Detailed Action
Claims 1-21 are currently pending.
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 .
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 1-18 and 21 are rejected under 35 U.S.C. 101 because the claimed invention is directed to an abstract idea without significantly more.
Regarding claim 1,
Step 1: Claim 1 recites a method for solving an integer programming problem or a mixed-integer programming problem using a quantum optical device, the method comprising: (b) implementing said quantum Hamiltonian on said quantum optical device. Therefore, it is directed to the statutory category of Processes.
2A Prong 1:
(c) providing a solution of said integer programming problem or said mixed-integer programming problem based at least in part on a measurement of said system of qumodes. (According to the spec para [99-100], it is directed to a mathematical concept)
2A Prong 2:
A method for solving an integer programming problem or a mixed-integer programming problem using a quantum optical device, the method comprising: (mere instructions to apply an exception using a computer MPEP 2106.05(f) – applying computer components to perform the abstract idea of providing a solution to a problem)
(a) obtaining an indication of a quantum Hamiltonian representative of said integer programming problem or said mixed-integer programming problem, wherein said quantum Hamiltonian comprises a class of operators corresponding to variables of said integer programming problem or said mixed-integer programming problem; (insignificant extra-solution activity MPEP 2106.05(g)(iii) of gathering statistics)
(b) implementing said quantum Hamiltonian on said quantum optical device, wherein said quantum optical device comprises a system of qumodes and at least one quantum gate configured to act on one or more qumodes in said system of qumodes (mere instructions to apply an exception of solving a problem using a computer component MPEP 2106.05(f), according to the paragraph [00011]), and wherein one or more operators in said class of operators corresponds to said one or more qumodes in said system of qumodes; (a field of use and technological environment MPEP 2106.05(h) – limiting the field of use of operators)
The additional elements as disclosed above alone or in combination do not integrate the judicial exception into practical application as they are mere insignificant extra solution activity, combination of generic computer functions that are restricted to field of use are implemented to perform the disclosed abstract idea above.
2B:
A method for solving an integer programming problem or a mixed-integer programming problem using a quantum optical device, the method comprising: (mere instructions to apply an exception using a computer MPEP 2106.05(f) – applying computer components to perform the abstract idea of providing a solution to a problem)
(a) obtaining an indication of a quantum Hamiltonian representative of said integer programming problem or said mixed-integer programming problem, wherein said quantum Hamiltonian comprises a class of operators corresponding to variables of said integer programming problem or said mixed-integer programming problem; (indicated as an insignificant extra-solution activity MPEP 2106.05(g)(iii) in Step 2A Prong 2. Therefore, it is re-evaluated in Step 2B as well understood, routine, and conventional activity MPEP 2106.05(d)(II)(iv) of gathering statistics)
(b) implementing said quantum Hamiltonian on said quantum optical device, wherein said quantum optical device comprises a system of qumodes and at least one quantum gate configured to act on one or more qumodes in said system of qumodes, (mere instructions to apply an exception using a computer component MPEP 2106.05(f), according to the paragraph [00011]) and wherein one or more operators in said class of operators corresponds to said one or more qumodes in said system of qumodes; (a field of use and technological environment MPEP 2106.05(h) – limiting the field of use of operators)
The additional elements as disclosed above in combination of the abstract idea are not sufficient to amount to significantly more than the judicial exception as they are well, understood, routine and conventional activity as disclosed in combination of generic computer functions and usage of elements that are restricted to field of use that are implemented to perform the disclosed abstract idea above.
Regarding claim 2,
Step 1: Processes, as above.
2A Prong 1: Incorporates the rejection of claim 1.
2A Prong 2: wherein said class of operators comprises one or more of photon-number operators and momentum and position operators of said quantum Hamiltonian. (a field of use and technological environment MPEP 2106.05(h) – limiting the usage of the operators to photon-number operators)
2B: wherein said class of operators comprises one or more of photon-number operators and momentum and position operators of said quantum Hamiltonian. (a field of use and technological environment MPEP 2106.05(h) – limiting the usage of the operators to photon-number operators)
Regarding claim 3,
Step 1: Processes, as above.
2A Prong 1: The method of claim 2, wherein integer variables of said integer programming problem or said mixed-integer programming problem correspond to said photon-number operators of said quantum Hamiltonian and wherein continuous variables of said mixed-integer programming problem correspond to said momentum and position operators of said quantum Hamiltonian. (According to the spec para [00090-00091], it is directed to a mathematical calculation)
2A Prong 2: This judicial exception is not integrated into a practical application.
2B: The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception.
Regarding claim 4,
Step 1: Processes, as above.
2A Prong 1: wherein a quantum state of said system of qumodes overlaps with a ground state of said quantum Hamiltonian. (According to the spec para [00099-00100], a mathematical concept)
2A Prong 2: This judicial exception is not integrated into a practical application.
2B: The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception.
Regarding claim 5,
Step 1: Processes, as above.
2A Prong 1: The method of claim 2, wherein said measurement comprises one or more of: (A) a measurement corresponding to said photon-number operators to obtain photon-number values, optionally comprising a photon-number-resolving measurement of said one or more qumodes; (B) a homodyne measurement corresponding to said position and momentum operators to obtain position and momentum values, optionally comprising a homodyne detection using a beam splitter and two photo-detectors for measuring two out-of-phase components of the optical electric field. (mental process of observation – observing the current state of qumodes)
2A Prong 2: This judicial exception is not integrated into a practical application.
