DETAILED ACTION
1. This office action is in response to the Application No. 17246020 filed on 03/04/2026. Claims 2 and 3 are cancelled. Claims 1, 4-22 are presented for examination and are currently pending.
Notice of Pre-AIA or AIA Status
2. The present application, filed on or after March 16, 2013, is being examined under the first inventor to file provisions of the AIA .
Continued Examination Under 37 CFR 1.114
3. A request for continued examination under 37 CFR 1.114, including the fee set
forth in 37 CFR 1.17(e), was filed in this application after final rejection. Since this
application is eligible for continued examination under 37 CFR 1.114, and the fee set
forth in 37 CFR 1.17(e) has been timely paid, the finality of the previous Office action
has been withdrawn pursuant to 37 CFR 1.114. Applicant’s submission filed on
03/04/2026 has been entered.
Response to Arguments
4. The Examiner is withdrawing the rejections in the previous Office action because Applicant’s amendment necessitated the new grounds of rejection presented in this Office action. As a result, the Applicant’s argument are moot.
However, some of the references in the previous office action have been applied
to the dependent claims.
In addition, Bartlett et al. and Douçot et al. are still been applied to independent
claim 19 because they teach many recited limitations of the claim. As a result,
independent claim 19 is obvious over the newly applied Zanardi as primary reference in
view of Bartlett and Douçot.
Claim Rejections - 35 USC § 103
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.
5. Claims 1, 15 are rejected under 35 U.S.C. 103 as being unpatentable over Zanardi et al. ("Dissipation and decoherence in a quantum register." Physical Review A 57.5 (1998): 3276) in view of Preskill ("Fault-tolerant quantum computation." Introduction to quantum computation and information. 1998. 213-269. arXiv:quant-ph/9712048v1 19 Dec 1997).
Regarding claim 1, Zanardi teaches a quantum-computation method (In this paper we address the problem of dynamically stable quantum encoding within a master equation formalism that allows us to deal directly with the marginal dynamics of the computational degrees of freedom, pg. 3276, right col., first para.), comprising:
receiving quantum-computer code (
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pg. 3281, right col., third para.) for execution on a quantum computer (quantum computation applications (pg. 3282, left col., last para.); ... a logical qubit can be encoded in each cluster, pg. 3281, left col., second para.; According to instant specification: “Considered particularly herein are qubits encoded in quantum spins” US20220374239 [0034]),
the quantum computer having a plurality of qubits associated with a corresponding plurality of particles (One can design a register that supports noiseless encodings if one is able to build R in such a way that (iii) is satisfied with m = 4 qubits for a cluster, pg. 3281, left col., second para.),
the plurality of particles defining a quantum state (is a qubit-qubit interaction. In quantum computation applications such a term might arise, for example, during the gate processing, pg. 3281, left col., last para. The Examiner notes initial quantum state of two particles is the qubit-qubit state);
decomposing the quantum-computer code into a sequence of operations including a total spin-state measurement on two particles (Hilbert space HR splits dynamically according the Clebsch-Gordan decomposition of the n-fold tensor representation of su(2) ... total spin eigenvalue S(S+1), pg. 3281, right col., first para. The Examiner notes total spin S can take values: Triplet states (S = 1) and Singlet state (S = 0)) corresponding to two of the qubits without revealing individual spin states of the two particles (... the self-Hamiltonian leaves the code invariant (pg. 3279, right col., second to the last para.); furthermore from the su(2) invariance of HR (self-Hamiltonian HR), pg. 3281, right col., third to the last para.; According to the instant specification: Provided that all of the terms in the environmental Hamiltonian are SU(2)-invariant, measurement into total spin states is protected [0027]. The Examiner notes the su(2) invariance of HR (self-Hamiltonian) ensures measurement into total spin states (either 0 or 1) is protected from revealing spin-state),
wherein the total spin-state measurement distinguishes a spin triplet of the two particles from a spin singlet of the two particles, is SU(2)-invariant (If HR = 0 these two states are energy degenerate; for nonvanishing qubit-qubit interaction the degeneracy is lifted. For example, if
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is a Heisenberg coupling between nearest-neighbor qubits arranged on a ring topology, one finds that │0› and │1› are energy eigenstates with eigenvalues ... Since HR1 is su(2) invariant, pg. 3281, right col., last para. The Examiner notes │0› indicates singlet │S=0› and │1› indicates triplet │S=1›), and
is therefore unresponsive to decoherence of the quantum state in a substantially SU(2)-invariant noise environment (This result is true for all decoherence times ... At finite temperature the excitations terms weighted ... are present as well ... the su(2) invariance of HR, pg. 3281, right col., second para.); and
applying the sequence of operations on the plurality of particles to thereby transform the quantum state according to the quantum-computer code (Furthermore we have shown that there exist cases with nontrivial cell dependence that can be mapped onto (ii) and (iii) by a suitable local gauge transformation. The degree of stability of the resulting codes depends on the covariance properties of the renormalized self-Hamiltonian, pg. 3283, right col., first para.)
