is also considered mere instructions to apply an exception using generic computer – see MPEP 2106.05(f)),
Since the claim does not recite additional elements that either integrate the judicial exception into a practical application, nor provide significantly more than the judicial exception, the claim is not patent eligible.
Claim 4:
Regarding claim 4, it is dependent upon claim 1, and thereby incorporates the limitations of, and corresponding analysis applied to claim 1. Further, claim 4 recites the following additional element:
The method according to claim 1, wherein the quantum mechanical process comprises a baseband-flux two-qubit controlled-Z gate for transmon qubits, (In step 2A, prong 2, this is considered mere instructions to apply an exception using generic computer – see MPEP 2106.05(f)), (In step 2B, this is also considered mere instructions to apply an exception using generic computer – see MPEP 2106.05(f)),
Since the claim does not recite additional elements that either integrate the judicial exception into a practical application, nor provide significantly more than the judicial exception, the claim is not patent eligible.
Claim 5:
Regarding claim 5, it is dependent upon claim 1, and thereby incorporates the limitations of, and corresponding analysis applied to claim 1. Further, claim 5 recites the following additional element:
The method according to claim 1, wherein the quantum mechanical process comprises a baseband-flux two-qubit pulse-train controlled-NOT gate for fluxonium qubits, (In step 2A, prong 2, this is considered mere instructions to apply an exception using generic computer – see MPEP 2106.05(f)), (In step 2B, this is also considered mere instructions to apply an exception using generic computer – see MPEP 2106.05(f)),
Since the claim does not recite additional elements that either integrate the judicial exception into a practical application, nor provide significantly more than the judicial exception, the claim is not patent eligible.
Claim 6:
Regarding claim 6, it is dependent upon claim 1, and thereby incorporates the limitations of, and corresponding analysis applied to claim 1. Further, claim 6 recites the following abstract idea:
The method according to claim 1, wherein forming the time-independent Hamiltonian comprises solving a Floquet problem, (This recites a mathematical relationship, mathematical formula or equation, or mathematical calculation, see from the specification in US PG Pub. US20250077928A1 [0021] stating “ To arrive at an quantum optimal control method, the original time-dependent problem is represented as a Floquet Hamiltonian. This can be done by first parameterizing the control(s) using a Fourier representation with potentially several fundamental frequencies (i.e., as a multi-tone Floquet problem)” showing solving a math problem, see figure 3B for details, see MPEP 2106.04(a)(2), subsection I),
If claim limitations, under their broadest reasonable interpretation, cover performance of the limitations as a math concept but for the recitation of generic computer components, then it falls within the math concept grouping of abstract ideas. Accordingly, the claim “recites” an abstract idea.
Since the claim does not recite additional elements that either integrate the judicial exception into a practical application, nor provide significantly more than the judicial exception, the claim is not patent eligible.
Claim 7:
Regarding claim 7, it is dependent upon claim 1, and thereby incorporates the limitations of, and corresponding analysis applied to claim 1. Further, claim 7 recites the following abstract idea:
The method according to claim 3, wherein the Floquet problem is multi-tonal, (This recites a mathematical relationship, mathematical formula or equation, or mathematical calculation, see figure 5G from the drawings,
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and from the specification in US PG Pub. US20250077928A1 [0021] stating “to arrive at an quantum optimal control method, the original time-dependent problem is represented as a Floquet Hamiltonian. This can be done by first parameterizing the control(s) using a Fourier representation with potentially several fundamental frequencies (i.e., as a multi-tone Floquet problem)” showing solving a math problem, see MPEP 2106.04(a)(2), subsection I),
If claim limitations, under their broadest reasonable interpretation, cover performance of the limitations as a math concept but for the recitation of generic computer components, then it falls within the math concept grouping of abstract ideas. Accordingly, the claim “recites” an abstract idea.
Since the claim does not recite additional elements that either integrate the judicial exception into a practical application, nor provide significantly more than the judicial exception, the claim is not patent eligible.
Claim 8:
Regarding claim 8, it is dependent upon claim 1, and thereby incorporates the limitations of, and corresponding analysis applied to claim 1. Further, claim 8 recites the following abstract idea:
The method according to claim 1, wherein solving the time-independent Schrödinger equation that includes the Hamiltonian comprises diagonalizing the Hamiltonian in an expanded Hilbert space, (This recites a mathematical relationship, mathematical formula or equation, or mathematical calculation, see in US PG Pub. US20250077928A1 in specification paragraph [0020] state “the described QOC method is based, at least in part, upon the inventors recognition that gate dynamics of a desired quantum computer can be inscribed into a time-periodic problem, where the fundamental period is a gate time and the fact that the Schrödinger equation associated with a time-periodic driven problem can be solved by diagonalizing an associated Floquet Hamiltonian, and the resulting Floquet time-propagator is exactly differentiable,” showing diagonalizing Hamiltonian is used in solving a math equation, see MPEP 2106.04(a)(2), subsection I),
Since the claim does not recite additional elements that either integrate the judicial exception into a practical application, nor provide significantly more than the judicial exception, the claim is not patent eligible.
Claim 9:
Regarding claim 9, it is dependent upon claim 1, and thereby incorporates the limitations of, and corresponding analysis applied to claim 1. Further, claim 8 recites the following additional element:
A system comprising one or more qubit gates that are controlled using electromagnetic pulses formed and applied according to the method of claim 1, (In step 2A, prong 2, this is considered mere instructions to apply an exception using generic computer – see MPEP 2106.05(f)), (In step 2B, this is also considered mere instructions to apply an exception using generic computer – see MPEP 2106.05(f)),
Since the claim does not recite additional elements that either integrate the judicial exception into a practical application, nor provide significantly more than the judicial exception, the claim is not patent eligible.
Claim 10:
Regarding claim 10, in step 1 of the 101-analysis set forth in MPEP 2106, the claim recites “10. A non-transitory computer-readable medium comprising instructions stored thereon, the instructions capable of being executed by a processor and comprising: constructing a Fourier representation of the time-dependent parameters to determine one or more fundamental frequencies; forming a time-independent Hamiltonian from quantum-mechanical operators derived from the fundamental frequencies; solving, in closed form, a time-independent Schrödinger equation that includes the Hamiltonian; forming an electromagnetic pulse according to the closed-form solution, wherein the electromagnetic pulse optimizes a cost function of the time-dependent parameters; and applying the electromagnetic pulse to the quantum mechanical process, thereby altering at least one observable property of the quantum mechanical process,” and a non-transitory computer-readable medium or system is one of the four statutory categories of invention.
