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 .
This office action is in response to submission of application on 12/16/2025.
Claims 1-15 are presented for examination.
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.
Claims 1-15 are rejected under 35 U.S.C. § 103 as being unpatentable over Lechner, W. (WO 2020/156680 A1, Method and Apparatus for Performing a Quantum Computation, herein Lechner), and Leipold, et al (Constructing driver Hamiltonians for optimization problems with linear constraints, herein Leipold).
Regarding claim 1,
Lechner teaches a method of performing a quantum computation, comprising:
providing a quantum system (Lechner, paragraph [0001], line 1 “ Embodiments described herein relate to apparatuses and methods for performing a quantum computation, more specifically apparatuses and methods for computing solutions to computational problems using a quantum system.” In other words, methods for performing a quantum computation is a method of performing a quantum computation, and using a quantum system is providing a quantum system.) comprising constituents;
encoding a computational problem into a problem Hamiltonian of the quantum system (Lechner, abstract, line 2 “The method includes encoding a computational problem into a problem Hamiltonian of the quantum system.” In other words, encoding a computational problem into a problem Hamiltonian of the quantum system is encoding a computational problem into a problem Hamiltonian of the quantum system. ), wherein
the problem Hamiltonian is a single-body Hamiltonian being a sum of summand problem Hamiltonians (Lechner, paragraph [0035], line 4 “The problem Hamiltonian is a single-body Hamiltonian comprising a plurality of adjustable parameters.” And, paragraph [0055], line 3 “A single body Hamiltonian may be the sum of a plurality of summand Hamiltonians.” In other words, problem Hamiltonian is problem Hamiltonian, and single body Hamiltonian may be the sum of a plurality of summand Hamiltonians is a single-body Hamiltonian being a sum of summand problem Hamiltonians.) ;
determining a constraint Hamiltonian of the quantum system (Lechner, paragraph [0198], line 1 “In reference to the above equation, two possible implementations of the constraint Hamiltonians may be considered.” In other words, implementation of constraint Hamiltonian is determining a constraint Hamiltonian. ), the constraint Hamiltonian being
a sum of summand constraint Hamiltonians (Lechner, paragraph [0197], line 1 The increased number of degrees of freedom of the quantum system compared to the Ising spin model is compensated by a short-range Hamiltonian which is the sum of M – n 4-body summand Hamiltonians Ci, called constraint Hamiltonians representing constraints for fixing a portion of the qubits.” In other words, summand Hamiltonians Ci called constraint Hamiltonians is sum of summand constraint Hamiltonians.), wherein
a ground state of a total Hamiltonian encodes a solution to the computational problem (Lechner, paragraph [0121], line 4 “The total Hamiltonian may have a ground state containing information regarding a solution to the computation problem.” In other words, ground state containing information regarding a solution to the computation problem is ground state of a total Hamiltonian encodes a solution to the computational problem.), wherein
the total Hamiltonian includes a sum of the problem Hamiltonian and the constraint Hamiltonian (Lechner, paragraph [0122], line 1 “The total Hamiltonian may be a sum of the problem Hamiltonian Hp and a short-range Hamiltonian HSR.” In other words, total Hamiltonian is total Hamiltonian, and sum of the problem Hamiltonian and short-range Hamiltonian is sum of the problem Hamiltonian and constraint Hamiltonian.);
determining a first subset (S1) of the summand constraint Hamiltonians of the constraint Hamiltonian and a second subset (S2) of the summand constraint Hamiltonians of the constraint Hamiltonian (Lechner, paragraphs [0127], line 1 “A further example of a short-range Hamiltonian described with reference to Fig. 6 is a plaquette Hamiltonian. A plaquette of the 2-dimensional square lattice 120 is an elementary square of the 2-dimensional square lattice 120, as illustrated in Fig. 6 with reference numeral 370. The plaquette 370 comprises qubits 371, 372, 373 and 374, wherein qubit 371 is arranged at the elementary distance O from qubit 372 and from qubit 374, and wherein qubit 373 is also arranged at the elementary distance O from qubits 372 and 374.” In other words, plaquette is subset of constraint Hamiltonian, and, each plaquette determines a subset of a constraint Hamiltonian is determining a first subset and a second subset of constraint Hamiltonians.);
performing N rounds of operations (Lechner, paragraph [0091], line 1 “According to embodiments, each i-th round of the N rounds of operations may include preparing an initial quantum state for the i-th round.” In other words, N rounds of operations is performing N rounds of operations.), wherein
N > 2, wherein each round comprises: preparing an initial quantum state (Lechner, paragraph [0093], line 1 “The N rounds of operations may include 2 or more, particularly 10 or more, more particularly 1000 or more rounds of operations.” In other words, N rounds of operations may include 2 or more is N > 2.) ;
evolving the quantum system according to a sequence of unitary operators, the sequence including problem-encoding unitary operators (Lechner, paragraph [0095], line 1 “The N rounds of operations may include a first sequence of unitary operators. The first sequence of unitary operators may include a first plurality of unitary operators, wherein each unitary operator of the first plurality of unitary operators is a time evolution of the problem Hamiltonian.” In other words, evolution of the problem Hamiltonian is evolving the quantum system, and sequence of unitary operators is according to a sequence of unitary operators.)