Zanardi teaches quantum computation but does not explicitly teach execution on a quantum computer.
Preskill teaches quantum-computer code for execution on a quantum computer (To see how quantum error correction is possible, it is very instructive to study a particular code (pg. 5, section 2); The code uses a 7-qubit “block” to encode one qubit of quantum information, that is, we can encode an arbitrary state in a two-dimensional Hilbert space spanned by two states: the “logical zero” |0icode and the “logical one” |1icode., (pg. 6, second para.); We will also want to be able to measure the encoded qubit, say by projecting onto the orthogonal basis {|0icode, |1icode}. If we don’t mind destroying the encoded block when we make the measurement, then it is sufficient to measure each of the seven qubits in the block by projecting onto the basis {|0i, |1i}, (pg. 11 second to the last para.)
on a quantum computer (Once the elementary gates of our quantum computer are sufficiently reliable, we can perform fault-tolerant quantum gates on encoded information, pg. 3, last para.)
It would have been obvious to a person having ordinary skill in the art before the effective filing date of the claimed invention to have modified the method of Zanardi to incorporate the teachings of Preskill for the benefit of performing quantum computation reliably (Preskill, pg. 1, first para.).
Regarding claim 15, Zanardi teaches a quantum computer, comprising:
a plurality of qubits associated with a corresponding plurality of particles (One can design a register that supports noiseless encodings if one is able to build R in such a way that (iii) is satisfied with m = 4 qubits for a cluster, pg. 3281, left col., second para.),
the plurality of particles defining a quantum state(is a qubit-qubit interaction. In quantum computation applications such a term might arise, for example, during the gate processing, pg. 3281, left col., last para. The Examiner notes initial quantum state of two particles is the qubit-qubit state);
an input engine configured to receive quantum-computer code (
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pg. 3281, right col., third para.) for execution on the quantum computer (quantum computation applications (pg. 3282, left col., last para.); ... a logical qubit can be encoded in each cluster, pg. 3281, left col., second para.; According to instant specification: “Considered particularly herein are qubits encoded in quantum spins” US20220374239 [0034]);
a decomposition engine configured to decompose the quantum-computer code into a sequence of operations including a total spin-state measurement on two particles (Hilbert space HR splits dynamically according the Clebsch-Gordan decomposition of the n-fold tensor representation of su(2) ... total spin eigenvalue S(S+1), pg. 3281, right col., first para. The Examiner notes total spin S can take values: Triplet states (S = 1) and Singlet state (S = 0)) corresponding to two of the qubits without revealing individual spin states of the two particles (... the self-Hamiltonian leaves the code invariant (pg. 3279, right col., second to the last para.); furthermore from the su(2) invariance of HR (self-Hamiltonian HR), pg. 3281, right col., third to the last para.; According to the instant specification: Provided that all of the terms in the environmental Hamiltonian are SU(2)-invariant, measurement into total spin states is protected [0027]. The Examiner notes the su(2) invariance of HR (self-Hamiltonian) ensures measurement into total spin states (either 0 or 1) is protected from revealing spin-state),
wherein the total spin-state measurement distinguishes a spin triplet of the two particles from a spin singlet of the two particles, is SU(2)-invariant (If HR = 0 these two states are energy degenerate; for nonvanishing qubit-qubit interaction the degeneracy is lifted. For example, if
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is a Heisenberg coupling between nearest-neighbor qubits arranged on a ring topology, one finds that │0› and │1› are energy eigenstates with eigenvalues ... Since HR1 is su(2) invariant, pg. 3281, right col., last para. The Examiner notes │0› indicates singlet │S=0› and │1› indicates triplet │S=1›), and
is therefore unresponsive to decoherence of the quantum state in a substantially SU(2)-invariant noise environment(This result is true for all decoherence times ... At finite temperature the excitations terms weighted ... are present as well ... the su(2) invariance of HR, pg. 3281, right col., second para.); and
an execution engine configured to apply the sequence of operations on the plurality of particles to thereby transform the quantum state according to the quantum-computer code (Furthermore we have shown that there exist cases with nontrivial cell dependence that can be mapped onto (ii) and (iii) by a suitable local gauge transformation. The degree of stability of the resulting codes depends on the covariance properties of the renormalized self-Hamiltonian, pg. 3283, right col., first para.).