In step 2A prong 1 of the 101-analysis set forth in the MPEP 2106, the examiner has determined that the following limitations recite a process that, under the broadest reasonable interpretation, covers a math concept but for recitation of generic computer components:
constructing a Fourier representation of the time-dependent parameters to determine one or more fundamental frequencies; (This recites a mathematical relationship, mathematical formula or equation, or mathematical calculation, see in US PG Pub. US20250077928A1 paragraph [0021] from the specification stating “To arrive at an quantum optimal control method, the original time-dependent problem is represented as a Floquet Hamiltonian. This can be done by first parameterizing the control(s) using a Fourier representation with potentially several fundamental frequencies (i.e., as a multi-tone Floquet problem), and then promoting the control-drive degrees of freedom to a quantum-mechanical operator representation. These steps remove the explicit time-dependence of the Schrödinger equation associated with the original control problem”, and see figure 5D
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, see MPEP 2106.04(a)(2), subsection I),
forming a time-independent Hamiltonian from quantum-mechanical operators derived from the fundamental frequencies; (This recites a mathematical relationship, mathematical formula or equation, or mathematical calculation, see in page 6, lines 1-9, or US PG Pub. US20250077928A1 paragraph [0021] from the specification stating “This can be done by first parameterizing the control(s) using a Fourier representation with potentially several fundamental frequencies (i.e., as a multi-tone Floquet problem), … These steps remove the explicit time-dependence of the Schrödinger equation associated with the original control problem, defining a new, time independent differential equation that can be solved by diagonalizing the Floquet Hamiltonian in an expanded Hilbert space”, see MPEP 2106.04(a)(2), subsection I),
solving, in closed form, a time-independent Schrödinger equation that includes the Hamiltonian; (This recites a mathematical relationship, mathematical formula or equation, or mathematical calculation, see in page 6, lines 1-9, or US PG Pub. US20250077928A1paragraph [0021] from the specification stating “This can be done by first parameterizing the control(s) using a Fourier representation with potentially several fundamental frequencies (i.e., as a multi-tone Floquet problem), … These steps remove the explicit time-dependence of the Schrödinger equation associated with the original control problem, defining a new, time independent differential equation that can be solved by diagonalizing the Floquet Hamiltonian in an expanded Hilbert space”, see MPEP 2106.04(a)(2), subsection I),
If claim limitations, under their broadest reasonable interpretation, cover performance of the limitations as a math concept but for the recitation of generic computer components, then it falls within the math concept grouping of abstract ideas. Accordingly, the claim “recites” an abstract idea.
In step 2A prong 2 of the 101-analysis set forth in MPEP 2106, the examiner has determined that the following additional elements do not integrate this judicial exception into a practical application:
10. A non-transitory computer-readable medium comprising instructions stored thereon, the instructions capable of being executed by a processor and comprising … (In step 2A, prong 2, this is considered a generic computer component being used as a tool. – see MPEP 2106.05(f)),
forming an electromagnetic pulse according to the closed-form solution, wherein the electromagnetic pulse optimizes a cost function of the time-dependent parameters; (In step 2A, prong 2, this recites mere instructions to apply an exception using generic computer – see MPEP 2106.05(f)),
and applying the electromagnetic pulse to the quantum mechanical process, thereby altering at least one observable property of the quantum mechanical process, (In step 2A, prong 2, this recites mere instructions to apply an exception using generic computer – see MPEP 2106.05(f)),
Since the claim as a whole, looking at the additional elements individually and in combination, does not contain any other additional elements that are indicative of integration into a practical application, the claim is “directed” to an abstract idea.
In step 2B of the 101-analysis set forth in the 2019 PEG, the examiner has determined that the claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception.
As discussed above, additional element iv recites a generic computer component being used as a tool. Additional elements v and vi recite mere instructions to apply the judicial exception using generic computer components, which are not indicative of significantly more.
Considering the additional elements individually and in combination, and the claim as a whole, the additional elements do not provide significantly more than the abstract idea. Therefore, the claim is not patent eligible.
Claims 11—18:
Since claims 11-18 recite similar limitations as corresponding dependent claims 2-9 listed above, they are rejected for similar reasons under 35 U.S.C. 101.
Claim Rejections - 35 USC § 103
In the event the determination of the status of the application as subject to AIA 35 U.S.C. 102 and 103 (or as subject to pre-AIA 35 U.S.C. 102 and 103) is incorrect, any correction of the statutory basis (i.e., changing from AIA to pre-AIA ) for the rejection will not be considered a new ground of rejection if the prior art relied upon, and the rationale supporting the rejection, would be the same under either status.
The following is a quotation of 35 U.S.C. 103 which forms the basis for all obviousness rejections set forth in this Office action:
A patent for a claimed invention may not be obtained, notwithstanding that the claimed invention is not identically disclosed as set forth in section 102, if the differences between the claimed invention and the prior art are such that the claimed invention as a whole would have been obvious before the effective filing date of the claimed invention to a person having ordinary skill in the art to which the claimed invention pertains. Patentability shall not be negated by the manner in which the invention was made.
The factual inquiries for establishing a background for determining obviousness under 35 U.S.C. 103 are summarized as follows:
1. Determining the scope and contents of the prior art.
2. Ascertaining the differences between the prior art and the claims at issue.
3. Resolving the level of ordinary skill in the pertinent art.
4. Considering objective evidence present in the application indicating obviousness or nonobviousness.
Claims 1, 8, 10, and 17 are rejected under 35 U.S.C. 103 as being unpatentable over Grifoni, M., et al., in “Driven quantum tunneling,” published on October 1st, 1998, available at: https://www.sciencedirect.com/science/article/pii/S0370157398000222 , and available in the March 6, 2024 IDS, (hereafter, Grifoni), in view of Lapert, M., et al., in "Monotonically Convergent Optimal Control Theory of Quantum Systems Under a Nonlinear Interaction With The Control Field", published on May 29, 2009, available at: https://arxiv.org/pdf/0905.4867, (hereafter, Lapert), further in view of Petrescu, A., et al., in “Accurate methods for the analysis of strong-drive effects in parametric gates,” published on July 6, 2021, available at: https://arxiv.org/abs/2107.02343v1 , and available in the March 6, 2024 IDS, (hereafter, Petrescu).
Claim 1:
Regarding claim 1, Grifoni teaches "A method comprising: (a) modeling a quantum mechanical process having one or more time-dependent parameters;"
See Grifoni in page 237 describe “next we discuss general features of quasienergies and Floquet modes with respect to their frequency and field dependence. As mentioned before, if εα=εα0 possesses the Floquet mode …”
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See Grifoni in page 285 mention “Moreover, J (ω ) is the real part of the Fourier transform J (ω ) of the time-dependent damping coefficient (t)…”
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Here, Grifoni shows that the equations 229 and 230 model a quantum mechanical process that includes a time-dependent variable, which in this case includes a time-dependent damping coefficient.
Further, see Grifoni in page 286, section 8.3, The environmental spectral density, describe “The model described by the Hamiltonian (226) is thus completely fixed by the mass m, the time-dependent potential V1(q,t) and by the spectral density J(ω ). Moreover, the latter is completely determined by the frequency-dependent damping coefficient J ( ω) which already ap pears in the classical equations of motion.” Here, Grifoni shows various time-dependent variables that are part of a quantum model. See page 284 for equation 226
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Further, Grifoni teaches "(c) forming a time-independent Hamiltonian from quantum-mechanical operators derived from the fundamental frequencies;"
See Grifoni in page 235, section 2.2 general properties, spectral representations, note “The quasienergy eigenvalue equation in Eq. (7) has the form of the time-independent Schrödinger equation in the composite Hilbert space R ⓧ T.” Here, Grifoni shows solving the time-independent Schrödinger equation.
Further, see Grifoni in page 237, after equation 29, mention “denoting the eigenfunctions and eigenvalues of the time-independent part H of the Hamiltonian in Eq. (3). Thus, when S = 0, the quasienergies depend linearly on frequency so that at some frequency values different levels intersect. When S [not equal] 0, the interaction operator mixes these levels, depending on the symmetry properties of the Hamiltonian.” Here, Grifoni shows the variable quasienergies depend on frequency, and this is part of the time-independent Hamiltonian operations.