constraint-enforcing unitary operators and unitary driver operators, wherein
each problem-encoding unitary operator is a unitary time evolution operator of a summand problem Hamiltonian of the problem Hamiltonian or is a unitary time evolution operator of a sum of summand problem Hamiltonians of the problem Hamiltonian (Lechner, abstract, line 2 “The method includes encoding a computational problem into a problem Hamiltonian of the quantum system. The problem Hamiltonian is a single-body Hamiltonian comprising a plurality of adjustable parameters.” and, paragraph [00210], part a “a unitary operator exp(iaHp) being a unitary time evolution of the problem Hamiltonian Hp = Σk Jk σz(k), wherein the plurality of adjustable parameters Jk are in the problem-encoding configuration…” And, paragraph [0055], line 4 “A single body Hamiltonian may be the sum of a plurality of summand Hamiltonians. Each summand Hamiltonian may act on a single qubit of the plurality of qubits. A single-body Hamiltonian may have the form H = Σ1 H1 wherein each Hi is a summand Hamiltonian acting solely on the i-th qubit.” And, claim 1, line 10 “a unitary operator being a unitary time evolution of the problem Hamiltonian” and, paragraph [00197], line 4 “The short-range Hamiltonian has the form Σ1 Ci, wherein the index 1 ranges from 1 to (n2 - 3n)/2 and wherein each summand Hamiltonian C1 is a constraint Hamiltonian.” In other words, unitary operator is unitary operator, C1 is constraint Hamiltonian is constraint enforcing unitary operators, unitary time evolution operator is a unitary time evolution operator, and summand Hamiltonian is summand problem Hamiltonian.), wherein
each constraint-enforcing unitary operator is a unitary time evolution operator of a summand constraint Hamiltonian taken from the first subset of the summand constraint Hamiltonians of the constraint Hamiltonian, or is a unitary time evolution operator of a sum of summand constraint Hamiltonians taken from said first subset (Lechner, paragraph [00210], part a “a unitary operator exp(iaHp) being a unitary time evolution of the problem Hamiltonian Hp = Σk Jk σz(k), wherein the plurality of adjustable parameters Jk are in the problem-encoding configuration…” And, paragraph [0055], line 4 “A single body Hamiltonian may be the sum of a plurality of summand Hamiltonians. Each summand Hamiltonian may act on a single qubit of the plurality of qubits. A single-body Hamiltonian may have the form H = Σ1 H1 wherein each Hi is a summand Hamiltonian acting solely on the i-th qubit.” In other words, a unitary operator exp(iaHp) being a unitary time evolution of the problem Hamiltonian is a unitary time evolution operator, and a single-body Hamiltonian may have the form H = Σ1 H1 wherein each Hi is a summand Hamiltonian acting solely on the i-th qubit is a sum of summand constraint Hamiltonians.) , and wherein
[each unitary driver operator is a unitary operator that commutes with every summand constraint Hamiltonian from the second subset of the summand constraint Hamiltonians of the constraint Hamiltonian]; and
performing a measurement of one or more constituents of the quantum system (Lechner, paragraph [0175], line 10 “The apparatus includes a measurement device
connected to the controller, the measurement device being configured to measure at least a
portion of the plurality of qubits.” In other words, measure at least a portion of the plurality of qubits is performing a measurement of one or more constituents.); and
outputting a result of the quantum computation (Lechner, paragraph [0185], line 1 “The controller may be configured for outputting a result of the quantum computation.” In other words, outputting a result of the quantum computation is outputting a result of the quantum computation.).