2B: The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception.
Regarding claim 6,
Step 1: Processes, as above.
2A Prong 1: Incorporates the rejection of claim 1.
2A Prong 2: wherein (b) further comprises: (i) using said quantum optical device to prepare a quantum state of said system of qumodes comprising performing one or more gate operations. (mere instructions to apply an exception using a generic computer component MPEP 2106.05(f))
2B: wherein (b) further comprises: (i) using said quantum optical device to prepare a quantum state of said system of qumodes comprising performing one or more gate operations. (mere instructions to apply an exception using a generic computer component MPEP 2106.05(f))
Regarding claim 7,
Step 1: Processes, as above.
2A Prong 1: The method of claim 6, further comprising simulating a Hamiltonian of a quantum adiabatic evolution. (According to the spec para [00099-00100], a mathematical concept)
2A Prong 2: This judicial exception is not integrated into a practical application.
2B: The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception.
Regarding claim 8,
Step 1: Processes, as above.
2A Prong 1: The method of claim 6, wherein (i) comprises an approximation of a quantum adiabatic evolution from a ground state of a mixing Hamiltonian to said quantum state of said system of qumodes. (mental process of evaluation – performing approximation of a quantum adiabatic evolution [00016])
2A Prong 2: This judicial exception is not integrated into a practical application.
2B: The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception.
Regarding claim 9,
Step 1: Processes, as above.
2A Prong 1: Incorporates the rejection of claim 8.
2A Prong 2: wherein said mixing Hamiltonian comprises operators which do not commute with photon-number operators. (a field of use and technological environment MPEP 2106.05(f) – limiting the variables included in the mixing Hamiltonian)
2B: wherein said mixing Hamiltonian comprises operators which do not commute with photon-number operators. (a field of use and technological environment MPEP 2106.05(f) – limiting the variables included in the mixing Hamiltonian)
Regarding claim 10,
Step 1: Processes, as above.
2A Prong 1: Incorporates the rejection of claim 8.
2A Prong 2: wherein said mixing Hamiltonian comprises position or momentum operators as non-commuting operators with photon-number operators. (a field of use and technological environment MPEP 2106.05(f) – limiting the variables included in the mixing Hamiltonian)
2B: wherein said mixing Hamiltonian comprises position or momentum operators as non-commuting operators with photon-number operators. (a field of use and technological environment MPEP 2106.05(f) – limiting the variables included in the mixing Hamiltonian)
Regarding claim 11,
Step 1: Processes, as above.
2A Prong 1: The method of claim 8, wherein said approximation of said quantum adiabatic evolution comprises one or more of: (A) a discretized quantum adiabatic algorithm (dQAA) procedure; (B) a quantum approximate optimization algorithm (QAOA) procedure. (mental process of evaluation – performing approximation of a quantum adiabatic evolution [00016])
2A Prong 2: This judicial exception is not integrated into a practical application.
2B: The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception.
Regarding claim 12,
Step 1: Processes, as above.
2A Prong 1: The method of claim 1, wherein (c) further comprises: (ii) performing said measurement of said system of qumodes. (mental process of observation – observing the current state of qumodes)
2A Prong 2: This judicial exception is not integrated into a practical application.
2B: The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception.
Regarding claim 13,
Step 1: Processes, as above.
2A Prong 1: Incorporates the rejection of claim 1.
2A Prong 2: wherein (b) comprises configuring said quantum optical device, wherein said configuring comprises setting one or more of: a rotation gate, a Kerr gate, a cross-Kerr gate, a P-gate, a quadratic phase gate, a displacement gate, a displacement momentum gate, a displacement position gate, a Fourier gate, a beam splitter, a squeezing gate, a controlled addition gate, a controlled phase gate, a two-mode squeezing gate, a position-rotation gate, a quadratic position-rotation gate, a cross-position-rotation gate, a momentum-rotation gate, a quadratic momentum-rotation gate, or a cross-momentum-rotation gate. (mere instructions to apply an exception using a computer MPEP 2106.05(f) – applying computer components to perform the abstract idea of providing a solution to a problem)
2B: wherein (b) comprises configuring said quantum optical device, wherein said configuring comprises setting one or more of: a rotation gate, a Kerr gate, a cross-Kerr gate, a P-gate, a quadratic phase gate, a displacement gate, a displacement momentum gate, a displacement position gate, a Fourier gate, a beam splitter, a squeezing gate, a controlled addition gate, a controlled phase gate, a two-mode squeezing gate, a position-rotation gate, a quadratic position-rotation gate, a cross-position-rotation gate, a momentum-rotation gate, a quadratic momentum-rotation gate, or a cross-momentum-rotation gate. (mere instructions to apply an exception using a computer MPEP 2106.05(f) – applying computer components to perform the abstract idea of providing a solution to a problem)
Regarding claim 14,
Step 1: Processes, as above.
2A Prong 1: Incorporates the rejection of claim 1.