Further, Grifoni teaches “(d) solving, … , a time-independent Schrödinger equation that includes the Hamiltonian;”
See Grifoni in page 236 mention “The part χαB of the overall phase χ describes an intrinsic property of a cyclic change of parameters in the periodic Hamiltonian H(t)=H(t+ 𝒯) that explicitly does not depend on the dynamical time interval of cyclic propagation 𝒯.”
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Here, Grifoni shows solving a periodic Hamiltonian that does not depend on the dynamic time interval (i.e. solving a time-independent equation that includes the Hamiltonian).
Further, see Grifoni in page 235, section 2.2 General properties, spectral representations, mention “The quasienergy eigenvalue equation in Eq. (7) has the form of the time-independent Schrödinger equation in the composite Hilbert space R ⓧ T.” Here, Grifoni shows solving the time-independent Schrödinger equation. These equations are part of a sequence in modeling a quantum mechanical process. See equation 7 on page 234 from Grifoni:
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However, Grifoni did not teach "ii. (b) constructing a Fourier representation of the time-dependent parameters to determine one or more fundamental frequencies;" or " (d) solving, in closed form, ..." or "v. (e) forming an electromagnetic pulse according to the closed-form solution, wherein the electromagnetic pulse optimizes a cost function of the time-dependent parameters;" or “and (f) applying the electromagnetic pulse to the quantum mechanical process, thereby altering at least one observable property of the quantum mechanical process.”
4) In an analogous art, Lapert teaches "(b) constructing a Fourier representation of the time-dependent parameters to determine one or more fundamental frequencies;"
See Lapert in page 3, section II. Optimal Control Theory, part 2.1. The model system, describe “We consider a quantum system interacting with an electromagnetic field whose dynamics is governed by the following time-dependent Schrödinger equation”. Here, Lapert mentions using the quantum system with an electromagnetic field.
Further, see Lapert in page 2, section Introduction, describe "Finally, we also analyze the structure of the Fourier transform of optimal control pulses. Our aim is to show that the optimal solutions can be well approximated by pulses that could be implemented experimentally [35–38]. Such pulses, tailored by genetic algorithms, have been successfully applied for experimentally and theoretically controlling different molecular processes [36–41]. In the frequency domain, they are characterized by the fact that both the amplitude and the phase of the Fourier transform (but only for a finite number of frequencies equally distributed over a given frequency interval) are optimized... Starting from the optimal solution obtained by the monotonic algorithm, we discretize the phase and the amplitude of its Fourier transform into 640 points or less (640 points correspond to the number of pixels usually used in pulse-shaping experiments). From this discretization, we then construct a piecewise constant Fourier transform and a new time-dependent electric field by an inverse Fourier transform [40,41]. We finally compare the optimal result and the one obtained with the discretized field. " Here, Lapert shows a method of using Fourier transform (i.e. Fourier representation) to represent time dependent parameters within an electric field using a pulse-shaping experiment. Lapert also mentions this helps to determine finite number of frequencies (i.e. viewed as one or more fundamental frequencies).
Further, see Lapert in page 8, section B. Zero rotational temperature describe “The CO molecule is taken as an example. The units used are atomic units unless otherwise specified. The molecule is described in a rigid-rotor approximation interacting with a linearly polarized laser pulse nonresonant with vibronic frequencies.” Here, Lapert shows that vibronic frequencies correspond to fundamental frequencies, since the vibronic refers to transitions from one state to another in molecules, and occur in discrete values.
Also, see Lapert in page 15, section D. Analysis of the Fourier spectrum, note "A similar behavior has been observed for the other optimal solutions. Another example is given by Fig. 10. The corresponding optimal solution obtained by the algorithm I presents rapid unwanted oscillations. To obtain a smooth solution displayed in Fig. 10(b), we filter this optimal pulse in the frequency domain." Here, Lapert shows filtering a pulse in the frequency domain, which relate to using a Fourier representation of variables to determine fundamental frequencies. Examiner construes determine to mean identify, use variable to calculate, or establish. Here, Lapert shows identifying frequencies using the Fourier transform operations. See Lapert in figure 8 for details.
Further, Lapert teaches "(e) forming an electromagnetic pulse according to the ... solution, wherein the electromagnetic pulse optimizes a cost function of the time-dependent parameters;"
See Lapert on page 16, note using a cost function.
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Here, Lapert describes using a cost function in equation 38 to determine optimal solutions, where ρ(t) and ρ(tf) show variables that are functions of time or a time-dependent parameters.
See also from Lapert in page 1, Introduction, describe “By construction, the optimal field is the field steering a dynamical system from the initial state to a desired target state and minimizing a cost functional which generally penalizes the energy or the duration of the field.” Here, Lapert shows minimizing a cost function relates to optimizing a cost function.
See Lapert in page 17, paragraph 2, mention “We also point out sharp variations of the optimal fields due to the use of a cost that is quartic in the control field.” Here, Lapert describes optimizing a cost function from page 16.
Also, see Lapert in page 1, abstract, describe “We consider the optimal control of quantum systems interacting nonlinearly with an electromagnetic field. We propose monotonically convergent algorithms to solve the optimal equations... Discretizing the amplitude and the phase of the Fourier transform of the optimal field, we show that the optimal solution can be well approximated by pulses that could be implemented experimentally.” Here, Lapert shows forming an electromagnetic pulse to implement optimal solutions for operations in quantum calculations.
Further, Lapert teaches "and (f) applying the electromagnetic pulse to the quantum mechanical process, thereby altering at least one observable property of the quantum mechanical process"
See Lapert in pages 7-8, Section 3. Control of Molecular Orientation, part A. Introduction mention “In this section, we investigate the control of orientation dynamics of a diatomic molecule driven by an electromagnetic field [28,29]. This control is taken as a prototype to test the efficiency of the algorithm. The application of OCT to molecular alignment and orientation is relatively recent [12,22,43]. One of the main results of Ref. [22] is that the optimal oriented state (see below for a definition) is reached by rotational ladder climbing, i.e., by successive rotational excitations. The corresponding optimal pulse is however very long, of the order of 20 rotational periods, which could be problematic for practical applications. We consider shorter durations in this paper of the order of the rotational period. We have chosen tf = Tper but other durations can be considered. Note that, for controls much shorter than Tper, the optimal solution is very close to the kick mechanism largely explored using the sudden-impact model [44]. The CO molecule is taken as an example. The units used are atomic units unless otherwise specified. The molecule is described in a rigid-rotor approximation interacting with a linearly polarized laser pulse nonresonant with vibronic frequencies.” Here, Lapert describes the method of controlling a pulse of a molecule driven by an electromagnetic field and apply to observe in a quantum mechanical process.
Later, see Lapert in page 8, section B. Zero rotational temperature note "In this section, we consider the limit of zero rotational temperature. We recall that the expectation value is usually taken as a quantitative measure of orientation [28,29]. Here, we replace this measure by the projection onto a target state . We consider target states recently introduced for the orientation which both maximize the field-free orientation and its duration [31,32]. To construct this target state, we restrict the Hilbert space to a finite-dimensional one defined by a maximum value of j denoted jopt. For CO, we have chosen jopt = 4 which leads to a maximum of ⟨cos θ⟩ of the order of 0.9." By restricting the Hilbert space to a finite dimension of the molecular orientation, Lapert shows this relates to altering at least one observable property of the quantum mechanical process.