Thus far, Lechner does not explicitly teach each unitary driver operator is a unitary operator that commutes with every summand constraint Hamiltonian from the second subset of the summand constraint Hamiltonians of the constraint Hamiltonian.
Leipold teaches each unitary driver operator is a unitary operator that commutes with every summand constraint Hamiltonian from the second subset of the summand constraint Hamiltonians of the constraint Hamiltonian (Leipold, abstract, line 3 “One of these advances has centered around the development of driver Hamiltonians that commute with the constraints of an optimization problem—allowing for another avenue to satisfying those constraints instead of imposing penalty terms for each of them.” In other words, driver Hamiltonians commute with the constraints of the problem is each operator is a unitary operator that commutes with every summand constraint Hamiltonian.)
Both Lechner and Leipold are directed to quantum computations, among other things. Lechner teaches a method of performing a quantum computation, comprising providing a quantum system comprising constituents, encoding a computational problem into a problem Hamiltonian of the quantum system, wherein the problem Hamiltonian is a single-body Hamiltonian being a sum of summand problem Hamiltonians, determining a constraint Hamiltonian of the quantum system, the constraint Hamiltonian being a sum of summand constraint Hamiltonians, wherein a ground state of a total Hamiltonian encodes a solution to the computational problem, wherein the total Hamiltonian includes a sum of the problem Hamiltonian and the constraint Hamiltonian, determining a first subset (S1) of the summand constraint Hamiltonians of the constraint Hamiltonian and a second subset (S2) of the summand constraint Hamiltonians of the constraint Hamiltonian, performing N rounds of operations, wherein N > 2, wherein each round comprises preparing an initial quantum state, and evolving the quantum system according to a sequence of unitary operators, the sequence including problem-encoding unitary operators, constraint- enforcing unitary operators and unitary driver operators; but does not explicitly teach each unitary driver operator is a unitary operator that commutes with every summand constraint Hamiltonian from the second subset of the summand constraint Hamiltonians of the constraint Hamiltonian. Leipold teaches each unitary driver operator is a unitary operator that commutes with every summand constraint Hamiltonian from the second subset of the summand constraint Hamiltonians of the constraint Hamiltonian.
In view of the teaching of Lechner, it would be obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to combine the teaching of Leipold into Lechner. This would result in a method of performing a quantum computation, comprising providing a quantum system comprising constituents, encoding a computational problem into a problem Hamiltonian of the quantum system, wherein the problem Hamiltonian is a single-body Hamiltonian being a sum of summand problem Hamiltonians, determining a constraint Hamiltonian of the quantum system, the constraint Hamiltonian being a sum of summand constraint Hamiltonians, wherein a ground state of a total Hamiltonian encodes a solution to the computational problem, wherein the total Hamiltonian includes a sum of the problem Hamiltonian and the constraint Hamiltonian, determining a first subset (S1) of the summand constraint Hamiltonians of the constraint Hamiltonian and a second subset (S2) of the summand constraint Hamiltonians of the constraint Hamiltonian, performing N rounds of operations, wherein N > 2, wherein each round comprises preparing an initial quantum state, evolving the quantum system according to a sequence of unitary operators, the sequence including problem-encoding unitary operators, constraint-enforcing unitary operators and unitary driver operators where each unitary driver operator is a unitary operator that commutes with every summand constraint Hamiltonian from the second subset of the summand constraint Hamiltonians of the constraint Hamiltonian.