2A Prong 2: wherein said at least one quantum gate is implemented using at least one of Kerr nonlinearity, quantum dots, Rydberg blockades, or four-wave mixing atomic systems. (mere instructions to apply an exception using a computer MPEP 2106.05(f) – applying computer components to perform the abstract idea of providing a solution to a problem)
2B: wherein said at least one quantum gate is implemented using at least one of Kerr nonlinearity, quantum dots, Rydberg blockades, or four-wave mixing atomic systems. (mere instructions to apply an exception using a computer MPEP 2106.05(f) – applying computer components to perform the abstract idea of providing a solution to a problem)
Regarding claim 15,
Step 1: Processes, as above.
2A Prong 1: Incorporates the rejection of claim 1.
2A Prong 2: wherein said quantum Hamiltonian is quadratic in photon- number operators and is quartic in momentum and position operators. (a field of use and technological environment MPEP 2106.05(h) – limiting the quantum Hamiltonian to ‘quadratic’)
2B: wherein said quantum Hamiltonian is quadratic in photon- number operators and is quartic in momentum and position operators. (a field of use and technological environment MPEP 2106.05(h) – limiting the quantum Hamiltonian to ‘quadratic’)
Regarding claim 16,
Step 1: Processes, as above.
2A Prong 1: The method of claim 1, … wherein (c) comprises (ii) performing a measurement of said system of qumodes, wherein (i), (ii), and (c) are repeated one or more times. (According to the spec para [00099-00100], a mathematical concept)
2A Prong 2: wherein (b) comprises (i) using said quantum optical device to prepare a quantum state of said system of qumodes (mere instructions to apply an exception using a computer MPEP 2106.05(f) – applying computer components to perform the abstract idea of providing a solution to a problem)
2B: wherein (b) comprises (i) using said quantum optical device to prepare a quantum state of said system of qumodes (mere instructions to apply an exception using a computer MPEP 2106.05(f) – applying computer components to perform the abstract idea of providing a solution to a problem)
Regarding claim 17,
Step 1: Processes, as above.
2A Prong 1: The method of claim 16, wherein (i), (ii), and (c) are repeated one or more times until a convergence condition is met, and, optionally, wherein said convergence condition comprises a threshold number of iterations or a threshold change in an objective function. (mathematical concept – repeating math calculation until the threshold condition is met, in lights of the paragraph [0099-0100])
2A Prong 2: This judicial exception is not integrated into a practical application.
2B: The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception.
Regarding claim 18,
Step 1: Processes, as above.
2A Prong 1: Incorporates the rejection of claim 1.
2A Prong 2: wherein said indication of the quantum Hamiltonian is obtained from a user or from a computer-implemented method for solving said integer programming problem or said mixed-integer programming problem. (insignificant extra-solution activity MPEP 2106.05(g)(iii) of gathering statistics)
2B: wherein said indication of the quantum Hamiltonian is obtained from a user or from a computer-implemented method for solving said integer programming problem or said mixed-integer programming problem. (indicated as an insignificant extra-solution activity MPEP 2106.05(g)(iii) in Step 2A Prong 2. Therefore, it is re-evaluated in Step 2B as well understood, routine, and conventional activity MPEP 2106.05(d)(II)(iv) of gathering statistics)
Regarding claim 21,
Step 1: Claim 21 recites a method for solving an integer programming problem, the method comprising at a digital computer operably connected to said quantum optical device. Therefore, it is directed to the statutory category of Processes.
2A Prong 1:
(c) providing a solution of said integer programming problem or said mixed- integer programming problem based at least in part on a measurement of said system of qumodes on said quantum optical device. (According to the spec para [00099-00100], it is directed to a mathematical concept)
2A Prong 2: A method for solving an integer programming problem or a mixed-integer programming problem using a quantum optical device, the method comprising at a digital computer operably connected to said quantum optical device: (mere instructions to apply an exception using a computer MPEP 2106.05(f) – applying computer components to perform the abstract idea of providing a solution to a problem)
(a) obtaining an indication of a quantum Hamiltonian representative of said integer programming problem or said mixed-integer programming problem, wherein said quantum Hamiltonian comprises a class of operators corresponding to variables of said integer programming problem or said mixed-integer programming problem; (insignificant extra-solution activity MPEP 2106.05(g)(iii) of gathering statistics)
(b) directing said quantum Hamiltonian to said quantum optical device to implement said quantum Hamiltonian on said optical device, wherein said quantum optical device comprises a system of qumodes and at least one quantum gate configured to act on one or more qumodes in said system of qumodes (mere instructions to apply an exception of solving a problem using a computer component MPEP 2106.05(f), according to the paragraph [00011]), and wherein one or more operators in said class of operators corresponds to said one or more qumodes in said system of qumodes; (a field of use and technological environment MPEP 2106.05(h) – limiting the field of use of operators)
The additional elements as disclosed above alone or in combination do not integrate the judicial exception into practical application as they are mere insignificant extra solution activity, combination of generic computer functions that are restricted to field of use are implemented to perform the disclosed abstract idea above.
