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 .
Information Disclosure Statement
The information disclosure statement (IDS) submitted on 03/07/2024 was filed before the mailing date of the first office action. The submission is in compliance with the provisions of 37 CFR 1.97. Accordingly, the information disclosure statement is being considered by the examiner.
Claim Objections
Claims 19-20 are objected to because of the following informalities:
Claim 19 recites “using the method of any of claim 12 to provide. . .”, but should be corrected to recite “using the method of claim 12 to provide. . .”.
Claim 20 recites “using the method of the method of any of claim 12 to provide . . .”, but should be corrected to recite “using the method of claim 12 to provide . . .”.
Appropriate correction is required.
Claim Interpretation
Examiner notes that claims 19-20 each contain limitations that have been interpreted as reciting conditional language. Both claims recite the limitations:
“(iii) comparing the calculated fidelity to a threshold value;
(iv) performing: (a) if the fidelity is above the threshold value, extraction of the parameters of said Lindblad master equation corresponding to physically controllable parameters of the operation; or (b) if the fidelity is below the threshold value, repetition of steps (i)-(iii) with a modified Lindblad master equation with modified parameters corresponding to physically controllable parameters of the operation until the calculated fidelity is above the threshold value, and extracting the modified parameters of the modified Lindblad master equation resulting in the calculated fidelity being above the threshold value”.
As per MPEP 2111.04, the broadest reasonable interpretation of a method (or process) claim having contingent limitations requires only those steps that must be performed and does not include steps that are not required to be performed because the condition(s) precedent are not met.
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.
Claim 16 is rejected under 35 U.S.C. 112(b) or 35 U.S.C. 112 (pre-AIA ), second paragraph, as being indefinite for failing to particularly point out and distinctly claim the subject matter which the inventor or a joint inventor (or for applications subject to pre-AIA 35 U.S.C. 112, the applicant), regards as the invention. Claim 16 recites the limitation “an open quantum system that is: (i) a CNOT-gate between a control qubit and a target qubit. . . and/or (ii) a Toffoli-gate between two control qubits and a target qubit”. It is not clear whether the quantum system must require a CNOT gate and a Toffoli gate or whether the quantum system only requires one of these gates. For purposes of examination, Examiner is interpreting that the quantum system only requires a CNOT gate between a control qubit and a target qubit or a Toffoli gate between two control qubits and a target qubit.
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 therefor, subject to the conditions and requirements of this title.
Claims 1-20 are rejected under 35 U.S.C. 101. Claims 1-8 are directed to a device comprising a memory and a processor, or a system, claim 9 is directed to a method, claim 10 is directed to a computer program executing a method by a processor, claim 11 is directed to a computer-readable storage medium, claims 12-17 and 19-20 are directed to a computer-implemented method, and claim 18 is directed a computer program or computer-readable data carrier. Claims 1-10, 12-17, and 19-20 fall within one of the four statutory categories (i.e., process, machine, manufacture, or composition of matter). However, claims 10-11 and 18 are directed to non-statutory matter because they recite computer programs and computer readable media that do not properly prohibit transitory signals and therefore do not fall within at least one of the four categories of patent eligible subject matter.
Claims 1-20 also fall within the judicial exception of an abstract idea, specifically the abstract ideas of “Mental Processes” (including observation, evaluation, and opinion) and “Mathematical Concepts (including mathematical calculations and relationships)”.
Claim 1:
Claim 1 is directed to a system; therefore, the claim does fall within one of the four statutory categories (i.e., process, machine, manufacture, or composition of matter).