One of ordinary skill in the art would be motivated to do this because recent advances in quantum computing have centered on using more advanced and novel Hamiltonians to solve optimization problems, necessitating finding driver Hamiltonians that commute with constraints. (Leipold, abstract, line 1 “Recent advances in the field of adiabatic quantum computing and the closely related field of quantum annealing have centered around using more advanced and novel Hamiltonian representations to solve optimization problems. One of these advances has centered around the development of driver Hamiltonians that commute with the constraints of an optimization problem—allowing for another avenue to satisfying those constraints instead of imposing penalty terms for each of them.”)
Regarding claim 2,
The combination of Lechner and Leipold teaches the method of claim 1, wherein, for each of the N rounds of operations, evolving the quantum system according to the sequence of unitary operators of the round comprises
implementing at least some unitary operators of the sequence by a quantum circuit comprising quantum gates (Lechner, Figure 14, and paragraph [00212], line 8 “These individual plaquette terms be can realized as shown in Fig. 14 using six CNOT gates 1410 and one single-qubit rotation 1420 (z-rotation).”
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In other words, six CNOT gates is a quantum circuit comprising a sequence of quantum gates.) .
Regarding claim 3,
The combination of Lechner and Leipold teaches the method of claim 1, wherein the quantum system includes
subsystems each comprising a subset of the constituents, wherein the subsystems are disjoint, wherein each subsystem has boundary constituents forming part of a boundary between the subsystem and one or more adjacent subsystems, wherein each boundary constituent participates in a quantum interaction represented by a summand constraint Hamiltonian of the first subset of the summand constraint Hamiltonians of the constraint Hamiltonian (Lechner, paragraph [0157], line 1 According to embodiments, the plurality of qubits can be arranged on a 2-dimensional lattice. The 2-dimensional lattice can have a plurality of plaquettes. Each ancillary particle of the plurality of ancillary particles may be located at a plaquette of the 2-dimensional lattice. The plurality of plaquettes may include a first plaquette. The plurality of ancillary particles may include a first ancillary particle. The method described herein may include coupling a first qubit of the first plaquette with the first ancillary particle. The method may include moving the first ancillary particle from the first qubit to a second qubit of the first plaquette. The method may include coupling the second qubit with the first ancillary particle.” In other words, plaquettes is disjoint constituents that are boundary constituents forming part of a boundary between the subsystem and one or more adjacent subsystems.)
Regarding claim 4,
The combination of Lechner and Leipold teaches the method of claim 3, wherein
each unitary driver operator acts fully inside one of the subsystems of the quantum system (Lechner, paragraph [0006], line 12 “Each round of the N rounds of operations includes evolving the quantum system by applying the sequence of unitary operators to the quantum system. Each round of the N rounds of operations includes performing a measurement of one or more qubits of the quantum system.” In other words, applying the sequence of unitary operators to the quantum system is each unitary operator acts fully inside one of the subsystems of the quantum system.) .
Regarding claim 5,
The combination of Lechner and Leipold teaches the method of claim 3, wherein
each subsystem has a total number of constituents that is independent of a size of the computational problem (Lechner, paragraph [0140], line 1 “A constant depth refers to a depth which is independent of the size of quantum system, more particularly independent of the number of qubits in the quantum system.” In other words, depth which is independent of the size of the quantum system is a number of constituents that is independent of a size of the computational problem.).
Regarding claim 6,
The combination of Lechner and Leipold teaches the method of claim 3, wherein
each unitary driver operator is realized by a quantum circuit of constant depth (Lechner, paragraph [0140], line 1 “A constant depth refers to a depth which is independent of the size of quantum system, more particularly independent of the number of qubits in the quantum system. A constant depth may be a depth which is much smaller than the number of qubits in the quantum system. For example, a constant depth may be a depth which is 30% or less, in particular 20% or less, more particularly 10% or less, of the number of qubits in the quantum system.” In other words, quantum system is quantum circuit, and constant depth is constant depth.).