It would have been obvious for one of ordinary skill in the art before the effective filing date of the claimed invention to combine the base reference of Grifoni and incorporate into the teachings of Lapert because both references teach using electromagnetic pulses to the quantum mechanical process.
One of ordinary skill in the art would be motivated to do so because “Discretizing the amplitude and the phase of the Fourier transform of the optimal field, we show that the optimal solution can be well-approximated by pulses that could be implemented experimentally,” (see Lapert in page 1, abstract).
However, Grifoni in view of Lapert did not teach “(d) solving, in closed form, a ... equation ...;” or “forming ...according to the closed-form solution...”
7) In an analogous art, Petrescu teaches "(d) solving, in closed form, a ... equation ...;"
See Petrescu in abstract in page 1, mention “Our analytical treatment, based on time-dependent Schrieffer-Wolff perturbation theory, yields closed-form expressions for gate frequencies and spurious interactions, and is valid for strong drives. From these calculations, we identify optimal regimes of operation for different types of gates.” Here, Petrescu mentions using a closed form expression for the math operation.
8) Further, Petrescu teaches "(e) forming ...according to the closed-form solution..."
See Petrescu in abstract in page 1, mention “Our analytical treatment, based on time-dependent Schrieffer-Wolff perturbation theory, yields closed-form expressions for gate frequencies and spurious interactions, and is valid for strong drives. From these calculations, we identify optimal regimes of operation for different types of gates.” Here, Petrescu mentions using a closed form expression for the math operation.
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to combine the references of Grifoni and Lapert, with the teachings of Petrescu by using the teachings of Grifoni and Lapert, and incorporate with Petrescu’s teaching of a closed form operation.
One of ordinary skill in the art would be motivated to do so because by integrating Petrescu’s framework into the methods of Grifoni and Lapert, one with ordinary skill in the art would achieve the goal of providing “the Floquet method is numerically efficient as compared to the simulation of the dynamics over the complete gate time … Due to its relatively small computational footprint, the Floquet method allows us to efficiently search for optimal gate parameters,” (see Petrescu in page 12, paragraph after equation 58).
Claim 8:
Regarding claim 8, Grifoni in view of Lapert, further in view of Petrescu, teach the limitations in claim 1. Further, Grifoni teaches “8. The method according to claim 1, wherein solving the time-independent Schrödinger equation that includes the Hamiltonian comprises diagonalizing the Hamiltonian in an expanded Hilbert space”
See Grifoni in page 234 mention "For the sake of simplicity only, we restrict ourselves here to the one-dimensional case. With H(q,t) = H 0(q) + H ext (q,t),
H ext (q,t) = H ext (q,t + T), (3)
the unperturbed Hamiltonian H(q) is assumed to possess a complete orthonormal set of eigen
functions H 0 (q) with corresponding eigenvalues {E n}." Here, examiner construes diagonalizing the Hamiltonian to mean finding its eigenvalues (the allowed energy levels) and eigenstates (the wavefunctions) of the operations here, which is in this case is the Hamiltonian. In an expanded Hilbert space, the Hamiltonian (energy operator) is written as a large matrix.
Further, see Grifoni in page 234 last paragraph, describe "For the Hermitian operator H(q,t) it is convenient to introduce the composite Hilbert space R ⓧ T made up of the Hilbert space R of square integrable functions on configuration space and the space T of functions which are periodic in t with period T = 2 π/Ω”. Here, Grifoni mentions that this operation involves a Hilbert space since combining R and T created a larger or expanded vector space where the variables depend on both R and T. This Hilbert space shows a mathematical framework used to solve time-dependent, periodic quantum systems using Floquet theory or Floquet operations.
Claim 10:
Regarding claim 10, Grifoni teaches “10. A non-transitory computer-readable medium comprising instructions stored thereon, the instructions capable of being executed by a processor …”
See Grifoni in page 315 in section 12.1.1.2. Markovian regime. In the following we discuss the Markovian limit T, ( , L ); ,2.Here τk is the characteristic memory time of the kernels of Eq. (290) which describe the influence of the environment and of the driving.”
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Here, Grifoni mentions a memory time of kernels, where memory kernels here are part of a computer RAM system of an operating system, and represent a non-transitory computer readable medium that inherently has a processor that runs operations of calculations shown by Grifoni throughout the paper.
Further, Grifoni teaches “forming a time-independent Hamiltonian from quantum-mechanical operators derived from the fundamental frequencies;”
See Grifoni in page 235, section 2.2 general properties, spectral representations, note “The quasienergy eigenvalue equation in Eq. (7) has the form of the time-independent Schrödinger equation in the composite Hilbert space R ⓧ T.” Here, Grifoni shows solving the time-independent Schrödinger equation.
Further, see Grifoni in page 237, after equation 29, mention “denoting the eigenfunctions and eigenvalues of the time-independent part H of the Hamiltonian in Eq. (3). Thus, when S = 0, the quasienergies depend linearly on frequency so that at some frequency values different levels intersect. When S [not equal] 0, the interaction operator mixes these levels, depending on the symmetry properties of the Hamiltonian.” Here, Grifoni shows the variable quasienergies depend on frequency, and this is part of the time-independent Hamiltonian operations.
Further, Grifoni teaches “solving, … , a time-independent Schrödinger equation that includes the Hamiltonian;”
See Grifoni in page 236 mention “The part χαB of the overall phase χ describes an intrinsic property of a cyclic change of parameters in the periodic Hamiltonian H(t)=H(t+ 𝒯) that explicitly does not depend on the dynamical time interval of cyclic propagation 𝒯.”
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Here, Grifoni shows solving a periodic Hamiltonian that does not depend on the dynamic time interval (i.e. solving a time-independent equation that includes the Hamiltonian).
Further, see Grifoni in page 235, section 2.2 General properties, spectral representations, mention “The quasienergy eigenvalue equation in Eq. (7) has the form of the time-independent Schrödinger equation in the composite Hilbert space R ⓧ T.” Here, Grifoni shows solving the time-independent Schrödinger equation. These equations are part of a sequence in modeling a quantum mechanical process. See equation 7 on page 234 from Grifoni:
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However, Grifoni did not teach “constructing a Fourier representation of the time-dependent parameters to determine one or more fundamental frequencies;” or “solving, in closed form, ...” or “forming an electromagnetic pulse according to the closed-form solution, wherein the electromagnetic pulse optimizes a cost function of the time-dependent parameters;" or “and applying the electromagnetic pulse to the quantum mechanical process, thereby altering at least one observable property of the quantum mechanical process.”
In an analogous art, Lapert teaches " … and comprising: constructing a Fourier representation of the time-dependent parameters to determine one or more fundamental frequencies;"
See Lapert in page 3, section II. Optimal Control Theory, part 2.1, The model system, describe “We consider a quantum system interacting with an electromagnetic field whose dynamics is governed by the following time-dependent Schrödinger equation.” Here, Lapert mentions using the quantum system with an electromagnetic field.