Claim 1 recites the following abstract ideas:
the open quantum system having a Hilbert space H and the one or more quantum entities each having a respective Hilbert space Hq, such that H =
⨂
q
=
1
n
H
q
, where n is the number of quantum entities and
⨂
denotes the tensor product, the one or more quantum entities each having a respective decoherence-free space D0,q which are exponential attractors and define together a decoherence-free space D0 of the open quantum system with
D0 =
⨂
q
=
1
n
D
0
,
q
, each decoherence-free space D0 having a respective orthonormal Hermitian basis
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where S0Bp,dBP is the dBp-th Hermitian operator of the orthonormal Hermitian basis of the decoherence-free space D0,Bp of the p-th second quantum entity and d0,Bp is the dimension of the decoherence-free space D0,Bp of the p-th second quantum entity (this limitation is interpreted as a further description of the quantum system being simulated by the mathematical relationships recited in this limitation),
a processor arranged to apply an explicit method to said data for generating a discrete-time expression of the Lindblad master equation, splitting said discrete-time expression of the Lindblad master equation into a local nominal dynamics portion and a perturbation portion K1 with an amplitude of said perturbation portion being at least five times than an amplitude of said local nominal dynamics portion (this limitation is interpreted as implementing a mathematical calculation. Wherein a processor is arranged to execute this calculation is interpreted as merely applying this abstract idea using generic computer components);
and to further apply a trace-preserving and completely-positive linear Kraus map formulation to said local nominal dynamics portion such that the Kraus map K0 of said local nominal dynamics portion is derived from the respective Kraus maps K0,q of said quantum entity specific local nominal dynamics with K0 =
⊗
K0,q, such that p(k +1) = K0(p(k)) + K1(p(k)), where p(k) is the k-th time value of the time-discrete density operator (this limitation is interpreted as applying a mathematical formula to implement a mathematical calculation. Wherein a processor is arranged to apply this formulation is interpreted as merely applying this abstract idea using generic computer components),
said processor being further arranged to determine a finite set of local operators L1q,μ and R1q,μ on the Hilbert space Hq such that, for any operator W on the Hilbert space H verifying W =
⨂
q
=
1
n
W
q
, Wq being a local operator on the Hilbert space
Hq: K1(W) =
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(this limitation is interpreted as applying a mathematical formula to implement a mathematical calculation. Wherein a processor is arranged to apply this formulation is interpreted as merely applying this abstract idea using generic computer components),
said processor being further arranged to calculate invariant operators
Jq,dq =
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of each quantum entity, where K*0,q is the conjugate transpose of the local nominal dynamics portion K0,q of the q-th second quantum entity (this limitation is interpreted as applying a mathematical formula to implement a mathematical calculation. Wherein a processor is arranged to apply this formulation is interpreted as merely applying this abstract idea using generic computer components),
said processor being further arranged to determine second-order approximation of matrices F(k) modeling the time evolution of the time-discrete density operator of the open quantum system by computing:
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where: I is the identity matrix on the Hilbert space H, F0(k) is a zero order part of the matrix F(k), F1(d’1,. . . ,d’n), (d1, . . ., dn)(k) is a coefficient of a first-order part F1(k) of the matrix F(k), F2(d’1,. . . , d’n), (di,. . . , dn)(k) is a coefficient of a second-order part F2(k) of the matrix F(k), and F(k) = F0(k) + F1(k) + F2(k) (this limitation is interpreted as applying a mathematical formula to implement a mathematical calculation. Wherein a processor is arranged to apply this formulation is interpreted as merely applying this abstract idea using generic computer components),
said processor being further arranged to determine a propagator P as a time product of the matrices F(k) for approximating a final state pf of the density operator p based on an initial state p0 of said density operator p (this limitation is interpreted as implementing a mathematical calculation. Wherein a processor is arranged to execute this calculation is interpreted as merely applying this abstract idea using generic computer components),
to execute said processor with said inputs and derive an approximated final state pf of the density operator p (this limitation is interpreted as implementing a mathematical calculation. Wherein a processor is arranged to execute this calculation is interpreted as merely applying this abstract idea using generic computer components).
Claim 1 recites the following additional elements:
a device for simulating an open quantum system including one or more quantum entities (the device comprising a processor and memory is interpreted as a generic computer component merely used to implement the claimed abstract ideas associated with simulating an open quantum system),
said device comprising: a memory arranged to store data representing the time evolution of a Lindblad master equation defining the dynamics of a density operator p of the open quantum system, said dynamics including at least a sum of quantum entity specific local nominal dynamics (the device comprising a processor and memory is interpreted as a generic computer component merely used to implement the claimed abstract ideas associated with simulating an open quantum system. Storing data representing the time evolution of a Lindblad master equation is interpreted as insignificant extra-solution activity directed to mere data gathering and the well-understood, routine, conventional activity of storing information in memory);
and the device being arranged to receive as inputs a Lindblad master equation defining the dynamics of the density operator p of an open quantum system including one or more quantum entities to be simulated, along with the respective decoherence-free spaces D0,q of said one or more quantum entities and an initial state po of said density operator p (receiving a Lindblad master equation and decoherence-free spaces as inputs are each interpreted as insignificant extra-solution activity directed to mere data gathering and the well-understood, routine, conventional activity of storing information in memory).