Regarding claim 7,
The combination of Lechner and Leipold teaches the method of claim 1, wherein
the initial quantum state of at least some of the N rounds is a ground state of a partial constraint Hamiltonian being a sum of all summand constraint Hamiltonians taken from the second subset of the summand constraint Hamiltonians (Lechner, See mapping of claim 1, office action, page 4, and, paragraph [00204], line 1 “A total Hamiltonian HT is considered, wherein the total Hamiltonian HT is the sum of the problem Hamiltonian Hp= Σk Jk σz(k) and the short-range Hamiltonian HSR = Σ1 C1. In other words, HT = Hp + HSR = Σk Jk σz(k) + Σ1 C1. In light of the above, the total Hamiltonian has the following property: if the quantum system is in the ground state of the final Hamiltonian, of portion of the qubits will be in a configuration of quantum basis states corresponding to a configuration of spins in the ground state of the Ising spin model. Particularly, the qubits in the portion 425 shown in Fig. 11 will be in a configuration of quantum basis states corresponding to a configuration of spins in the ground state of the Ising spin model.” In other words, ground state is ground state, and portion is partial constraint Hamiltonian.).
Regarding claim 8,
The combination of Lechner and Leipold teaches the method of claim 1, further comprising:
determining a driver Hamiltonian being a sum of summand driver Hamiltonians, wherein the driver Hamiltonian commutes with every summand constraint Hamiltonian of the second subset of the summand constraint Hamiltonians, wherein each unitary driver operator is a unitary time evolution operator of a summand driver Hamiltonian of the driver Hamiltonian or is a unitary time evolution operator of a sum of two or more summand driver Hamiltonians of the driver Hamiltonian (Lechner, paragraph 0216], line 16 “The first protocol P1 alternates between time evolutions of the total Hamiltonian and time evolutions of the driver Hamiltonian. The second protocol P2 makes use of the splitting between local field terms and interaction terms and optimizes the parameters a, b and c separately, but keeps the parameter c the same for all plaquettes. The third protocol P3 also includes an update of the constraint strengths and thus the total Hamiltonian itself.” In other words, driver Hamiltonian is driver Hamiltonian, and time evolutions of the total Hamiltonian is a unitary time evolution operator of a sum of two or more summand driver Hamiltonians of the driver Hamiltonian.).
Regarding claim 9,
The combination of Lechner and Leipold teaches the method of claim 1, wherein
the sequence of unitary operators of at least some of the N rounds of operations has the form A1 A2… Ap, or includes at least a sub-sequence of said form, wherein p >=3, wherein each A1 is a product of the form Xi Yi Zi, wherein one of Xi, Yi and Zi is a problem-encoding unitary operator, another one of Xi, Yi and Zi is constraint-enforcing unitary operator and yet another one of Xi, Yi and Zi is a unitary driver operator (Lechner, paragraph [0093], line 1 “The N rounds of operations may include 2 or more, particularly 10 or more, more particularly 1000 or more rounds of operations. [0094] For each of the N rounds of operations, the sequence of unitary operators of a round may include 2 or more, particularly 5 or more, more particularly 200 or more unitary operators.” And, paragraph [0099], line 1 “The sequence of unitary operators of each of the N rounds of operations may be a sequence of alternations of the form A1, B1, A2, B2, •••. Each A1 may be a unitary time evolution of the problem Hamiltonian, wherein the plurality of adjustable parameters of the problem Hamiltonian are in the problem-encoding configuration.” And paragraph [00202], line 7 “To enforce the constraint corresponding to the closed loop of three spins, a 3-body constraint Hamiltonian C1 may be considered acting on the corresponding group of three qubits. Alternatively, an additional line of n- 2 auxiliary qubits fixed in the quantum basis state|1> may be included in the quantum system, as shown in Fig. 11 by the circles with dashed lines. To enforce a constraint corresponding to a closed loop of three spins, e.g. the closed loop corresponding to the qubits 12, 23 and 13, a constraint Hamiltonian C1 may be considered acting on the corresponding three qubits and on one of the auxiliary qubits, namely the auxiliary qubit 1101 shown in Fig. 11.” In other words, N rounds of operations is N rounds of operations, sequence of unitary operators is sequence of unitary operators, 5 or more is >= 3, of the form A1, B1, A2, B2, ••• is of the form A1 A2… Ap, and enforce constraint is enforce constraint.).