Zanardi does not explicitly teach execution of quantum-computer code on a quantum computer.
Preskill teaches quantum-computer code for execution (To see how quantum error correction is possible, it is very instructive to study a particular code (pg. 5, section 2); The code uses a 7-qubit “block” to encode one qubit of quantum information, that is, we can encode an arbitrary state in a two-dimensional Hilbert space spanned by two states: the “logical zero” |0icode and the “logical one” |1icode., (pg. 6, second para.); We will also want to be able to measure the encoded qubit, say by projecting onto the orthogonal basis {|0icode, |1icode}. If we don’t mind destroying the encoded block when we make the measurement, then it is sufficient to measure each of the seven qubits in the block by projecting onto the basis {|0i, |1i}, (pg. 11 second to the last para.)
on a quantum computer (Once the elementary gates of our quantum computer are sufficiently reliable, we can perform fault-tolerant quantum gates on encoded information, pg. 3, last para.)
It would have been obvious to a person having ordinary skill in the art before the effective filing date of the claimed invention to have modified the method of Zanardi to incorporate the teachings of Preskill for the benefit of performing quantum computation reliably (Preskill, pg. 1, first para.).
6. Claim 7 is rejected under 35 U.S.C. 103 as being unpatentable over Zanardi et al. ("Dissipation and decoherence in a quantum register." Physical Review A 57.5 (1998): 3276) in view of Preskill, ("Fault-tolerant quantum computation." Introduction to quantum computation and information. 1998. 213-269. arXiv:quant-ph/9712048v1 19 Dec 1997) in view Bartlett et al. ("Reference frames, superselection rules, and quantum information." Reviews of Modern Physics 79.2 (2007): 555-609) and further in view of Cafaro et al. ("A geometric algebra perspective on quantum computational gates and universality in quantum computing." Advances in Applied Clifford Algebras 21 (2011): 493-519)
Regarding claim 7, Modified Zanardi teaches the method of claim 1, Bartlett teaches the total spin-state measurement (Under the SSR, Bob is restricted to performing measurements which are diagonal in total spin (page 602, right col. first paragraph)).
It would have been obvious to a person having ordinary skill in the art before the effective filing date of the claimed invention to have modified the method of Modified Zanardi to incorporate the teachings of Bartlett for the benefit of performing task more efficiently (Bartlett, pg. 602, right col., third para.).
Modified Zanardi does not explicitly teach wherein each of the sequence of operations is selected from: a pair of orthogonal single-qubit Clifford operations;
Cafaro teaches wherein each of the sequence of operations is selected from: a pair of orthogonal single-qubit Clifford operations (We consider simple circuit models of quantum computation with 1-qubit quantum gates in the GA formalism, (pg. 500, third para.); We investigate the utility of geometric (Clifford) algebras (GA) methods in two specific applications to quantum information science. First, using the multiparticle spacetime algebra (MSTA, the geometric algebra of a relativistic configuration space), (abstract); A suitable basis for the MSTA is given by the set ... These basis vectors satisfy the orthogonality conditions ... Vectors from different particle spaces anticommute as a consequence of their orthogonality (pg. 496, second para.); Therefore, Hˆ can be envisioned (up to an overall phase) as a θ = π rotation about the axis nˆ = 1/√ 2 (ˆn1 + ˆn3) that rotates ˆx to ˆz and vice versa, Hˆ = −iCR 1/√ 2 (ˆn1+ˆn3) (π). In GA, rotations are handled by means of rotors… It is straightforward to show that the action of the rotor Hˆ (GA) on the 1-qubit computational basis states satisfies (up to an overall irrelevant phase shift) the transformation laws (pg. 503, second para.)); and
It would have been obvious to a person having ordinary skill in the art before the effective filing date of the claimed invention to have modified the method of Modified Zanardi to incorporate the teachings of Cafaro for the benefit of investigating the utility of geometric (Clifford) algebras (GA) methods in two specific applications to quantum information science and an explicit algebraic description of one and two-qubit quantum states together with a MSTA (multiparticle spacetime algebra) characterization of one and two-qubit quantum computational gate (Cafaro, abstract)
7. Claims 8-13, 21 and 22 are rejected under 35 U.S.C. 103 as being unpatentable over Zanardi et al. ("Dissipation and decoherence in a quantum register." Physical Review A 57.5 (1998): 3276) in view of Preskill, ("Fault-tolerant quantum computation." Introduction to quantum computation and information. 1998. 213-269. arXiv:quant-ph/9712048v1 19 Dec 1997) in view Bartlett et al. ("Reference frames, superselection rules, and quantum information." Reviews of Modern Physics 79.2 (2007): 555-609)
Regarding claim 8, Modified Zanardi teaches the method of claim 1, Bartlett teaches wherein the quantum-computer code defines a concurrent two-qubit measurement (Let Alice and Bob share two copies of this mixed state. With these states, they attempt to perform the following simple entanglement purification protocol: they each apply a controlled-NOT (CNOT) on the two qubits in their possession, and then perform an X measurement on the target qubit. Each party obtains a measurement outcome ±1 (page 604, left column, last paragraph)).