Further, see Lapert in page 2, section Introduction, describe "Finally, we also analyze the structure of the Fourier transform of optimal control pulses. Our aim is to show that the optimal solutions can be well approximated by pulses that could be implemented experimentally [35–38]. Such pulses, tailored by genetic algorithms, have been successfully applied for experimentally and theoretically controlling different molecular processes [36–41]. In the frequency domain, they are characterized by the fact that both the amplitude and the phase of the Fourier transform (but only for a finite number of frequencies equally distributed over a given frequency interval) are optimized... Starting from the optimal solution obtained by the monotonic algorithm, we discretize the phase and the amplitude of its Fourier transform into 640 points or less (640 points correspond to the number of pixels usually used in pulse-shaping experiments). From this discretization, we then construct a piecewise constant Fourier transform and a new time-dependent electric field by an inverse Fourier transform [40,41]. We finally compare the optimal result and the one obtained with the discretized field. " Here, Lapert shows a method of using Fourier transform (i.e. Fourier representation) to represent time dependent parameters within an electric field using a pulse-shaping experiment. Lapert also mentions this helps to determine finite number of frequencies (i.e. viewed as one or more fundamental frequencies).
Further, see Lapert in page 8, section B. Zero rotational temperature describe “The CO molecule is taken as an example. The units used are atomic units unless otherwise specified. The molecule is described in a rigid-rotor approximation interacting with a linearly polarized laser pulse nonresonant with vibronic frequencies.” Here, Lapert shows that vibronic frequencies correspond to fundamental frequencies, since the vibronic refers to transitions from one state to another in molecules, and occur in discrete values.
Also, see Lapert in page 15, section D. Analysis of the Fourier spectrum, note "A similar behavior has been observed for the other optimal solutions. Another example is given by Fig. 10. The corresponding optimal solution obtained by the algorithm I presents rapid unwanted oscillations. To obtain a smooth solution displayed in Fig. 10(b), we filter this optimal pulse in the frequency domain." Here, Lapert shows filtering a pulse in the frequency domain, which relate to using a Fourier representation of variables to determine fundamental frequencies. Examiner construes determine to mean identify, use variable to calculate, or establish. Here, Lapert shows identifying frequencies using the Fourier transform operations. See Lapert in figure 8 for details.
Further, Lapert teaches " forming an electromagnetic pulse according to the ... solution, wherein the electromagnetic pulse optimizes a cost function of the time-dependent parameters;"
See Lapert in page 16, note using a cost function.
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Here, Lapert describes using a cost function in equation 38 to determine optimal solutions, where ρ(t) and ρ(tf) show variables that are functions of time or a time-dependent parameters.
See also from Lapert in page 1, Introduction, describe “By construction, the optimal field is the field steering a dynamical system from the initial state to a desired target state and minimizing a cost functional which generally penalizes the energy or the duration of the field.” Here, Lapert shows minimizing a cost function relates to optimizing a cost function.
See Lapert in page 17, paragraph 2, mention “We also point out sharp variations of the optimal fields due to the use of a cost that is quartic in the control field.” Here, Lapert describes optimizing a cost function from page 16.
Also, see Lapert in page 1, abstract, describe “We consider the optimal control of quantum systems interacting nonlinearly with an electromagnetic field. We propose monotonically convergent algorithms to solve the optimal equations... Discretizing the amplitude and the phase of the Fourier transform of the optimal field, we show that the optimal solution can be well approximated by pulses that could be implemented experimentally.” Here, Lapert shows forming an electromagnetic pulse to implement optimal solutions for operations in quantum calculations.
Further, Lapert teaches "and applying the electromagnetic pulse to the quantum mechanical process, thereby altering at least one observable property of the quantum mechanical process"
See Lapert in pages 7-8, Section 3. Control of Molecular Orientation, part A. Introduction mention “In this section, we investigate the control of orientation dynamics of a diatomic molecule driven by an electromagnetic field [28,29]. This control is taken as a prototype to test the efficiency of the algorithm. The application of OCT to molecular alignment and orientation is relatively recent [12,22,43]. One of the main results of Ref. [22] is that the optimal oriented state (see below for a definition) is reached by rotational ladder climbing, i.e., by successive rotational excitations. The corresponding optimal pulse is however very long, of the order of 20 rotational periods, which could be problematic for practical applications. We consider shorter durations in this paper of the order of the rotational period. We have chosen tf = Tper but other durations can be considered. Note that, for controls much shorter than Tper, the optimal solution is very close to the kick mechanism largely explored using the sudden-impact model [44]. The CO molecule is taken as an example. The units used are atomic units unless otherwise specified. The molecule is described in a rigid-rotor approximation interacting with a linearly polarized laser pulse nonresonant with vibronic frequencies.” Here, Lapert describes the method of controlling a pulse of a molecule driven by an electromagnetic field and apply to observe in a quantum mechanical process.
Later, see Lapert in page 8, section B. Zero rotational temperature note "In this section, we consider the limit of zero rotational temperature. We recall that the expectation value is usually taken as a quantitative measure of orientation [28,29]. Here, we replace this measure by the projection onto a target state . We consider target states recently introduced for the orientation which both maximize the field-free orientation and its duration [31,32]. To construct this target state, we restrict the Hilbert space to a finite-dimensional one defined by a maximum value of j denoted jopt. For CO, we have chosen jopt = 4 which leads to a maximum of ⟨cos θ⟩ of the order of 0.9." By restricting the Hilbert space to a finite dimension of the molecular orientation, Lapert shows this relates to altering at least one observable property of the quantum mechanical process.
It would have been obvious for one of ordinary skill in the art before the effective filing date of the claimed invention to combine the base reference of Grifoni and incorporate into the teachings of Lapert because both references teach using electromagnetic pulses to the quantum mechanical process.
One of ordinary skill in the art would be motivated to do so because “Discretizing the amplitude and the phase of the Fourier transform of the optimal field, we show that the optimal solution can be well-approximated by pulses that could be implemented experimentally,” (see Lapert in page 1, abstract).
However, Grifoni in view of Lapert did not teach " solving, in closed form, a ... equation ...;" or "forming ...according to the closed-form solution..."
7) In an analogous art, Petrescu teaches " solving, in closed form, a ... equation ...;"
See Petrescu in abstract in page 1, mention “Our analytical treatment, based on time-dependent Schrieffer-Wolff perturbation theory, yields closed-form expressions for gate frequencies and spurious interactions, and is valid for strong drives. From these calculations, we identify optimal regimes of operation for different types of gates.” Here, Petrescu mentions using a closed form expression for the math operation.
8) Further, Petrescu teaches " forming ...according to the closed-form solution..."
See Petrescu in abstract in page 1, mention “Our analytical treatment, based on time-dependent Schrieffer-Wolff perturbation theory, yields closed-form expressions for gate frequencies and spurious interactions, and is valid for strong drives. From these calculations, we identify optimal regimes of operation for different types of gates.” Here, Petrescu mentions using a closed form expression for the math operation.
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to combine the references of Grifoni and Lapert, with the teachings of Petrescu by using the teachings of Grifoni and Lapert, and incorporate with Petrescu’s teaching of a closed form operation.
One of ordinary skill in the art would be motivated to do so because by integrating Petrescu’s framework into the methods of Grifoni and Lapert, one with ordinary skill in the art would achieve the goal of providing “the Floquet method is numerically efficient as compared to the simulation of the dynamics over the complete gate time … Due to its relatively small computational footprint, the Floquet method allows us to efficiently search for optimal gate parameters,” (see Petrescu in page 12, paragraph after equation 58).