Regarding claim 10,
The combination of Lechner and Leipold teaches the method of claim 1, wherein
the N rounds of operations include one or more adaptive rounds of operations, wherein, for each adaptive round of operations, the unitary operators of the sequence of unitary operators of the adaptive round are determined based on at least one measurement outcome of a measurement performed in a previous round of the N rounds of operations (Lechner, See above mapping, and, paragraph [00100], line 4 “The N rounds of operations may include one or more adaptive rounds of operations. For each adaptive round of operations. the unitary operators of the sequence of unitary operators of the adaptive round are determined based on at least one measurement outcome of a measurement performed in a previous round of the N rounds of operations.” In other words, adaptive round is adaptive round and based on at least one measurement outcome is based on at least one measurement outcome of a measurement performed in a previous round.) .
Regarding claim 11,
The combination of Lechner and Leipold teaches the method of claim 1, wherein the N rounds of operations include a first round of operations, wherein evolving the quantum system according to the sequence of unitary operators of the first round of operations results in a first quantum state of the quantum system, wherein performing the measurement in the first round comprises:
measuring an energy of the first quantum state (Lechner, See above mapping, and, paragraph [00112], line 1 “A method according to embodiments described herein may include measuring an energy, particularly an average energy or expected energy, of the first quantum state. Measuring an energy of the first quantum state may include measuring a Hamiltonian of the quantum system. Measuring an energy of the first quantum state may include measuring an expectation value of a Hamiltonian of the quantum system.” In other words, measuring an energy of the first quantum state is measuring an energy of the first quantum state.).
Regarding claim 12,
The combination of Lechner and Leipold teaches the method of claim 11, wherein
the N rounds of operations include a second round of operations performed after the first round of operations, wherein evolving the quantum system according to the sequence of unitary operators of the second round of operations results in a second quantum state of the quantum system, wherein performing the measurement in the second round comprises: measuring an energy of the second quantum state (Lechner, paragraph [00116], line 1 “The method may include comparing the energy of the first quantum state with the energy of the second quantum state. The method may include determining the sequence of unitary operators to be applied in a third round of the N rounds of operations, wherein the third round is to be performed after the second round. The sequence of unitary operators to be applied in the third round may be determined based at least on the comparison of the energy of the first quantum state with the energy of the second quantum state.” In other words, comparing the energy of the first quantum state with the energy of the second quantum state is measuring an energy of the second quantum state. ); wherein the method comprises:
comparing the energy of the first quantum state with the energy of the second quantum state (Lechner, paragraph [00116], line 1 “The method may include comparing the energy of the first quantum state with the energy of the second quantum state.” In other words, comparing the energy of the first quantum state with the energy of the second quantum state is comparing the energy of the first quantum state with the energy of the second quantum state.) ; and
determining the sequence of unitary operators to be applied in a third round of the N rounds of operations, wherein the third round is to be performed after the second round, wherein the sequence of unitary operators to be applied in the third round is determined based at least on the comparison of the energy of the first quantum state with the energy of the second quantum state (Lechner, paragraph [00116], line 1 The method may include comparing the energy of the first quantum state with the energy of the second quantum state. The method may include determining the sequence of unitary operators to be applied in a third round of the N rounds of operations, wherein the third round is to be performed after the second round. The sequence of unitary operators to be applied in the third round may be determined based at least on the comparison of the energy of the first quantum state with the energy of the second quantum state.” In other words, determining the sequence of unitary operators is determining the sequence of unitary operators, third round of the N rounds is third round of the N rounds, and sequence of operators …may be determined based on the comparison of the energy of the first quantum state with energy of the second quantum state is the sequence of unitary operators to be applied in the third round is determined based at least on the comparison of the energy of the first quantum state with the energy of the second quantum state.).