It would have been obvious to a person having ordinary skill in the art before the effective filing date of the claimed invention to have modified the method of Modified Zanardi to incorporate the teachings of Bartlett for the benefit of performing task more efficiently (Bartlett, pg. 602, right col., third para.).
Regarding claim 9, Modified Zanardi teaches the method of claim 8, Bartlett teaches wherein the concurrent two-qubit measurement is a two-qubit measurement in a Bell basis (…a maximally entangled Bell state of a pair of qubits of Alice’s and Bob’s quantum registers (page 603, right column, second to the last paragraph))
The same motivation to combine dependent claim 8 applies here.
Regarding claim 10, Modified Zanardi teaches the method of claim 1, Bartlett teaches wherein the sequence of operations provides teleportation of one or more qubit states onto the plurality of qubits (It also follows that such entangled states can be used for quantum teleportation of logical qubits (page 568, left column, first paragraph))
It would have been obvious to a person having ordinary skill in the art before the effective filing date of the claimed invention to have modified the method of Modified Zanardi to incorporate the teachings of Bartlett for the benefit of performing task more efficiently (Bartlett, pg. 602, right col., third para.).
Regarding claim 11, Modified Zanardi teaches the method of claim 1, Bartlett teaches wherein the quantum-computer code includes preparation of a pure state in one of the plurality of qubits (For simplicity, we restrict our attention to pure state, left column, first full paragraph); Denote the pure state of the test spin-1/2 system that is aligned (antialigned) with the initial RF by... For a spin-1/2 system prepared in the state… with equal probability, the average probability of success using a quantum RF state is… (page 600, left column, last paragraph))
It would have been obvious to a person having ordinary skill in the art before the effective filing date of the claimed invention to have modified the method of Modified Zanardi to incorporate the teachings of Bartlett for the benefit of performing task more efficiently (Bartlett, pg. 602, right col., third para.).
Regarding claim 12, Modified Zanardi teaches the method of claim 1, Bartlett teaches wherein the quantum-computer code includes application of a Hadamard gate or an S gate (Finally, Alice performs a Hadamard transformation HA (in her frame) and measures the observable OA=−Z (pg. 592, right col., last para.); By repeating this procedure n1 times, i.e., sending n1 independent qubits and averaging the results, Alice obtains OA, the estimate of OA (pg. 593, left col., first para). The Examiner notes Hadamard transform functions applies an H gate on each qubit of the register inputted to the function, and the quantum-computer code includes application of a Hadamard gate).
It would have been obvious to a person having ordinary skill in the art before the effective filing date of the claimed invention to have modified the method of Modified Zanardi to incorporate the teachings of Bartlett for the benefit of performing task more efficiently (Bartlett, pg. 602, right col., third para.).
Regarding claim 13, Modified Zanardi teaches the method of claim 1, Bartlett teaches wherein the quantum-computer code includes a single-qubit Pauli measurement, the method further comprising accumulating a series of standards to support the single-qubit Pauli measurement (To estimate the first bit t1, Alice prepares a single qubit in the state … (relative to her phase reference and sends the qubit to Bob. Bob then performs his operation XB and sends the qubit back to Alice, where XB is the Pauli bit-flip operator according to Bob. She then performs her operation XA (page 592, right column, last paragraph)).
It would have been obvious to a person having ordinary skill in the art before the effective filing date of the claimed invention to have modified the method of Modified Zanardi to incorporate the teachings of Bartlett for the benefit of performing task more efficiently (Bartlett, pg. 602, right col., third para.).
Regarding claim 21, Modified Zanardi teaches the method of claim 1, Bartlett teaches wherein the quantum state is entangled over at least two of the qubits (Denoting the logical qubit that can be encoded using three physical qubits in Alice’s (Bob’s) possession by
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a triple of physical qubits in Alice’s possession can be maximally entangled with a triple in Bob’s possession using the state
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(page 568, left col., first para.).
It would have been obvious to a person having ordinary skill in the art before the effective filing date of the claimed invention to have modified the method of Modified Zanardi to incorporate the teachings of Bartlett for the benefit of performing task more efficiently (Bartlett, pg. 602, right col., third para.).