Regarding claim 10, the claim recites similar additional limitations as independent claim 1, and is rejected under the same reasons and rationale under 35 U.S.C. 103 as claim 1.
Claim 17:
Since claim 17 recites similar limitations as corresponding dependent claim 8 listed above, this claim is rejected for similar reasons with similar rationale under 35 U.S.C. 103.
Claims 2 and 11 are rejected under 35 U.S.C. 103 as being unpatentable over Grifoni in view of Lapert, further in view of Petrescu, and further in view of Nguyen, L., et al., in “Blueprint for a high-performance fluxonium quantum processor,” published on August 5th, 2022; available at: https://journals.aps.org/prxquantum/abstract/10.1103/PRXQuantum.3.037001 , (hereafter, Nguyen).
Claim 2:
Regarding claim 2, Grifoni in view of Lapert, further in view of Petrescu, teaches the limitations in claim 1.
However, Grifoni in view of Lapert, further in view of Petrescu, did not teach "2. The method of claim 1, wherein the quantum mechanical process comprises a single-qubit gate for fluxonium qubits."
In an analogous art, Nguyen teaches "2. The method of claim 1, wherein the quantum mechanical process comprises a single-qubit gate for fluxonium qubits"
See Nguyen in page 037001-2, in Introduction, paragraph 4, describe "In addition, fluxonium’s large anharmonicity can be exploited to operate high-fidelity single-qubit operations, with a microwave control error of approximately 10−4 using an 80- ns-long pulse [55], and fast flux control error of approximately 10−3 using a 20- ns-long pulse [54]. High readout fidelity with an error of approximately 10−2 using over a hundred of resonator photons has been demonstrated..." Here, Nguyen shows using fluxonium as part of the system.
Later see Nguyen in page 037001-3 , Introduction , paragraph 7, note "Since these gates involve only high-coherence computational states, gate error due to decoherence is small. Moreover, they can be implemented using the same control lines and microwave electronics for single-qubit gates, improving resource efficiency in scaling up." Here, Nguyen shows that fluxonium can be used for single-qubit gates via single-qubit operations to create fluxonium qubits. See Nguyen in figure 1 for details.
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It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to combine the references of Grifoni, Lapert, and Petrescu with the teachings of Nguyen by using the teachings of Grifoni, Lapert, and Petrescu, and incorporate with Nguyen’s teaching of a single-qubit gate for fluxonium qubits.
One of ordinary skill in the art would be motivated to do so because by integrating Nguyen’s framework into the methods of Grifoni, Lapert, and Petrescu, one with ordinary skill in the art would achieve the goal of providing “ show that, in principle, this platform will have suppressed crosstalk, reduced design complexity, improved operational efficiency, high-fidelity gates, and resistance to parameter fluctuations,” (see Nguyen in page 037001-2, in section I. Introduction).
Claim 11:
Since claim 11 recites similar limitations as corresponding dependent claim 2 listed above, this claim is rejected for similar reasons with similar rationale under 35 U.S.C. 103.
Claims 3, 7, 12, and 16 are rejected under 35 U.S.C. 103 as being unpatentable over Grifoni in view of Lapert, further in view of Petrescu, and further in view of Qi, Z., et al., in “Controlled-Z gate for transmon qubits coupled by semiconductor junctions,” published on April 23, 2018, available at: https://journals.aps.org/prb/abstract/10.1103/PhysRevB.97.134518 , (hereafter, Qi).
Claim 3:
Regarding claim 3, Grifoni in view of Lapert, further in view of Petrescu, teaches the limitations in claim 1. However, Grifoni in view of Lapert, further in view of Petrescu, did not teach “The method according to claim 1, wherein the quantum mechanical process comprises a microwave two-qubit controlled-Z gate for transmon qubits.”
In an analogous art, Qi teaches “The method according to claim 1, wherein the quantum mechanical process comprises a microwave two-qubit controlled-Z gate for transmon qubits”
See Qi in page 1, abstract note “We analyze the coupling of two qubits via an epitaxial semiconducting junction. In particular, we consider three configurations that include pairs of transmons or gatemons as well as gatemonlike two qubits formed by an epitaxial four-terminal junction. These three configurations provide electrical control of the interaction between the qubits by applying voltage to a metallic gate near the semiconductor junction and can be utilized to naturally realize a controlled-Z gate (CZ).” Here, Qi mentions using a two-qubit controlled Z gate with transmons, where using transmons relate to using transmon qubits.
Later, see Qi in page 1, Introduction, note “Over the last 10 years, superconducting circuits based on tunnel Josephson junctions (JJ) have clearly became a leading platform for implementing a solid-state based quantum computer [1–6]. Many factors contribute to this leadership. Absence of normal carriers helps to reduce decoherence; reproducibility of junction fabrication allows the pursuit of complex devices; and the availability of quantum optics type of control of qubits, such as interactions of superconducting circuits with microwave cavities [7–12], helps to achieve the highest degree of control at times even surpassing the benchmarks of conventional atomic systems.” Here, Qi mentions using microwaves and in abstract shows using transmons two-qubit for a controlled-Z gate.
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to combine the references of Grifoni, Lapert, and Petrescu with the teachings of Qi by using the teachings of Grifoni, Lapert, and Petrescu, and incorporate with Qi’s teaching of a quantum mechanical process comprises a microwave two-qubit controlled-Z gate for transmon qubits.
One of ordinary skill in the art would be motivated to do so because by integrating Qi’s framework into the methods of Grifoni, Lapert, and Petrescu, one with ordinary skill in the art would achieve the goal of providing “When the coupling between transmons through the junction is turned on, the additional Josephson energy associated with the ABS introduces an effective interaction between two qubits and changes the energy spectrum of the two-qubit system.” (See Qi in page 134518-1, fifth paragraph in Introduction).
Claim 7:
Regarding claim 7, Grifoni in view of Lapert, further in view of Petrescu, and further in view of Qi, teach the limitations in claim 3.
Further, Petrescu teaches “7. The method according to claim 3, wherein the Floquet problem is multi-tonal”
See Petrescu in page 13, section B. Full circuit simulation describe ""we apply the Floquet numerical method to the full circuit Hamiltonian of Sec. IV A. We study the dependence of the coupling constants in the effective gate Hamiltonian versus DC flux and as a function of the drive amplitude. ..To exemplify the full extent of the Floquet analysis, we generate two-tone spectroscopy data from our simulations according to Eqs. (F2) and (F3) in Appendix F, by focusing on the experimentally relevant situation where the parametric drive is on," Here, Petrescu mentions using Floquet analysis (or solving problems that involve Floquet operations) on two tone (i.e. relates to multi-tonal ) spectroscopy.
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to combine the references of Grifoni and Lapert, with the teachings of Petrescu by using the teachings of Grifoni and Lapert, and incorporate with Petrescu’s teaching of Floquet problem is multi-tonal.
One of ordinary skill in the art would be motivated to do so because by integrating Petrescu’s framework into the methods of Grifoni and Lapert, one with ordinary skill in the art would achieve the goal of providing “the Floquet method is numerically efficient as compared to the simulation of the dynamics over the complete gate time … Due to its relatively small computational footprint, the Floquet method allows us to efficiently search for optimal gate parameters,” (see Petrescu in page 12, paragraph after equation 58).
Claim 12:
Since claim 12 recites similar limitations as corresponding dependent claim 3 listed above, this claim is rejected for similar reasons with similar rationale under 35 U.S.C. 103.