These additional elements, when considered as a whole with the aforementioned abstract ideas, do not integrate those abstract ideas into a practical application or amount to significantly more than those abstract ideas (see MPEP 2106.05(f) and MPEP 2106.05(d)).
Claim 2 recites wherein the processor (5) is arranged to apply an explicit Euler scheme as the explicit method. Applying an explicit Euler scheme is interpreted as an abstract idea directed to a mathematical calculation.
Claim 3 recites wherein the processor is arranged to apply the Kraus map formulation using the following Kraus map:
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Lindblad operator of the Lindblad master equation and H is a Hamiltonian of the Lindblad master equation.
Applying a Kraus map formulation using this equation is interpreted as an abstract idea directed to a mathematical formula used to implement a mathematical calculation. Wherein a processor is arranged to apply this formulation is interpreted as merely applying this abstract idea using generic computer components, and, when considered as a whole with the aforementioned abstract ideas, does not integrate those abstract ideas into a practical application or amount to significantly more than those abstract ideas (see MPEP 2106.05(f)).
Claim 4 recites wherein the perturbation K1 is time independent and the processor is arranged to determine the propagator
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, where ∆t is the time step of the explicit method and T is a time quantity over which the Lindblad master equation rules the open quantum system.
Determining the propagator using the claimed equation is interpreted as an abstract idea directed to a mathematical formula used to implement a mathematical calculation. Wherein the perturbation is time independent is interpreted as further description of the perturbation term from the mathematical formulas recited in claim 1. Wherein a processor is arranged to apply this equation is interpreted as merely applying this abstract idea using generic computer components, and, when considered as a whole with the aforementioned abstract ideas, does not integrate those abstract ideas into a practical application or amount to significantly more than those abstract ideas (see MPEP 2106.05(f)).
Claim 5 recites wherein the perturbation K1 is time dependent and the processor is arranged to determine the propagator as a time-ordered product
P =
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where ∆tk is the time step of the explicit method corresponding to the k-th time value of the time-discrete density operator, T is a time quantity over which the Lindblad master equation rules the open quantum system,
∧
is the number of time step ∆tk over the time quantity T, and ∆t0 is equal to 0 by convention.
Determining the propagator using the claimed equation is interpreted as an abstract idea directed to a mathematical formula used to implement a mathematical calculation. Wherein the perturbation is time independent is interpreted as further description of the perturbation term from the mathematical formulas recited in claim 1. Wherein a processor is arranged to apply this equation is interpreted as merely applying this abstract idea using generic computer components, and, when considered as a whole with the aforementioned abstract ideas, does not integrate those abstract ideas into a practical application or amount to significantly more than those abstract ideas (see MPEP 2106.05(f)).
Claim 6 recites wherein said device is arranged to receive as inputs a Lindblad master equation defining the dynamics of the density operator p of an open quantum system including only one quantum entity to be simulated, and wherein the processor is arranged to determine a Q-order approximation of the matrix modeling the time evolution of the time-discrete density operator of the open quantum system, Q being an integer greater than two, by implementing the following recurrence process:
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with
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where: d0 is the dimension of the decoherence-free space D0 of the open quantum system, and Frd’,d is a coefficient of a r-order part Fr of the matrix F, and
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Determining a Q-order approximation of the matrix modeling the time evolution of the time-discrete density operator of the open quantum system, Q being an integer greater than two, by implementing the recurrence process as described in the claimed equations is interpreted as an abstract idea directed to mathematical formulas used to implement mathematical calculations.
Receiving as input a Lindblad master equation defining the dynamics of a density operator of an open quantum system including one quantum entity is interpreted as an additional element directed to mere data gathering and the well-understood, routine, conventional activity of receiving data over a network. Wherein a processor is arranged to apply these equations is interpreted as merely applying this abstract idea using generic computer components, and, when considered as a whole with the aforementioned abstract ideas, does not integrate those abstract ideas into a practical application or amount to significantly more than those abstract ideas (see MPEP 2106.05(f)).
Claim 7 recites wherein said device is arranged to receive as inputs a Lindblad master equation defining the dynamics of the density operator p of an open quantum system that is a quantum logic gate.
Receiving as input a Lindblad master equation defining the dynamics of a density operator of an open quantum system is interpreted as an additional element directed to mere data gathering and the well-understood, routine, conventional activity of receiving data over a network.