Regarding claim 22, Modified Zanardi teaches the quantum computer of claim 15, Bartlett teaches wherein the quantum state is entangled over at least two of the qubits (Denoting the logical qubit that can be encoded using three physical qubits in Alice’s (Bob’s) possession by
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a triple of physical qubits in Alice’s possession can be maximally entangled with a triple in Bob’s possession using the state
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(page 568, left col., first para.).
It would have been obvious to a person having ordinary skill in the art before the effective filing date of the claimed invention to have modified the method of Modified Zanardi to incorporate the teachings of Bartlett for the benefit of performing task more efficiently (Bartlett, pg. 602, right col., third para.)9
8. Claims 5, 6, 17 and 18 are rejected under 35 U.S.C. 103 as being unpatentable over Zanardi et al. ("Dissipation and decoherence in a quantum register." Physical Review A 57.5 (1998): 3276) in view of Preskill, ("Fault-tolerant quantum computation." Introduction to quantum computation and information. 1998. 213-269. arXiv:quant-ph/9712048v1 19 Dec 1997) and further in view of Cafaro et al. ("A geometric algebra perspective on quantum computational gates and universality in quantum computing." Advances in Applied Clifford Algebras 21 (2011): 493-519)
Regarding claim 5, Modified Zanardi teaches the method of claim 1, but does not explicitly teach wherein the sequence of operations further includes a pair of orthogonal single-qubit Clifford operations.
Cafaro teaches wherein the sequence of operations further includes a pair of orthogonal single-qubit Clifford operations (We consider simple circuit models of quantum computation with 1-qubit quantum gates in the GA formalism, (pg. 500, third para.); We investigate the utility of geometric (Clifford) algebras (GA) methods in two specific applications to quantum information science. First, using the multiparticle spacetime algebra (MSTA, the geometric algebra of a relativistic configuration space), (abstract); A suitable basis for the MSTA is given by the set ... These basis vectors satisfy the orthogonality conditions ... Vectors from different particle spaces anticommute as a consequence of their orthogonality (pg. 496, second para.); Therefore, Hˆ can be envisioned (up to an overall phase) as a θ = π rotation about the axis nˆ = 1/√ 2 (ˆn1 + ˆn3) that rotates ˆx to ˆz and vice versa, Hˆ = −iCR 1/√ 2 (ˆn1+ˆn3) (π). In GA, rotations are handled by means of rotors… It is straightforward to show that the action of the rotor Hˆ (GA) on the 1-qubit computational basis states satisfies (up to an overall irrelevant phase shift) the transformation laws (pg. 503, second para.)).
It would have been obvious to a person having ordinary skill in the art before the effective filing date of the claimed invention to have modified the method of Modified Zanardi to incorporate the teachings of Cafaro for the benefit of investigating the utility of geometric (Clifford) algebras (GA) methods in two specific applications to quantum information science and an explicit algebraic description of one and two-qubit quantum states together with a MSTA (multiparticle spacetime algebra) characterization of one and two-qubit quantum computational gate (Cafaro, abstract)
Regarding claim 6, Modified Zanardi teaches the method of claim 1, Modified Zanardi does not explicitly teach wherein the pair of orthogonal single-qubit Clifford operations includes a Clifford X rotation operation and a Clifford Z rotation operation.
Cafaro teaches wherein the pair of orthogonal single-qubit Clifford operations (We consider simple circuit models of quantum computation with 1-qubit quantum gates in the GA formalism, (pg. 500, third para.); We investigate the utility of geometric (Clifford) algebras (GA) methods in two specific applications to quantum information science. First, using the multiparticle spacetime algebra (MSTA, the geometric algebra of a relativistic configuration space), (abstract); A suitable basis for the MSTA is given by the set ... These basis vectors satisfy the orthogonality conditions ... Vectors from different particle spaces anticommute as a consequence of their orthogonality (pg. 496, second para.)) includes
a Clifford X rotation operation and a Clifford Z rotation operation (For instance, the Hadamard gate Hˆ acting on a single qubit has the properties Hˆ Σˆ1Hˆ = Σˆ3 … Therefore, Hˆ can be envisioned (up to an overall phase) as a θ = π rotation about the axis nˆ = 1/√2 (ˆn1 + ˆn3) that rotates ˆx to ˆz and vice versa, Hˆ = −iCR 1/√2(ˆn1+ˆn3) (π). In GA, rotations are handled by means of rotors… It is straightforward to show that the action of the rotor Hˆ (GA) on the 1-qubit computational basis states satisfies (up to an overall irrelevant phase shift) the transformation laws (pg. 503, second para.)).