Claim 16:
Since claim 16 recites similar limitations as corresponding dependent claim 7 listed above, this claim is rejected for similar reasons with similar rationale under 35 U.S.C. 103.
Claims 4 and 13 are rejected under 35 U.S.C. 103 as being unpatentable over Grifoni in view of Lapert, further in view of Petrescu, and further in view of Sagastizabal, R., et al., in “Variational preparation of finite-temperature states on a quantum computer,” published on August 20th, 2021, available at: https://www.nature.com/articles/s41534-021-00468-1 , (hereafter, Sagastizabal).
Claim 4:
Regarding claim 4, Grifoni in view of Lapert, further in view of Petrescu, teaches the limitations in claim 1. However, Grifoni in view of Lapert, further in view of Petrescu, did not teach “The method according to claim 1, wherein the quantum mechanical process comprises a baseband-flux two-qubit controlled-Z gate for transmon qubits.”
In an analogous art, Sagastizabal teaches “The method according to claim 1, wherein the quantum mechanical process comprises a baseband-flux two-qubit controlled-Z gate for transmon qubits.”
See Sagastizabal in page 4, section METHODS, Quantum circuit note “We map the theoretical circuit in Fig. 1(b) to an equivalent circuit conforming to the native gate set in our control architecture and exploiting virtual Z-gate compilation28 to minimize circuit depth. Single-qubit rotations RXY(ϕ, θ), by arbitrary angle θ around any equatorial axis on the Bloch sphere, are realized using 20ns DRAG pulses29,30. Two-qubit CZ gates are realized by baseband flux pulsing31,32 using the Net Zero scheme…” Here, Sagastizabal shows using Two-qubit CZ gates with baseband flux pulse methods.
Later, see Sagastizabal in page 1, Introduction, paragraph 1, note “In this work, we demonstrate the use of a variational quantum-classical algorithm to realize Gibbs states using (ideally unitary) gate control on a transmon quantum processor.” Here, Sagastizabal shows this work applies the method on a transmon processor, using the methods of a two-qubit controlled Z gate with baseband flux to create transmon qubits,
Further, see Sagastizabal in page 2, section Experiment note “We implement the algorithm using four of seven transmons in a monolithic quantum processor [Fig. 2(a)]. The four transmons (labeled A1, A2, B1, and B2) have square connectivity provided by coupling bus resonators, and are thus ideally suited for implementing the circuit in Fig. 1(b). Each transmon has a microwave-drive line for single-qubit gating, a flux-bias line for two-qubit controlled-Z (CZ) gates, and a dispersively coupled resonator with dedicated Purcell filter 22,23. The four transmons can be simultaneously and independently read out by frequency multiplexing,” Here, Sagastizabal shows using a transmon qubit.
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to combine the references of Grifoni, Lapert, and Petrescu with the teachings of Sagastizabal by using the teachings of Grifoni, Lapert, and Petrescu, and incorporate with Sagastizabal’s teaching of a quantum mechanical process that has a baseband-flux two-qubit controlled-Z gate for transmon qubits.
One of ordinary skill in the art would be motivated to do so because by integrating Sagastizabal’s framework into the methods of Grifoni, Lapert, and Petrescu, one with ordinary skill in the art would achieve the goal of providing “The engineered cost function achieves an average improvement of 54% across the β range covered ([10−2,102] in units of 1/g), as well as a maximum improvement of up to 98% for intermediate temperatures (β~1).” (see Sagastizabal in page 2, second to last paragraph, in Results, Theory section).
Claim 13:
Since claim 13 recites similar limitations as corresponding dependent claim 4 listed above, this claim is rejected for similar reasons with similar rationale under 35 U.S.C. 103.
Claims 5 and 14 rejected under 35 U.S.C. 103 as being unpatentable over Grifoni in view of Lapert, further in view of Petrescu, and further in view of Nesterov, K., et al., in “CNOT gates for fluxonium qubits via selective darkening of transitions,” published on September 23, 2022, available at: https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.18.034063 , (hereafter, Nesterov)., further in view of Rol, M. et al., in “Time-domain characterization and correction of on-chip distortion of control pulses in a quantum processor,” published on February 3, 2020, available at: https://pubs.aip.org/aip/apl/article/116/5/054001/38884 , and available in the March 6, 2024 IDS, (hereafter, Rol).
Claim 5:
Regarding claim 5, Grifoni in view of Lapert, further in view of Petrescu, teaches the limitations in claim 1. However, Grifoni in view of Lapert, further in view of Petrescu, did not teach “5. The method according to claim 1, wherein the quantum mechanical process comprises a baseband-flux two-qubit pulse-train controlled-NOT gate for fluxonium qubits.”
In an analogous art, Nesterov teaches “5. The method according to claim 1, wherein the quantum mechanical process comprises a baseband-flux two-qubit pulse-train controlled-NOT gate for fluxonium qubits”
See Nesterov in page 034063-1, Abstract , describe “we analyze the cross-resonance effect for fluxonium circuits and investigate a two-qubit gate scheme based on selective darkening of a transition. In this approach, two microwave pulses at the frequency of the target qubit are applied simultaneously with a proper ratio between their amplitudes to achieve a controlled-not operation.” Here, Nesterov describes a process that uses a two-qubit gate method while applying two microwave pulses simultaneously to achieve a controlled-not operation (i.e. controlled NOT gate) on specifically fluxonium circuits, and see in Intro , paragraph 2, where Nesterov specifically mention fluxonium qubits.
Further, see Nesterov in page 34063-1, Introduction, paragraph 2, note “One of the microwave-activated two-qubit gate schemes that has been implemented experimentally with fluxonium qubits is based on driving in proximity with transitions leading to higher (noncomputational) excited states of the two-qubit spectrum [27,28]..” Here, Nesterov describes a process that uses a two-qubit gate on fluxonium qubits.
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to combine the references of Grifoni, Lapert, and Petrescu with the teachings of Nesterov by using the teachings of Grifoni, Lapert, and Petrescu, and incorporate with Nesterov’s teaching of using a two-qubit gate on fluxonium qubits.
One of ordinary skill in the art would be motivated to do so because by integrating Nesterov’s framework into the methods of Grifoni, Lapert, and Petrescu, one with ordinary skill in the art would achieve “ This basic scheme can be improved by using an echo sequence of two CR drives of opposite signs and of additional π rotations of the control qubit, which eliminates various spurious terms in the effective Hamiltonian…” (see Nesterov in page 034063-2, first paragraph).
However, Nesterov did not teach “5. The method according to claim 1, wherein the quantum mechanical process comprises a baseband-flux …”
In an analogous art, Rol teaches … “5. The method according to claim 1, wherein the quantum mechanical process comprises a baseband-flux ...”
See Rol in page 054001-1, in abstract describe “We introduce Cryoscope, a method for sampling on-chip baseband pulses used to dynamically control qubit frequency in a quantum processor. We specifically use Cryoscope to measure the step response of the dedicated flux control lines of two-junction transmon qubits in circuit QED processors with the temporal resolution of the room-temperature arbitrary waveform generator producing the control pulses. As a first application, we iteratively improve this step response using optimized real-time digital filters to counter the linear-dynamical distortion in the control line, as needed for high-fidelity repeatable one- and two-qubit gates based on dynamical control of qubit frequency.” Here, Rol shows using baseband pulses, (i.e. which relate to baseband flux) on the system.