2B: A method for solving an integer programming problem or a mixed-integer programming problem using a quantum optical device, the method comprising at a digital computer operably connected to said quantum optical device: (mere instructions to apply an exception using a computer MPEP 2106.05(f) – applying computer components to perform the abstract idea of providing a solution to a problem)
(a) obtaining an indication of a quantum Hamiltonian representative of said integer programming problem or said mixed-integer programming problem, wherein said quantum Hamiltonian comprises a class of operators corresponding to variables of said integer programming problem or said mixed-integer programming problem; (indicated as an insignificant extra-solution activity MPEP 2106.05(g)(iii) in Step 2A Prong 2. Therefore, it is re-evaluated in Step 2B as well understood, routine, and conventional activity MPEP 2106.05(d)(II)(iv) of gathering statistics)
(b) directing said quantum Hamiltonian to said quantum optical device to implement said quantum Hamiltonian on said optical device, wherein said quantum optical device comprises a system of qumodes and at least one quantum gate configured to act on one or more qumodes in said system of qumodes (mere instructions to apply an exception of solving a problem using a computer component MPEP 2106.05(f), according to the paragraph [00011]), and wherein one or more operators in said class of operators corresponds to said one or more qumodes in said system of qumodes; (a field of use and technological environment MPEP 2106.05(h) – limiting the field of use of operators)
The additional elements as disclosed above in combination of the abstract idea are not sufficient to amount to significantly more than the judicial exception as they are well, understood, routine and conventional activity as disclosed in combination of generic computer functions and usage of elements that are restricted to field of use that are implemented to perform the disclosed abstract idea above.
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 1-21 are rejected under 35 U.S.C. 103 as being unpatentable over Stollenwerk et al. (“Toward Quantum Gate-Model Heuristics for Real-World Planning Problems”, 2020) in view of Loock (“Optical hybrid approaches to quantum information”, 2011).
Regarding claim 1, Stollenwerk teaches:
A method for solving an integer programming problem or a mixed-integer programming problem using a quantum [Stollenwerk, page 1, ABSTRACT, last 3 lines] discloses that the method explains how to implement quantum circuits for solving real-world planning problems including integer programming problem (e.g., flight gate assignment problem). [Stollenwerk, page 2, right col, II. FLIGHT-GATE ASSIGNMENT PROBLEM, lines 5 - 22] indicates that the Flight-Gate Assignment Problem includes integerprogramming)
(a) obtaining an indication of a quantum Hamiltonian representative of said integer programming problem or said mixed-integer programming problem, wherein said quantum Hamiltonian comprises a class of operators corresponding to variables of said integer programming problem or said mixed-integer programming problem; ([Stollenwerk, page 2, right col, II. FLIGHT-GATE ASSIGNMENT PROBLEM, lines 5 - 22] indicates that the Flight-Gate Assignment Problem includes integerprogramming. [Stollenwerk, page 6, left col, B. PHASE SEPARATION OPERATOR, line 1 – right col, line 14] disclose encoding the problem (the cost function c(x) in (2)) as the diagonal cost Hamiltonian C (indication of a quantum Hamiltonian representative of the problem) that acts on nk-qubit computational basis. Many classes of operators such as Pauli Z operator corresponding to the qubit with index
i
a
(variables), mixer operators
U
M
, the first phase operator
U
P
(
γ
1
)
are used)
(b) implementing said quantum Hamiltonian on said quantum [Stollenwerk, page 6, left col, A. INITIAL STATE, lines 1-12] and [page 6, Section III, B. PHASE SEPARATION OPERATOR, line 1 – right col, line 14] disclose encoding the problem (the cost function c(x) in (2)) as the diagonal cost Hamiltonian C that acts on nk-qubit computational basis by obtaining Hamiltonian and initial states. The qubit is interpreted as qumodes because both are the basic computation unit used in quantum computing. The standard QAOA phase separation operator construction is employed to construct the cost Hamiltonian. Many classes of operators such as Pauli Z operator acting on the qubit with index
i
a
, mixer operators
U
M
, the first phase operator
U
P
(
γ
1
)
are used. [page 11, left col, lines 1-last line] and [Figures 7, 8 and 9] discloses physically implementing the phase separations disclosed in Section III-B using Toffoli gates (quantum devices))
(c) providing a solution of said integer programming problem or said mixed-integer programming problem based at least in part on a measurement of said system of qumodes. ([Stollenwerk, page 5, right col, III. QAOA FOR FLIGHT-GATE ASSIGNMENT, lines 5-31] The paragraph and the step 2) disclose ‘measure in the computational basis (which returns a feasible flight-gate assignment x)’. The feasible flight-gate is the solution of the programming problem, and the ‘measurement of qubit (or qumode)’ is required to obtain the solution)
However, Stollenwerk does not specifically disclose:
A method … using a quantum optical device
wherein said quantum optical device comprises a system of qumodes
Loock teaches:
A method … using a quantum optical device ([Loock, page 170, left col, lines 1-13] and [Loock, page 172, left col, lines 1-23] collectively disclose that quantum optical devices such as phase shifters, beam splitters, and single-mode squeezers are used to implement the system)
wherein said quantum optical device comprises a system of qumodes ([Loock, page 170, left col, lines 1-13], [Loock, page 172, left col, lines 1-23] collectively disclose that quantum optical devices such as phase shifters, beam splitters, and single-mode squeezers are used to implement the system. [Loock, page 170, right col, 2.2. Qubits versus qumodes, 13-18] discloses that Qubits and Qumodes are analogous. [Loock, page 173, left col, line 12 – right col, line 7] The universality for qumodes can be defined and achieved similarly to the qubit case, by using elementary gate set including non-Gaussian gates)
Before the effective filing date of the invention to a person of ordinary skill in the art, it would
have been obvious, having the teachings of Stollenwerk and Loock to use the method of substituting qubits of Stollenwerk with qumodes of Loock to implement the quantum computing method of present invention. The suggestion and/or motivation for doing so is to improve the efficiency and performance of the quantum computing method by utilizing optical states of photons which allow much more room for encoding quantum information [Loock, page 170, right col, 2.2. Qubits versus qumodes].