It would have been obvious to a person having ordinary skill in the art before the effective filing date of the claimed invention to have modified the method of Modified Zanardi to incorporate the teachings of Cafaro for the benefit of investigating the utility of geometric (Clifford) algebras (GA) methods in two specific applications to quantum information science and an explicit algebraic description of one and two-qubit quantum states together with a MSTA (multiparticle spacetime algebra) characterization of one and two-qubit quantum computational gate (Cafaro, abstract)
Regarding claim 17, claim 17 is similar to claim 5. It is rejected in the manner and reasoning applying.
Regarding claim 18, claim 18 is similar to claim 6. It is rejected in the manner and reasoning applying.
9. Claim 14 is rejected under 35 U.S.C. 103 as being unpatentable over Zanardi et al. ("Dissipation and decoherence in a quantum register." Physical Review A 57.5 (1998): 3276) in view of Preskill, ("Fault-tolerant quantum computation." Introduction to quantum computation and information. 1998. 213-269. arXiv:quant-ph/9712048v1 19 Dec 1997) and further in view of Jordan ("Permutational quantum computing." arXiv preprint arXiv:0906.2508 (2009)).
Regarding claim 14, Modified Zanardi teaches the method of claim 1, but does not explicitly teach wherein the quantum-computer code defines a permutational quantum computation, and wherein the sequence of operations provides a weak-model simulation of the permutational quantum computation.
Jordan teaches wherein the quantum-computer code defines a permutational quantum computation (In this section we consider a modified version of permutational quantum computation in which the initial state is highly mixed, pg. 17, section 7), and
wherein the sequence of operations provides a weak-model simulation of the permutational quantum computation (In this section we consider a modified version of permutational quantum computation in which the initial state is highly mixed. We then show that the resulting complexity class is contained in BPP. In contrast, if we take the standard quantum circuit model and analogously apply it to highly mixed initial states, we obtain a complexity class DQC1 which appears to extend beyond BPP, although it is probably weaker than BQP, pg. 17, section 7).
It would have been obvious to a person having ordinary skill in the art before the effective filing date of the claimed invention to have modified the method of Modified Zanardi to incorporate the teachings of Jordan for the benefit of proving that permutational computers are efficiently simulatable by quantum circuits and present evidence that the class of problems solvable with polynomial resources on a permutational quantum computer (Jordan, pg. 2, first para.)
10. Claim 16 is rejected under 35 U.S.C. 103 as being unpatentable over Zanardi et al. ("Dissipation and decoherence in a quantum register." Physical Review A 57.5 (1998): 3276) in view of Preskill, ("Fault-tolerant quantum computation." Introduction to quantum computation and information. 1998. 213-269. arXiv:quant-ph/9712048v1 19 Dec 1997) in view Bartlett et al. ("Reference frames, superselection rules, and quantum information." Reviews of Modern Physics 79.2 (2007): 555-609) and further in view of Xue ("Measurement based controlled not gate for topological qubits in a Majorana fermion and quantum-dot hybrid system." The European Physical Journal D 67 (2013): 1-4).
Regarding claim 16, Modified Zanardi teaches quantum computer of claim 15, Bartlett teaches wherein each of the plurality of particles comprises a confined fermion (For example, in the position representation of two indistinguishable particles, a wave function of two particles is expressed as
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where the ± cases correspond … fermions (pg. 572, right col., second para.), and
It would have been obvious to a person having ordinary skill in the art before the effective filing date of the claimed invention to have modified the method of Modified Zanardi to incorporate the teachings of Bartlett for the benefit of performing task more efficiently (Bartlett, pg. 602, right col., third para.).
Modified Zanardi does not explicitly teach wherein the quantum state is a product state over each of the confined fermions.
Xue teaches wherein the quantum state is a product state over each of the confined fermions (A pair of MF can be combined into a complex fermion … we combine four MF to form a topological qubit. In this way, coherent superposition is permitted for the two encoded qubit subspaces with same fermion parity … we can use the subspace with fermion parity is even as the encoded qubit states, i.e., the two states of the topological qubit are encoded as |00› and |11› of the four MF (Majorana fermions, abstract)., pg. 2, right col., second para.).