Examiner notes that wherein the open quantum system is a quantum logic gate is interpreted as a further description of the quantum system and merely describing the kind of data being gathered and received over a network and, when considered as a whole with the aforementioned abstract ideas, does not integrate those abstract ideas into a practical application or amount to significantly more than those abstract ideas (see MPEP 2106.05(d)(II) and MPEP 2106.05(g)).
Claim 8 recites wherein said device is arranged to receive as inputs a Lindblad master equation defining the dynamics of the density operator p of an open quantum system that is a Z-gate, a ZZ-gate, a ZZZ-gate, a CNOT-gate or a Toffoli-gate.
Receiving as input a Lindblad master equation defining the dynamics of a density operator of an open quantum system is interpreted as an additional element directed to mere data gathering and the well-understood, routine, conventional activity of receiving data over a network.
Examiner notes that wherein the open quantum system is at least a Z-gate is interpreted as a further description of the quantum system and merely describing the kind of data being gathered and received over a network and, when considered as a whole with the aforementioned abstract ideas, does not integrate those abstract ideas into a practical application or amount to significantly more than those abstract ideas (see MPEP 2106.05(d)(II) and MPEP 2106.05(g)).
Claim 9 is a method claim and its limitation is included in claim 1. The only difference is that claim 9 requires a method. Therefore, claim 9 is rejected for the same reasons as claim 1.
Claim 10 is a computer program claim (see the header for statutory analysis) comprising instructions to implement the method of claim 9. Therefore, its limitation is included in claim 9 and claim 10 is rejected for the same reasons.
Claim 11 is a computer-readable storage medium claim (see the header for statutory analysis) comprising the computer program of claim 10. Therefore, its limitation is included in claim 10 and claim 11 is rejected for the same reasons.
Claim 12:
Claim 12 is directed to a method; therefore, the claim does fall within one of the four statutory categories (i.e., process, machine, manufacture, or composition of matter).
Claim 12 recites the following abstract ideas:
the plurality of quantum entities including: (i) one or more first quantum entities each having a respective Hilbert space HAq, where Aq denotes the q-th first quantum entity, and each being stabilized around a respective decoherence-free space D0,Aq which is an exponential attractor, each decoherence-free space D0,Aq having a respective orthonormal Hermitian basis
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where S0Aq,dAq is the dAq-th Hermitian operator of the orthonormal Hermitian basis of the decoherence-free space D0,Aq of the q-th first quantum entity and d0,Aq is the dimension of the decoherence-free space D0,Aq of the q-th first quantum entity (this limitation is interpreted as a further description of the quantum system being simulated by the mathematical relationships recited in this limitation),
(ii) one or more second quantum entities each having a respective Hilbert space HBp where Bp denotes the p-th second quantum entity, wherein each second quantum entity has an unstabilized component during a time period T such that a respective decoherence-free space cannot be defined for each second quantum entity during time period T; wherein the open quantum system has a Hilbert space H such that H = (
⨂
A
q
H
A
q
)
⨂
(
⨂
B
p
H
B
p
)
, where
⨂
denotes the tensor product (this limitation is interpreted as a further description of the quantum system being simulated by the mathematical relationships recited in this limitation);
applying an explicit method to said Lindblad master equation for generating a discrete-time expression thereof, splitting said discrete-time expression of the Lindblad master equation into a local nominal dynamics portion of the one or more first quantum entities and a perturbation portion K1 with an amplitude of said perturbation portion being at least five times smaller than an amplitude of said local nominal dynamics portion (this limitation is interpreted as implementing a mathematical calculation);
applying a trace-preserving and completely-positive linear Kraus map formulation to said local nominal dynamics portion such that the Kraus map K0 of said local nominal dynamics portion is derived from the respective Kraus maps K0,Aq of said first quantum entity specific local nominal dynamics with K0 =
⊗
Aq K0,Aq, such that p(k +1) = K0(p(k)) + K1(p(k)), where p(k) is the k-th time value of the time-discrete density operator (this limitation is interpreted as applying a mathematical formula to implement a mathematical calculation);
determining a finite set of local operators L1m,μ(k) and R1q,μ(k) on the Hilbert space Hm where m = Aq,Bp such that, for any operator W on the Hilbert space H verifying W =
⨂
m
W
m
, Wm being a local operator on the Hilbert space Hm: K1(W) =
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where μ is finite (this limitation is interpreted as applying a mathematical formula to implement a mathematical calculation);
calculating invariant operators
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of each first quantum entity, where K*0,Aq is the conjugate transpose of the local nominal dynamics portion K0,Aq of the q-th second quantum entity (this limitation is interpreted as applying a mathematical formula to implement a mathematical calculation);
determining a second-order equation of the time-discrete dynamics of the contributions of the d’Aq-th Hermitian operator of the decoherence-free space D0,A’q of the q-th first quantum entity on the p-th second quantum entity p(B1, . . ., Bp), (d’A1, . . ., d’Aq), by computing:
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where ∆t is the time step of the explicit method, where the sum over index j is truncated at a threshold such that the difference between the penultimate and final summed terms is smaller than 10-8, and where Tr() denotes the trace (this limitation is interpreted as applying a mathematical formula to implement a mathematical calculation);
determining a propagator P by numerically integrating
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over the time period T (this limitation is interpreted as applying a mathematical formula to implement a mathematical calculation);
and deriving an approximated final state of the density operator p by applying said propagator P to the initial state p(O) of said density operator p of the open quantum system (this limitation is interpreted as applying a mathematical formula to implement a mathematical calculation).