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to combine the references of Grifoni, Lapert, Petrescu, and Nesterov, with the teachings of Rol by using the teachings of Grifoni, Lapert, Petrescu, and Nesterov, and incorporate with Rol’s teaching of using baseband flux.
One of ordinary skill in the art would be motivated to do so because by integrating Rol’s framework into the methods of Grifoni, Lapert, Petrescu, and Nesterov, one with ordinary skill in the art would achieve the goal of providing “As a first application, we iteratively improve this step response using optimized real-time digital filters to counter the linear-dynamical distortion in the control line, as needed for high-fidelity repeatable one- and two-qubit gates based on dynamical control of qubit frequency,” (see Rol in page 116, 054001-1, abstract).
Claim 14:
Since claim 14 recites similar limitations as corresponding dependent claim 5 listed above, this claim is rejected for similar reasons with similar rationale under 35 U.S.C. 103.
Claims 6 and 15 are rejected under 35 U.S.C. 103 as being unpatentable over Grifoni in view of Lapert, further in view of Petrescu, and further in view of Dai, C. et al., in “Floquet theorem with open systems and its applications,” published on March 15, 2016, available at: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.93.032121 , (hereafter, Dai).
Claim 6:
Regarding claim 6, Grifoni in view of Lapert, further in view of Petrescu, teaches the limitations in claim 1. However, Grifoni in view of Lapert, further in view of Petrescu, did not teach “6. The method according to claim 1, wherein forming the time-independent Hamiltonian comprises solving a Floquet problem.”
See Dai in page 1, Introduction, paragraph 4, describe “The first part stems from the periodic time dependence of the driven system similar to the micromotion in closed systems, while the second contribution, which leads to deviations from the periodic evolution, originates from a time-independent Lindbladian. Using the Floquet theorem of open systems, in Sec. III, we calculate the dynamics of a dissipative two-level system with periodic Hamiltonian or Lindblad operators. We define a fidelity to quantify the deviation of the exact dynamics to that by the Floquet theorem,…” Here, Dai shows using a Hamiltonian that uses calculations from the Floquet theorem.
See Dai in page 1, Introduction, paragraph 2 mention “In quantum mechanics, the Floquet theorem tells us that for a closed system governed by a time-periodic Hamiltonian, its evolution operator can be decomposed into two parts, one can be given by a time-independent effective Hamiltonian (called the Floquet Hamiltonian) and another is periodic in time describing the periodic micromotion of the driven system (called the micromotion operator). Mathematically, for closed systems governed by a time-periodic Hamiltonian 𝐻(𝑡+𝑇)=𝐻(𝑡), the unitary time-evolution operator takes 𝑈(𝑡,0)=𝒯𝑒−𝑖ℏ∫𝑡0𝐻(𝜏)𝑑𝜏. Considering 𝐻(𝑡+𝑇)=𝐻(𝑡), it is convenient to define a time-independent Hamiltonian 𝐻𝐹 by 𝑒−𝑖ℏ𝐻𝐹𝑇=𝑈(𝑇,0).
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” Here, Dai define a time-independent Hamiltonian using the math operators as part of Floquet theorem operations.
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to combine the references of Grifoni, Lapert, and Petrescu with the teachings of Dai by using the teachings of Grifoni, Lapert, and Petrescu, and incorporate with Dai’s teaching of a time-independent Hamiltonian in solving a Floquet problem.
One of ordinary skill in the art would be motivated to do so because by integrating Dai’s framework into the methods of Grifoni, Lapert, and Petrescu, one with ordinary skill in the art would achieve the goal of “ extend the Floquet theorem from closed to open systems based on the master equation of the Lindblad form. The theorem allows us to obtain an effective time independent Lindbladian in different driving regimes,” (see Dai in page 032121-5, section IV. Conclusions and Discussions).
Claim 15:
Since claim 15 recites similar limitations as corresponding dependent claim 6 listed above, this claim is rejected for similar reasons with similar rationale under 35 U.S.C. 103.
Claims 9 and 18 are rejected under 35 U.S.C. 103 as being unpatentable over Grifoni in view of Lapert, further in view of Petrescu, and further in view of Willsch, D., in "Supercomputer simulations of transmon quantum computers," published on August 31, 2020, available at: https://arxiv.org/abs/2008.13490 , (hereafter, Willsch).
Claim 9:
Regarding claim 9, Grifoni in view of Lapert, further in view of Petrescu, teaches the limitations in claim 1. However, Grifoni in view of Lapert, further in view of Petrescu, did not teach “9. A system comprising one or more qubit gates that are controlled using electromagnetic pulses formed and applied according to the method of claim 1.”
In an analogous art, Willsch teaches “9. A system comprising one or more qubit gates that are controlled using electromagnetic pulses formed and applied according to the method of claim 1”
See Willsch in page 25, section 3.1.4 Cooper pair box, mention "A system known as the Cooper pair box (CPB) [Bou1998] can be obtained by applying an external voltage bias Vg(t) to the Josephson junction shown in Fig. 3.1(b). The voltage bias can be used to control the number of charges (i.e., Cooper pairs) stored on the capacitor of the Josephson junction. The external voltage is modeled by a time-dependent offset to the number of charges given by ng(t) = CgVg(t)/ 2e, where Cg is the capacitance of the gate through which the voltage is applied. The Hamiltonian HJJ given in Eq. (3.6) then needs to be replaced by the time-dependent Hamiltonian
HCPB = 4EC(ˆn−ng(t))2 −EJ cos ˆϕ. (3.7)
An important property of the CPB is that the dynamics of the system can be controlled externally through an electromagnetic pulse described by ng(t). In quantum computing systems, ng(t) represents the pulses that are used to implement quantum gates (see Chapter 5)." Here, Willsch shows that an electromagnetic pulse controls the system called Cooper pair box and also control the ng(t) operation, which relates to quantum gates. Examiner construes quantum gate and qubit gate to have the same definition since a quantum gate is a general term for a basic building block in a quantum circuit that alters quantum information, where a qubit gate is a more specific way to refer to that same gate, highlighting that the operation directly acts upon and modifies a qubit (or multiple qubits). Willsch also notes that this method uses a time-dependent Hamiltonian and operations similar to implementing these steps on modeling a quantum mechanical process with time-dependent parameters.
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to combine the references of Grifoni, Lapert, and Petrescu with the teachings of Willsch by using the teachings of Grifoni, Lapert, and Petrescu, and incorporate with Willsch’s teaching of using electromagnetic pulses that control the quantum system.
One of ordinary skill in the art would be motivated to do so because by integrating Willsch’s framework into the methods of Grifoni, Lapert, and Petrescu, one with ordinary skill in the art would achieve the goal of providing “we use a quantum master equation approach. This allows us to address the transition from a closed system over the system bath model to the effective evolution described by a quantum master equation,” (See Willsch in page 72, section 4.2 Transmon-resonator system coupled to a bath).
Claim 18:
Since claim 18 recites similar limitations as corresponding dependent claim 9 listed above, this claim is rejected for similar reasons with similar rationale under 35 U.S.C. 103.
Conclusion
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/WenWei Zeng/Examiner, Art Unit 2146
/USMAAN SAEED/Supervisory Patent Examiner, Art Unit 2146
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