It would have been obvious to a person having ordinary skill in the art before the effective filing date of the claimed invention to have modified the method of Modified Zanardi to incorporate the teachings of Xue for the benefit of implementing controlled not gate for topological qubits in a quantum-dot and Majorana fermion hybrid system (Xue, abstract)
11. Claims 19 and 4 are rejected under 35 U.S.C. 103 as being unpatentable over Zanardi et al. ("Dissipation and decoherence in a quantum register." Physical Review A 57.5 (1998): 3276) in view of Bartlett et al. ("Reference frames, superselection rules, and quantum information." Reviews of Modern Physics 79.2 (2007): 555-609) and further in view of Douçot et al. ("Physical implementation of protected qubits." Reports on Progress in Physics 75.7 (2012): 072001)
Regarding claim 19, Zanardi teaches a quantum-computation method (In this paper we address the problem of dynamically stable quantum encoding within a master equation formalism that allows us to deal directly with the marginal dynamics of the computational degrees of freedom, pg. 3276, right col., first para.), comprising:
receiving quantum-computer code (
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pg. 3281, right col., third para.) for execution on a quantum computer (quantum computation applications (pg. 3282, left col., last para.); ... a logical qubit can be encoded in each cluster, pg. 3281, left col., second para.; According to instant specification: “Considered particularly herein are qubits encoded in quantum spins” US20220374239 [0034]),
the plurality of particles defining a quantum state (is a qubit-qubit interaction. In quantum computation applications such a term might arise, for example, during the gate processing, pg. 3281, left col., last para. The Examiner notes initial quantum state of two particles is the qubit-qubit state);
decomposing the quantum-computer code into a sequence of operations including a simultaneous, total spin-state measurement on particles (Hilbert space HR splits dynamically according the Clebsch-Gordan decomposition of the n-fold tensor representation of su(2) ... total spin eigenvalue S(S+1), pg. 3281, right col., first para. The Examiner notes total spin S can take values: Triplet states (S = 1) and Singlet state (S = 0)) corresponding to two or more of the qunits without revealing individual spin states of the particles (... the self-Hamiltonian leaves the code invariant (pg. 3279, right col., second to the last para.); furthermore from the su(2) invariance of HR (self-Hamiltonian HR), pg. 3281, right col., third to the last para.; According to the instant specification: Provided that all of the terms in the environmental Hamiltonian are SU(2)-invariant, measurement into total spin states is protected [0027]. The Examiner notes the su(2) invariance of HR (self-Hamiltonian) ensures measurement into total spin states (either 0 or 1) is protected from revealing spin-state); and
applying the sequence of operations on the plurality of particles to thereby transform the quantum state according to the quantum-computer code (Furthermore we have shown that there exist cases with nontrivial cell dependence that can be mapped onto (ii) and (iii) by a suitable local gauge transformation. The degree of stability of the resulting codes depends on the covariance properties of the renormalized self-Hamiltonian, pg. 3283, right col., first para.).
Zanardi does not explicitly teach the quantum computer having a plurality of qunits associated with a corresponding plurality of particles of a spin greater than spin-1/2, total spin-state measurement on particles corresponding to two or more of the qunits
Bartlett teaches the quantum computer having a plurality of qunits associated with a corresponding plurality of particles of a spin greater than spin-1/2 (For example, in the position representation of two indistinguishable particles, a wave function of two particles is expressed as
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where the ± cases correspond … fermions (pg. 572, right col., second para.); Note that because the third spin 1/2 can couple to either j1=0 or j1=1 to yield j =1/2, the latter representation has multiplicity 2. We let |1/2, ±1/2, … denote a basis of Hj=1/2 in the coupled representation (pg. 566, right col., second para.). The Examiner notes each qunit comprises a qubit and each of the corresponding plurality of particles comprises a spin ½)
a simultaneous, total spin-state measurement on particles corresponding to two or more of the qunits (For example, in the position representation of two indistinguishable particles, a wave function of two particles is expressed as
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where the ± cases correspond … fermions (pg. 572, right col., second para.); To see how three spin-1/2 systems couple to total spin, imagine coupling the first pair to a spin j1 and then coupling this to the third:
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Note that because the third spin 1/2 can couple to either j1=0 or j1=1 to yield j =1/2, pg. 566, right col., second para.);
It would have been obvious to a person having ordinary skill in the art before the effective filing date of the claimed invention to have modified the method of Zanardi to incorporate the teachings of Bartlett for the benefit of performing task more efficiently (Bartlett, pg. 602, right col., third para.).
Modified Zanardi the quantum computer having a plurality of qunits associated with a corresponding plurality of particles.
Douçot teaches the quantum computer having a plurality of qunits associated with a corresponding plurality of particles (The natural generalizations of the spin flip and phase flip operators for a qubit are Pauli operators Z = exp(iφ) and X = exp(−i 2π n p) for a qunit (n-state system) whose action on the grid states ... These operators generate a discrete group of transformations of a qunit wave-function. A more general group of discrete unitary transformations of a qunit wave-function is known as the Clifford group (pg. 8, left col., second para.); The simplest example of the protected qubit formed by in a continuous system is provided by a quantum particle moving on a line, whose position is denoted by φ. The conjugated momentum is p = −i ∂ ∂φ . …. These two operators, cos(2πp) and cos(nφ), can be used as error syndromes for a qunit (n state quantum bit) based on a continuous variable φ (pg. 6, right col., second para.); a four junction circuit shown in figure 2 that implements a quantum spin, pg. 9, right col. last para.).