Claim 12 recites the following additional elements:
a computer-implemented method carried out by a conventional computer for simulating an open quantum system including a plurality of quantum entities (a conventional computer used to simulate an open quantum system is interpreted as a generic computer component merely used to implement the claimed abstract ideas),
the method comprising the following operations: receiving, as inputs: (i) a Lindblad master equation defining the dynamics, at time 0 < t < T, of a density operator p of the open quantum system to be simulated including one or more first quantum entities and one or more second quantum entities, wherein said dynamics includes first quantum entity specific local nominal dynamics
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is the local nominal dynamics of the q-th first quantum entity;
(ii) the respective decoherence-free spaces D0,Aq of the one or more first quantum entities; (iii) an initial state p(0) of said density operator p; and (iv) time period T during which each second quantum entity has an unstabilized component (receiving a Lindblad master equation, decoherence-free spaces, and initial state of a density operator, and a time period as inputs are each interpreted as insignificant extra-solution activity directed to mere data gathering and the well-understood, routine, conventional activity of receiving data over a network).
These additional elements, when considered as a whole with the aforementioned abstract ideas, do not integrate those abstract ideas into a practical application or amount to significantly more than those abstract ideas (see MPEP 2106.05(d) and MPEP 2106.05(f)).
Claim 13 recites wherein, when t = 0 and when t ≥ T, each second quantum entity is stabilized around a respective decoherence-free space D0,Bp which is an exponential attractor, each decoherence-free space D0,Bp having a respective orthonormal Hermitian basis
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, where S0Bp,dBP is the dBp-th Hermitian operator of the orthonormal Hermitian basis of the decoherence-free space D0,Bp of the p-th second quantum entity and d0,Bp is the dimension of the decoherence-free space D0,Bp of the p-th second quantum entity (this limitation is interpreted as a further description of the quantum system being simulated by the mathematical relationships recited in this limitation);
wherein the method further comprises: receiving, as inputs:
(v) a second Lindblad master equation defining the dynamics, at time t = 0 and t ≥ T, of the density operator p of the open quantum system to be simulated, wherein said dynamics includes quantum entity specific local nominal dynamics
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, where L0,Bp is the local nominal dynamics of the p-th second quantum entity; and
(vi) the respective decoherence-free spaces D0,Bp of the one or more second quantum entities (receiving a Lindblad master equation and decoherence-free spaces as inputs are each interpreted as insignificant extra-solution activity directed to mere data gathering and the well-understood, routine, conventional activity of storing information in memory);
applying an explicit method to said second Lindblad master equation for generating a second discrete-time expression thereof, splitting said second discrete-time expression of the second Lindblad master equation into a second local nominal dynamics portion of the plurality of quantum entities and a second perturbation portion K(2)1 with an amplitude of said second perturbation portion being at least five times than an amplitude of said second local nominal dynamics portion (this limitation is interpreted as implementing a mathematical calculation. Wherein a processor is arranged to execute this calculation is interpreted as merely applying this abstract idea using generic computer components);
applying a trace-preserving and completely-positive linear Kraus map formulation to said second local nominal dynamics portion such that the Kraus map K(2)0 of said second local nominal dynamics portion is derived from the respective Kraus maps K(2)0,m of said quantum entity specific local nominal dynamics with K(2)0 =
⊗
K(2)0,m, where m = Aq, Bp such that p(k +1) = K(2)0(p(k)) + K(2)1(p(k)) + K(2)0(p(k)), p(k) is the k-th time value of the time-discrete density operator (this limitation is interpreted as applying a mathematical formula to implement a mathematical calculation. Wherein a processor is arranged to apply this formulation is interpreted as merely applying this abstract idea using generic computer components);
calculating invariant operators
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of each quantum entity, where K(2)*0,Bp is the conjugate transpose of the local nominal dynamics portion K(2)0,Bp of the p-th second quantum entity (this limitation is interpreted as applying a mathematical formula to implement a mathematical calculation. Wherein a processor is arranged to apply this formulation is interpreted as merely applying this abstract idea using generic computer components); and
where determining propagator P comprising calculating each propagator coefficient contributing to propagator P for a particular dA1, . . ., dAq, dB1, . . ., dBp, using:
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wherein
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is computed numerically integrating
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from an initial state
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where m = Aq,Bp for the particular dA1, . . ., dAq, dB1, . . ., dBp (this limitation is interpreted as applying a mathematical formula to implement a mathematical calculation. Wherein a processor is arranged to apply this formulation is interpreted as merely applying this abstract idea using generic computer components).