Regarding claim 13,
The combination of Lechner and Leipold teaches the method of claim 1, wherein:
the problem Hamiltonian has the form
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wherein
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is a Pauli operator of a k-th constituent of the quantum system, wherein each Jk is a coefficient, and wherein each term
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is a summand problem Hamiltonian; and/or the constraint Hamiltonian has the form
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wherein each
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has the form
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=
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wherein
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is a tensor product of Pauli σz operators, I is the identity operator, and a1 and b1 are coefficients, and wherein each
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is a summand constraint Hamiltonian (Lechner, paragraph [0032], line 1 “The problem Hamiltonian as described herein is a single-body Hamiltonian which encodes the computational problem to be solved. That is, at an initial ("pre-processing") stage of the computation, the computational problem to be solved can be mapped, by a classical computing system, to the problem Hamiltonian. Several approaches for designing a problem Hamiltonian can be provided. For example, the problem Hamiltonian can have the form Hprob = Σk Jk σk, wherein σz(k) is a Pauli operator acting on a k-th qubit of the plurality of qubits, and wherein each Jk is an adjustable parameter determined by one or more external entities, e.g. magnetic fields, which can be adjusted at every qubit k individually. For example, h may be the strength of an adjustable magnetic field influencing the k-th qubit.” In other words, problem Hamiltonian is problem Hamiltonian, Pauli operator is Pauli operator, and Hprob = Σk Jk σk is the form
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=
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.)
20. Regarding claim 14,
The combination of Lechner and Leipold teaches the method of claim 1, wherein each unitary driver operator has the form exp(it
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), wherein t is a coefficient and
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is an operator of the form
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, wherein each bj is a coefficient and each
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is a tensor product of Pauli σx operators or a single Pauli ax operator, wherein the notation Σj denotes a sum of two or more terms or a single term (Lechner, paragraph [0032], line 1 “The problem Hamiltonian as described herein is a single-body Hamiltonian which encodes the computational problem to be solved. That is, at an initial ("pre-processing") stage of the computation, the computational problem to be solved can be mapped, by a classical computing system, to the problem Hamiltonian. Several approaches for designing a problem Hamiltonian can be provided. For example, the problem Hamiltonian can have the form Hprob = Σk Jk σk, wherein σz(k) is a Pauli operator acting on a k-th qubit of the plurality of qubits, and wherein each Jk is an adjustable parameter determined by one or more external entities, e.g. magnetic fields, which can be adjusted at every qubit k individually. For example, h may be the strength of an adjustable magnetic field influencing the k-th qubit.” In other words, Σk Jk σk, is an operator of the form
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where Σj denotes a sum of two or more terms or a single term. ).
Claim 15 is an apparatus claim for performing a quantum computation comprising a quantum system including a classical computing system corresponding to method claim 1, Otherwise, they are not patentably distinct. The combination of Lechner and Leipold teaches an apparatus (Lechner, claim 14 “An apparatus for quantum computing, comprising: a quantum system comprising a plurality of qubits; a classical computing system…” ). Therefore, claim 15 is rejected for the same reasons as claim 1.
The prior art made of record and not used is considered pertinent to applicant’s disclosure:
Ding, et al (US 2024/0013082 A1) “Systems and Methods for Simulation of Quant Circuits using Decoupled Hamiltonians” discloses a method to perform operations including generating a transformed Hamiltonian corresponding to a quantum circuit where the transformed Hamiltonian can include transformed local and coupling Hamiltonians.
Harju, A., “Quantum Orbifolds” discloses a study of orbifold-quotients of quantum groups (quantum orbifolds Ɵ ⇒ Gq ). These structures have been studied extensively in the case of the quantum SU2 group. A generalized theory of quantum orbifolds over compact simple and simply connected quantum groups is developed. Associated with a quantum orbifold there is an invariant subalgebra and a crossed product algebra. For each spin quantum orbifold, there is a unitary equivalence class of Dirac spectral triples over the invariant subalgebra, and for each effective spin quantum orbifold associated with a finite group action, there is a unitary equivalence class of Dirac spectral triples over the crossed product algebra.
Hen, et al “Driver Hamiltonians for constrained optimization in quantum annealing” discloses general guidelines for the construction of driver Hamiltonians given an arbitrary set of constraints and illustrate the broad applicability of the method by analyzing several diverse examples, namely, graph isomorphism, not-all-equal 3SAT, and the so-called Lechner, Hauke and Zoller constraints.
Conclusion
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