It would have been obvious to a person having ordinary skill in the art before the effective filing date of the claimed invention to have modified the method of Modified Zanardi to incorporate the teachings of Douçot for the benefit of enriching the possibilities to use physical qubits in non-trivial quantum algorithms (Douçot, pg. 19, right col., second to the last para.).
Regarding claim 4, Modified Zanardi teaches the method of claim 19, Bartlett teaches wherein the total spin-state measurement is SU (2)-invariant (Thus all states and operations must be diagonal in total spin quantum number j (page 602, left column, second para.); The inequivalent representations of SU(2) are labeled by the total angular momentum J2 quantum number j (page 566, right col., section, section b. Two transmitted qubits: A classical channel) and
therefore unresponsive to decoherence of the quantum state in a substantially SU(2)-invariant noise environment (The efficiency of the above schemes can be increased through the use of more qubits, because the sizes of the decoherence-free subsystems can grow exponentially with increasing number of qubits. For simplicity, we consider only the case where N is even. The collective (tensor) representation of SU(2) on N spin-1/2 systems, R(Ω)N, can again be decomposed into a direct sum of SU(2) irreps, each with angular momentum quantum number j ranging from 0 to N/2 (pg. 567, left col., section d. Asymptotic behavior); As we will see, the lack of a reference frame can be treated within the quantum formalism as a form of decoherence—quantum noise pg. 557, left col., second para.).
It would have been obvious to a person having ordinary skill in the art before the effective filing date of the claimed invention to have modified the method of Zanardi to incorporate the teachings of Bartlett for the benefit of performing task more efficiently (Bartlett, pg. 602, right col., third para.).
12. Claim 20 is rejected under 35 U.S.C. 103 as being unpatentable over Zanardi et al. ("Dissipation and decoherence in a quantum register." Physical Review A 57.5 (1998): 3276) in view of Bartlett et al. ("Reference frames, superselection rules, and quantum information." Reviews of Modern Physics 79.2 (2007): 555-609) in view of Douçot et al. ("Physical implementation of protected qubits." Reports on Progress in Physics 75.7 (2012): 072001) and further in view of Ashrafi (US20200118026 filed 10/22/2019)
Regarding claim 20, Modified Zanardi teaches the method of claim 19, Douçot teaches wherein each of the plurality of qunits comprises a qubit (The natural generalizations of the spin flip and phase flip operators for a qubit are Pauli operators Z = exp(iφ) and X = exp(−i 2π n p) for a qunit (n-state system) whose action on the grid states ... These operators generate a discrete group of transformations of a qunit wave-function. A more general group of discrete unitary transformations of a qunit wave-function is known as the Clifford group (pg. 8, left col., second para.); The simplest example of the protected qubit formed by in a continuous system is provided by a quantum particle moving on a line, whose position is denoted by φ. The conjugated momentum is p = −i ∂ ∂φ . …. These two operators, cos(2πp) and cos(nφ), can be used as error syndromes for a qunit (n state quantum bit) based on a continuous variable φ (pg. 6, right col., second para.)) and
It would have been obvious to a person having ordinary skill in the art before the effective filing date of the claimed invention to have modified the method of Modified Zanardi to incorporate the teachings of Douçot for the benefit of enriching the possibilities to use physical qubits in non-trivial quantum algorithms (Douçot, pg. 19, right col., second to the last para.).
Modified Zanardi does not explicitly teach each of the corresponding plurality of particles comprises a spin 1/2 fermion.
Ashrafi teaches each of the corresponding plurality of particles comprises a spin 1/2 fermion (Examples of Majorana-like “particles” can be found in different scenarios like in condensed matter physics where composite states of particles behave like Majorana fermions, for which a particle and its antiparticle must coincide and acquire mass from a self-interaction mechanism [0369]; Also, one can make two Majoranas from one Fermion according to: x=½(Ψ+Ψ†) [0396]).
It would have been obvious to a person having ordinary skill in the art before the effective filing date of the claimed invention to have modified the method of Modified Zanardi to incorporate the teachings of Ashrafi for the benefit of braid group representations related to Majorana fermions … and these braiding representations have important applications in quantum informatics and topology. Majorana operators give rise to a particularly robust representation of the braid group that is then further represented to find the phases of the fermions under their exchanges in a plane space (Ashrafi [0388])
Conclusion
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/M.G./Examiner, Art Unit 2148
/MICHELLE T BECHTOLD/Supervisory Patent Examiner, Art Unit 2148
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