Claim 14 recites wherein the Kraus map formulation is applied by using the following Kraus map:
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Lindblad operator of the Lindblad master equation and H is a Hamiltonian of the Lindblad master equation.
Applying a Kraus map formulation using the claimed equation is interpreted as an abstract idea directed to a mathematical formula used to implement a mathematical calculation.
Claim 15 recites wherein each of the one or more first quantum entities is a cat qubit stabilized by two-photon driven dissipation, and wherein each of the one or more second quantum entities is a cat qubit which: (i) is stabilized by two photon driven dissipation when t = 0 and when t ≥ T, and (ii) is not stabilized by two-photon driven dissipation during time 0 < t < T.
This limitation is interpreted as a further description of the kind of quantum entities being simulated by the abstract ideas directed to mathematical calculations recited in claim 12 and, when considered as a whole with those aforementioned abstract ideas, does not integrate those abstract ideas into a practical application or amount to significantly more than those abstract ideas.
Claim 16 recites receiving, as inputs, a Lindblad master equation defining the dynamics of the density operator p of an open quantum system that is: (i) a CNOT-gate between a control qubit and a target qubit, wherein the control qubit is one of said one or more first quantum entities and the target qubit is one of said one or more second quantum entities; and/or (ii) a Toffoli-gate between two control qubits and a target qubit, wherein the control qubits are of said one or more first quantum entities and the target qubit is one of said one or more second quantum entities.
Receiving a Lindblad master equation defining the dynamics of the density operator of an open quantum system is interpreted as an additional element directed to mere data gathering and the well-understood, routine, conventional activity of receiving data over a network.
Examiner notes that claim 16 is being interpreted based on the 112(b) rejection such that only one of the CNOT gate or Toffoli gate is required in the open quantum system. Given this interpretation, Examiner notes that this description of the quantum system is interpreted as merely describing the kind of data being gathered and received over a network and, when considered as a whole with the aforementioned abstract ideas, does not integrate those abstract ideas into a practical application or amount to significantly more than those abstract ideas (see MPEP 2106.05(d)(II) and MPEP 2106.05(g)).
Claim 17 recites wherein the index j is truncated at a threshold such that the difference between the between the penultimate and final summed terms is at machine precision of the conventional computer.
Examiner notes that the broadest reasonable interpretation of “machine precision of the conventional computer” is made in light of paragraph [0303] of Applicant’s published specification as including values between 10−8 and 10−16. Truncating an index at a threshold such that the difference between penultimate and final summed terms is at this precision is interpreted as a mental step directed to observation, judgement – a person could decide to truncate an index value to a value such that the difference between observed penultimate and final summed terms is between 10−8 and 10−16 in their mind based on an observed or mentally determined threshold.
Claim 18 is a computer program claim (see the header for statutory analysis) comprising instructions to implement the method of claim 12. Therefore, its limitation is included in claim 12 and claim 18 is rejected for the same reasons.