Regarding claim 2, Stollenwerk in view of Loock teaches:
The method of claim 1, wherein said class of operators comprises one or more of photon-number operators and momentum and position operators of said quantum Hamiltonian. ([Loock, page 171, right col, 2.2.2. Photonic qumodes, lines 1-9] discloses a quantum Hamiltonian with photon number operator
a
k
Ɨ
^
a
k
^
for mode k with position operator
x
k
^
and momentum operator
p
k
^
for each oscillator k)
Regarding claim 3, Stollenwerk in view of Loock teaches:
The method of claim 2, wherein integer variables of said integer programming problem or said mixed-integer programming problem correspond to said photon-number operators of said quantum Hamiltonian and wherein continuous variables of said mixed-integer programming problem correspond to said momentum and position operators of said quantum Hamiltonian. ([Loock, page 170, right col, 2.2. Qubits versus qumodes, lines 9-14] indicates that the photon numbers are discrete (integer). Additionally, photon number is an integer, because a photon is a particle and there cannot be 1.354 number of photons. [Loock, page 171, right col, 2.2.2. Photonic qumodes, lines 1-9] discloses a quantum Hamiltonian with photon number operator
a
k
Ɨ
^
a
k
^
for mode k with position operator
x
k
^
and momentum operator
p
k
^
for each oscillator k. The momentum and position are inherently continuous)
Regarding claim 4, Stollenwerk in view of Loock teaches:
The method of claim 1, wherein a quantum state of said system of qumodes overlaps with a ground state of said quantum Hamiltonian. ([Loock, page 177, right col, last para – page 178, left col, lines 10] and [page 181, left col, las para] collectively disclose a Hamiltonian of a qumode with both ground state and excited state
0
>
<
0
-
|
1
>
<
1
|
, where
0
>
denotes the ground state and
|
1
>
denotes the excited state)
Regarding claim 5, Stollenwerk in view of Loock teaches:
The method of claim 2, wherein said measurement comprises one or more of: (A) a measurement corresponding to said photon-number operators to obtain photon-number values, optionally comprising a photon-number-resolving measurement of said one or more qumodes; ([Loock, page 171, right col, 2.2.2. Photonic qumodes, lines 1-9] discloses a quantum Hamiltonian with photon number operator
a
k
Ɨ
^
a
k
^
for mode k (indicates that the photon countings are measured) with position operator
x
k
^
and momentum operator
p
k
^
for each oscillator k. [Loock, page 180, left col, last para and a following annotation 5] The experimental implementation of Loock are to be combined with frequency-resolved homodyne detection or time-resolved homodyning (photon-number-resolving measurements) in order to synchronize the CV operations with DV photon counting events) (B) a homodyne measurement corresponding to said position and momentum operators to obtain position and momentum values, optionally comprising a homodyne detection using a beam splitter and two photo-detectors for measuring two out-of-phase components of the optical electric field. ([Loock, page 171, right col, 2.2.2. Photonic qumodes, lines 1-9] discloses a quantum Hamiltonian with photon number operator
a
k
Ɨ
^
a
k
^
for mode k with position operator
x
k
^
and momentum operator
p
k
^
for each oscillator k. [Loock, page 172, left col, lines 1-23] The projection measurements are approximated by homodyne detections. The detection is performed using a beam splitter, an ancilla coherent state and on/off detectors (i.e., two photo-detectors for measuring two out-of-phase components))
Regarding claim 6, Stollenwerk in view of Loock teaches:
The method of claim 1, wherein (b) further comprises: (i) using said quantum optical device to prepare a quantum state of said system of qumodes comprising performing one or more gate operations. ([Loock, page 171, right col, 2.2.2. Photonic qumodes, lines 1-9] discloses a quantum Hamiltonian with photon number operator
a
k
Ɨ
^
a
k
^
for mode k with position operator
x
k
^
and momentum operator
p
k
^
for each oscillator k. The photon number, position, and momentum are the quantum state of the qumodes)
Regarding claim 7, Stollenwerk in view of Loock teaches:
The method of claim 6, further comprising simulating a Hamiltonian of a quantum adiabatic evolution. ([Loock, page 186, right col, 3.3.2. Hybrid Hamiltonians, lines 1-10] The adiabatic evolution is a special type of the unitary evolution where the Hamiltonians changes slowly)
Regarding claim 8, Stollenwerk in view of Loock teaches:
The method of claim 6, wherein (i) comprises an approximation of a quantum adiabatic evolution from a ground state of a mixing Hamiltonian to said quantum state of said system of qumodes. ([Loock, page 177, right col, last para – page 178, left col, lines 10] and [page 181, left col, las para] collectively disclose a Hamiltonian of a qumode with both ground state and excited state