Claim 19 recites the plurality of quantum entities including: (I) one or more first quantum entities each being stabilized around a respective decoherence-free space; and (II) one or more second quantum entities, wherein each second quantum entity has an unstabilized component during a time period T such that a respective decoherence-free space cannot be defined for each second quantum entity during time period T (this limitation is interpreted as a further description of the kind of quantum entities being simulated by the abstract ideas directed to mathematical calculations recited in claim 12);
providing a desired final state of a density operator p of the open quantum system after a known operation is to be performed on a known initial state of the open quantum system for time period T (providing a desired final state of a density operator after a known operation is to be performed on an open quantum system is interpreted as an additional element directed to mere data gathering and the well-understood, routine, conventional activity of transmitting data over a network);
(i) using the method of the method of any of claim 12 to provide an approximated final state of the density operator, wherein said initial state of said density operator p models the known initial state of the open quantum system and wherein said Lindblad master equation defining the dynamics models the evolution of the system under the known operation (using the method of claim 12 to provide an approximated final state of a density operator is interpreted as an abstract idea utilizing the mathematical formulas in claim 12 to perform an additional mathematical calculation. Wherein the density operator models an initial state of an open quantum system and a Lindblad master equation models the evolution of that quantum system under a known operation are interpreted as further descriptions of the use of the claimed mathematical formulas and calculations);
(ii) calculating a fidelity between the approximated final state and the desired final state (mental step directed to observation, evaluation – a person could calculate a fidelity in their mind between an observed approximated final state and an observed desired state. Examiner notes that the broadest reasonable interpretation of calculating this fidelity could also include a mathematical calculation);
(iii) comparing the calculated fidelity to a threshold value (mental step directed to observation, evaluation – a person could compare an observed or mentally determined calculated fidelity to an observed threshold value in their mind);
(iv) performing: (a) if the fidelity is above the threshold value, extraction of the parameters of said Lindblad master equation corresponding to physically controllable parameters of the plurality quantum entities; or
(b) if the fidelity is below the threshold value, repetition of steps (i)-(iii) with a modified Lindblad master equation with modified parameters corresponding to physically controllable parameters of the plurality of quantum entities until the calculated fidelity is above the threshold value, and extracting the modified parameters of the plurality of quantum entities of the modified Lindblad master equation resulting the calculated fidelity being above the threshold value (Examiner notes that based on the conditional language recited in this claim (see the claim interpretation section), only step (a) or step (b) is required by the claim. The broadest reasonable interpretation of extracting parameters of a Lindblad master equation corresponding to physically controllable parameters of the quantum entities includes a mental step directed to observation, evaluation – as a person could observe whether a calculated fidelity is above an observed threshold in their mind and evaluate, or extract, parameters of an observed mathematical Lindblad calculation simulating parameters of quantum entities in their mind); and
(v) physically performing the operation on the open quantum system using the extracted parameters (physically performing an operation on an open quantum system using extracted parameters is interpreted as an additional element directed to insignificant extra-solution activity utilizing a generic quantum computing system, as no particular quantum system or technical operations are recited by the claim to limit the broadest reasonable interpretation of “physically performing an operation”).
Examiner notes that the claimed additional elements as noted here, when considered as a whole with those aforementioned abstract ideas, do not integrate those abstract ideas into a practical application or amount to significantly more than those abstract ideas (see MPEP 2106.05(d), MPEP 2106.05(f), and MPEP 2106.05(g)).