0
>
<
0
-
|
1
>
<
1
|
, where
0
>
denotes the ground state and
|
1
>
denotes the excited state. [Loock, page 186, right col, 3.3.2. Hybrid Hamiltonians, lines 1-10] The adiabatic evolution is a special type of the unitary evolution where the Hamiltonians changes slowly)
Regarding claim 9, Stollenwerk in view of Loock teaches:
The method of claim 8, wherein said mixing Hamiltonian comprises operators which do not commute with photon-number operators. ([Loock, page 171, right col, 2.2.2. Photonic qumodes, lines 10-16] The commutators [
a
k
Ɨ
^
,
a
k
^
] indicates that photon number
a
k
Ɨ
^
does not commute with the photon number
a
k
^
. If both commutes, the result of the commutator operator should be 0)
Regarding claim 10, Stollenwerk in view of Loock teaches:
The method of claim 8, wherein said mixing Hamiltonian comprises position or momentum operators as non-commuting operators with photon-number operators. ([Loock, page 171, right col, 2.2.2. Photonic qumodes, lines 10-16] The commutators [
a
k
Ɨ
^
,
a
k
^
] indicates that photon number
a
k
Ɨ
^
does not commute with the photon number
a
k
^
. If both commutes, the result of the commutator operator should be 0. The non-commuting
a
k
Ɨ
^
,
a
k
^
=
δ
k
l
is mixed with [
x
k
Ɨ
^
,
p
l
^
] which results to
x
k
Ɨ
^
,
p
l
^
=
i
h
δ
k
l
)
Regarding claim 11, Stollenwerk teaches:
The method of claim 8, wherein said approximation of said quantum adiabatic evolution comprises one or more of: (A) a discretized quantum adiabatic algorithm (dQAA) procedure; (B) a quantum approximate optimization algorithm (QAOA) procedure. ([Stollenwerk, page 1, ABSTRACT] Stollenwerk presents novel efficient quantum alternating operator ansatz (QAOA) constructions for optimization algorithms. Therefore, Stollenwerk teaches at least one of the one or more of (A) or (B))
Regarding claim 12, Stollenwerk in view of Loock teaches:
The method of claim 1, wherein (c) further comprises: (ii) performing said measurement of said system of qumodes. ([Loock, page 171, right col, 2.2.2. Photonic qumodes, lines 1-9] discloses a quantum Hamiltonian with photon number operator
a
k
Ɨ
^
a
k
^
for mode k with position operator
x
k
^
and momentum operator
p
k
^
for each oscillator k. [Loock, page 172, left col, lines 1-23] The projection measurements are approximated by homodyne detections. The detection is performed using a beam splitter, an ancilla coherent state and on/off detectors (i.e., two photo-detectors for measuring two out-of-phase components))
Regarding claim 13, Stollenwerk in view of Loock teaches:
The method of claim 1, wherein (b) comprises configuring said quantum optical device, wherein said configuring comprises setting one or more of: a rotation gate, a Kerr gate, a cross-Kerr gate, a P-gate, a quadratic phase gate, a displacement gate, a displacement momentum gate, a displacement position gate, a Fourier gate, a beam splitter, a squeezing gate, a controlled addition gate, a controlled phase gate, a two-mode squeezing gate, a position-rotation gate, a quadratic position-rotation gate, a cross-position-rotation gate, a momentum-rotation gate, a quadratic momentum-rotation gate, or a cross-momentum-rotation gate. ([Loock, page 173, left col, line 12 – right col, line 7] The universality for qumodes can be defined and achieved similarly to the qubit case, by using elementary gate set including non-Gaussian gates. [Loock, page 173, right col, Figure 6] and [page 174, right col, Figure 7 and a following paragraph] The controlled sign gate and the probabilistic controlled sign gate are implemented using Kerr nonlinearities (i.e., Kerr gate). Since the conjunction is ‘or’, the examiner is not required to provide teachings regarding every type of gate disclosed in the claim)
Regarding claim 14, Stollenwerk in view of Loock teaches:
The method of claim 1, wherein said at least one quantum gate is implemented using at least one of Kerr nonlinearity, quantum dots, Rydberg blockades, or four-wave mixing atomic systems. ([Loock, page 173, right col, Figure 6] and [page 174, right col, Figure 7 and a following paragraph] The controlled sign gate and the probabilistic controlled sign gate are implemented using Kerr nonlinearities)
Regarding claim 15, Stollenwerk teaches:
The method of claim 1, wherein said quantum Hamiltonian is quadratic. ([Stollenwerk, page 6, right col, lines 1-8] discloses that the Hamiltonian is quadratic)
However, Stollenwerk does not specifically disclose:
wherein said quantum Hamiltonian is quadratic in photon- number operators and is quartic in momentum and position operators.
Loock teaches:
wherein said quantum Hamiltonian is quadratic in photon- number operators and is quartic in momentum and position operators. ([Loock, page 169, left col, 2.1. Linear versus nonlinear operations, lines 4-30] discloses the arbitrary quadratic Hamiltonian operator with position and momentum. [Loock, page 171, right col, 2.2.2. Photonic qumodes, lines 1-9] discloses a quantum Hamiltonian with photon number operator
a
k
Ɨ
^
a
k
^
for mode k with position operator
x
k
^
and momentum operator
p
k
^
for each oscillator k)
Regarding claim 16, Stollenwerk teaches:
The method of claim 1, wherein (b) comprises (i) using said quantum optical device to prepare a quantum state of said system of [Stollenwerk, page 5, left col, Algorithm 1] and [Stollenwerk, page 5, right col, III. QAOA FOR FLIGHT-GATE ASSIGNMENT, lines 10 – 31] disclose 1) creating the ansztz state for algorithm parameters (corresponds to (b) and (i)), 2) measure in the computation basis (corresponds to the (c) and (ii)), and 3) repeating the first two steps a number of times, keeping the best solution found)
However, Stollenwerk does not specifically disclose:
using said quantum optical device to prepare a quantum state of said system of qumodes … performing a measurement of said system of qumodes
Loock teaches:
using said quantum optical device to prepare a quantum state of said system of qumodes … performing a measurement of said system of qumodes ([Loock, page 171, right col, 2.2.2. Photonic qumodes, lines 1-9] discloses a quantum Hamiltonian with photon number operator
a
k
Ɨ
^
a
k
^
for mode k with position operator
x
k
^
and momentum operator
p
k
^
for each oscillator k. The photon number, position, and momentum are the quantum state of the qumodes. [Loock, page 172, left col, lines 1-23] discloses the measurement of qumodes)
Regarding claim 17, Stollenwerk teaches:
The method of claim 16, wherein (i), (ii), and (c) are repeated one or more times until a convergence condition is met, and, optionally, wherein said convergence condition comprises a threshold number of iterations or a threshold change in an objective function. ([Stollenwerk, page 5, left col, Algorithm 1] and [Stollenwerk, page 5, right col, III. QAOA FOR FLIGHT-GATE ASSIGNMENT, lines 10 – 31] disclose 1) creating the ansztz state for algorithm parameters, 2) measure in the computation basis, and 3) repeat the first two steps a number of times, keeping the best solution found. ‘A number of times (for i=1 to n)’ is the threshold number)
Regarding claim 18, Stollenwerk teaches:
The method of claim 1, wherein said indication of the quantum Hamiltonian is obtained from a user or from a computer-implemented method for solving said integer programming problem or said mixed-integer programming problem. ([Stollenwerk, page 5, left col, Algorithm 1] and [Stollenwerk, page 5, right col, III. QAOA FOR FLIGHT-GATE ASSIGNMENT, lines 10 – 31] disclose 1) creating the ansztz state for algorithm parameters, and [page 6, left col, B. PHASE SEPARATION OPERATOR, lines 1-3] discloses encoding the cost function to a Hamiltonian C. The encoding process is the computer-implemented method for obtaining the quantum Hamiltonian)
Regarding claim 19, Stollenwerk in view of Loock teaches:
A quantum optical device comprising a system of qumodes and at least one quantum gate configured to act on one or more qumodes of said system of qumodes, wherein said at least one quantum gate comprises at least one member of the group including a rotation gate, a Kerr gate, a cross-Kerr gate, a P-gate, a quadratic phase gate, a displacement gate, a displacement momentum gate, a displacement position gate, a Fourier gate, a beam splitter, a squeezing gate, a controlled addition gate, a controlled phase gate, a two-mode squeezing gate, a position-rotation gate, a quadratic position-rotation gate, a cross-position-rotation gate, a momentum-rotation gate, a quadratic momentum-rotation gate, or a cross-momentum-rotation gate. ([Loock, page 173, left col, line 12 – right col, line 7] The universality for qumodes can be defined and achieved similarly to the qubit case, by using elementary gate set including non-Gaussian gates. [Loock, page 173, right col, Figure 6] and [page 174, right col, Figure 7 and a following paragraph] The controlled sign gate and the probabilistic controlled sign gate are implemented using Kerr nonlinearities (i.e., Kerr gate). Since the conjunction is ‘or’, the examiner is not required to provide teachings regarding every type of gate disclosed in the claim)
Regarding claim 20, Stollenwerk teaches:
The quantum optical device of claim 19 is configured to at least: (i) implement a quantum Hamiltonian; (ii) prepare a quantum state of said system of [Stollenwerk, page 5, left col, Algorithm 1] and [Stollenwerk, page 5, right col, III. QAOA FOR FLIGHT-GATE ASSIGNMENT, lines 10 – 31] disclose 1) creating the ansztz state for algorithm parameters (corresponds to (i) and (ii)), measure in the computation basis (corresponds to (iii)). [Stollenwerk, page 6, left col, A. INITIAL STATE, lines 1-12] and [page 6, Section III, B. PHASE SEPARATION OPERATOR, line 1 – right col, line 14] discloses the steps (i) and (ii) with additional details)
Loock teaches:
(ii) prepare a quantum state of said system of qumodes; ([Loock, page 171, right col, 2.2.2. Photonic qumodes, lines 1-9] discloses a quantum Hamiltonian with photon number operator
a
k
Ɨ
^
a
k
^
for mode k with position operator
x
k
^
and momentum operator
p
k
^
for each oscillator k. The photon number, position, and momentum are the quantum state of the qumodes) and (iii) perform measurements of said system of qumodes; ([Loock, page 172, left col, lines 1-23] discloses the measurement of qumodes)
wherein said quantum optical device is operatively coupled to a digital computer, said digital computer comprising a memory comprising instructions, wherein said digital computer is configured to execute said instructions to at least: ([Loock, page 168, right col, 1.1. CV versus DV, lines 1-11] discloses simulation of Hamiltonian can be efficiently simulated by a classical computer. Therefore, the steps disclosed by the Stollenwerk can be efficiently simulated by a digital computer)