Claim 20 recites the plurality of quantum entities including: (i) one or more first quantum entities each being stabilized around a respective decoherence-free space; and (II) one or more second quantum entities, wherein each second quantum entity has an unstabilized component during a time period T such that a respective decoherence-free space cannot be defined for each second quantum entity during time period T (this limitation is interpreted as a further description of the kind of quantum entities being simulated by the abstract ideas directed to mathematical calculations recited in claim 12);
providing a desired final state of a density operator p of the open quantum system after a known operation is to be performed on a known initial state of the open quantum system for time period T (providing a desired final state of a density operator after a known operation is to be performed on an open quantum system is interpreted as an additional element directed to mere data gathering and the well-understood, routine, conventional activity of transmitting data over a network);
(i) using the method of the method of any of claim 12 to provide an approximated final state of the density operator, wherein said initial state of said density operator p models the known initial state of the open quantum system and wherein said Lindblad master equation defining the dynamics models the evolution of the system under the known operation (using the method of claim 12 to provide an approximated final state of a density operator is interpreted as an abstract idea utilizing the mathematical formulas in claim 12 to perform an additional mathematical calculation. Wherein the density operator models an initial state of an open quantum system and a Lindblad master equation models the evolution of that quantum system under a known operation are interpreted as further descriptions of the use of the claimed mathematical formulas and calculations);
(ii) calculating a fidelity between the approximated final state and the desired final state (mental step directed to observation, evaluation – a person could calculate a fidelity in their mind between an observed approximated final state and an observed desired state. Examiner notes that the broadest reasonable interpretation of calculating this fidelity could also include a mathematical calculation);
(iii) comparing the calculated fidelity to a threshold value (mental step directed to observation, evaluation – a person could compare an observed or mentally determined calculated fidelity to an observed threshold value in their mind);
(iv) performing: (a) if the fidelity is above the threshold value, extraction of the parameters of said Lindblad master equation corresponding to physically controllable parameters of the plurality quantum entities; or
(b) if the fidelity is below the threshold value, repetition of steps (i)-(iii) with a modified Lindblad master equation with modified parameters corresponding to physically controllable parameters of the plurality of quantum entities until the calculated fidelity is above the threshold value, and extracting the modified parameters of the plurality of quantum entities of the modified Lindblad master equation resulting the calculated fidelity being above the threshold value (Examiner notes that based on the conditional language recited in this claim (see the claim interpretation section), only step (a) or step (b) is required by the claim. The broadest reasonable interpretation of extracting parameters of a Lindblad master equation corresponding to physically controllable parameters of the quantum entities includes a mental step directed to observation, evaluation – as a person could observe whether a calculated fidelity is above an observed threshold in their mind and evaluate, or extract, parameters of an observed mathematical Lindblad calculation simulating parameters of quantum entities in their mind); and
(v) designing the plurality of quantum entities to have the extracted parameters (mental step directed to observation, evaluation – a person could design a plurality of quantum entities with observed or mentally determined extracted parameters in their mind).
Examiner notes that the claimed additional elements as noted here, when considered as a whole with those aforementioned abstract ideas, do not integrate those abstract ideas into a practical application or amount to significantly more than those abstract ideas (see MPEP 2106.05(d), MPEP 2106.05(f), and MPEP 2106.05(g)).
Viewed as a whole, these additional claim elements do not provide meaningful limitations to transform the abstract idea into a patent eligible application of the abstract idea such that the claims amount to significantly more than the abstract idea itself. Therefore, the claims are rejected under 35 U.S.C. 101.
Allowable Subject Matter
Claims 1-20 are allowable over the prior art. The following is a statement of reasons for the indication of allowable subject matter: the prior art of record does not teach the specific claimed method of simulating quantum entities with respective decoherence-free spaces in an open quantum system using all of a discrete-time expression of the Lindblad master equation, a Kraus map formulation, invariant operators calculation, and deriving an approximated final state pr of the density operator.
The prior art made of record and not relied upon is considered pertinent to applicant's disclosure:
The closest prior art of record is “Models and Feedback Stabilization of Open Quantum Systems” (Rouchon), which teaches a method for simulating an open quantum system with a Lindblad master equation and a Kraus map formulation but does not teach the specific claimed method of simulating quantum entities with respective decoherence-free spaces in an open quantum system.
“A short introduction to the Lindblad master equation” (Manzano) teaches a derivation of the Lindblad master equation and its role in a general generator of Markovian dynamics in quantum systems, but does not teach the specific claimed method of simulating quantum entities with respective decoherence-free spaces in an open quantum system.
“Universal Lindblad equation for open quantum systems” (Nathan et al) teaches a method for deriving a Lindblad master equation using a Markov approximation for an open quantum system, but does not teach the specific claimed method of simulating quantum entities with respective decoherence-free spaces in an open quantum system.
“Quantum computation with cat qubits” (Guillaud et al) teaches a method for utilizing Kraus maps and a Lindblad master equation to mitigate decoherence when performing quantum operations for a two-photon driven dissipation system, but does not teach the specific claimed method of simulating quantum entities with respective decoherence-free spaces in an open quantum system.
“Introduction to dissipation and decoherence in quantum systems” (Marquardt et al) teaches a derivation of a Lindblad form from a Kraus matrix decomposition, but does not teach the specific claimed method of simulating quantum entities with respective decoherence-free spaces in an open quantum system
Conclusion
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/L.M.F./ Examiner, Art Unit 2147
/VIKER A LAMARDO/Supervisory Patent Examiner, Art Unit 2147
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