Regarding claim 21, Stollenwerk teaches:
A method for solving an integer programming problem or a mixed-integer programming problem using a quantum [Stollenwerk, page 1, ABSTRACT, last 3 lines] discloses that the method explains how to implement quantum circuits for solving real-world planning problems including integer programming problem (e.g., flight gate assignment problem). [Stollenwerk, page 2, right col, II. FLIGHT-GATE ASSIGNMENT PROBLEM, lines 5 - 22] indicates that the Flight-Gate Assignment Problem includes integerprogramming)
(a) obtaining an indication of a quantum Hamiltonian representative of said integer programming problem or said mixed-integer programming problem, wherein said quantum Hamiltonian comprises a class of operators corresponding to variables of said integer programming problem or said mixed-integer programming problem; ([Stollenwerk, page 2, right col, II. FLIGHT-GATE ASSIGNMENT PROBLEM, lines 5 - 22] indicates that the Flight-Gate Assignment Problem includes integerprogramming. [Stollenwerk, page 6, left col, B. PHASE SEPARATION OPERATOR, line 1 – right col, line 14] disclose encoding the problem (the cost function c(x) in (2)) as the diagonal cost Hamiltonian C (indication of a quantum Hamiltonian representative of the problem) that acts on nk-qubit computational basis. Many classes of operators such as Pauli Z operator corresponding to the qubit with index
i
a
(variables), mixer operators
U
M
, the first phase operator
U
P
(
γ
1
)
are used)
(b) directing said quantum Hamiltonian to said quantum optical device to implement said quantum Hamiltonian on said optical device, wherein said quantum optical device comprises a system of qumodes and at least one quantum gate configured to act on one or more qumodes in said system of qumodes, and wherein one or more operators in said class of operators corresponds to said one or more qumodes in said system of qumodes; and ([Stollenwerk, page 6, left col, A. INITIAL STATE, lines 1-12] and [page 6, Section III, B. PHASE SEPARATION OPERATOR, line 1 – right col, line 14] disclose encoding the problem (the cost function c(x) in (2)) as the diagonal cost Hamiltonian C that acts on nk-qubit computational basis by obtaining Hamiltonian and initial states. The qubit is interpreted as qumodes because both are the basic computation unit used in quantum computing. The standard QAOA phase separation operator construction is employed to construct the cost Hamiltonian. Many classes of operators such as Pauli Z operator acting on the qubit with index
i
a
, mixer operators
U
M
, the first phase operator
U
P
(
γ
1
)
are used. [page 11, left col, lines 1-last line] and [Figures 7, 8 and 9] discloses physically implementing the phase separations disclosed in Section III-B using Toffoli gates (quantum devices))
(c) providing a solution of said integer programming problem or said mixed- integer programming problem based at least in part on a measurement of said system of [Stollenwerk, page 5, right col, III. QAOA FOR FLIGHT-GATE ASSIGNMENT, lines 5-31] The paragraph and the step 2) disclose ‘measure in the computational basis (which returns a feasible flight-gate assignment x)’. The feasible flight-gate is the solution of the programming problem, and the ‘measurement of qubit (or qumode)’ is required to obtain the solution)
However, Stollenwerk does not specifically disclose:
A method … using a quantum optical device … the method comprising at a digital computer operably connected to said quantum optical device
wherein said quantum optical device comprises a system of qumodes … measurement of said system of qumodes on said quantum optical device.
Loock teaches:
A method … using a quantum optical device … the method comprising at a digital computer operably connected to said quantum optical device ([Loock, page 168, right col, 1.1. CV versus DV, lines 1-11] discloses simulation of Hamiltonian can be efficiently simulated by a classical computer. Therefore, the steps disclosed by the Stollenwerk can be efficiently simulated by a digital computer. [Loock, page 170, left col, lines 1-13] and [Loock, page 172, left col, lines 1-23] collectively disclose that quantum optical devices such as phase shifters, beam splitters, and single-mode squeezers are used to implement the system)
wherein said quantum optical device comprises a system of qumodes … measurement of said system of qumodes on said quantum optical device. ([Loock, page 170, left col, lines 1-13] and [Loock, page 172, left col, lines 1-23] collectively disclose that quantum optical devices such as phase shifters, beam splitters, and single-mode squeezers are used to implement the system. [Loock, page 170, right col, 2.2. Qubits versus qumodes, 13-18] discloses that Qubits and Qumodes are analogous. [Loock, page 173, left col, line 12 – right col, line 7] The universality for qumodes can be defined and achieved similarly to the qubit case, by using elementary gate set including non-Gaussian gates. [Loock, page 172, left col, lines 1-23] discloses the measurement of qumodes)
Before the effective filing date of the invention to a person of ordinary skill in the art, it would
have been obvious, having the teachings of Stollenwerk and Loock to use the method of substituting qubits of Stollenwerk with qumodes of Loock to implement the quantum computing method of present invention. The suggestion and/or motivation for doing so is to improve the efficiency and performance of the quantum computing method by utilizing optical states of photons which allow much more room for encoding quantum information [Loock, page 170, right col, 2.2. Qubits versus qumodes].
Conclusion
Any inquiry concerning this communication or earlier communications from the examiner should be directed to JUN KWON whose telephone number is (571)272-2072. The examiner can normally be reached Monday – Friday 7:30AM – 4:30PM ET.
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/JUN KWON/Examiner, Art Unit 2127
/ABDULLAH AL KAWSAR/Supervisory Patent Examiner, Art Unit 2127
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