IP Library › Granted Patent US 12,468,975
Granted Patent B2
US 12,468,975 · App. 17/930,339 · Granted Nov 11, 2025

Method for reducing quantum circuit depth for amplitude estimation

Inventors: Matthias Rosenkranz (Cambridge, GB); Michael Lubasch (Orpington, GB); Mattia Fiorentini (London, GB); Kirill Plekhanov (London, GB)
Assignee: Quantinuum Ltd
G06N10/60G06N10/40G06N10/80G06N20/00
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Quick Facts
Patent No.
US 12,468,975
App. No.
17/930,339
Granted
Nov 11, 2025
Kind
B2
Abstract

A quantum computing system includes a classical computer coupled in combination with a quantum computing system, wherein the quantum computing system is configurable to execute program instructions to process input data to generate corresponding output data. The quantum computing system is configured to execute a variational quantum amplitude estimation (VQAE) algorithm by iteratively executing a sequence of quantum operations including a maximum likelihood amplitude estimation and performing a variational approximation after an iteration to determine a variational quantum state associated with the outcome of the maximum likelihood amplitude estimation. The quantum computing system may also execute an adaptive VQAE by performing a rescaling process to reduce the variational cost of the VQAE.

Claims (44)

1 . A quantum computing system configured to perform a quantum computational task, the quantum computing system comprising:

a quantum computer comprising:

an array of qubits;

at least one quantum circuit comprising one or more quantum gates configured to act on the qubits to generate processed qubits; and

at least one measuring device configured to determine states of the processed qubits to generate measurement data; and

a classical computing system in communication with the quantum computer, the classical computing system comprising a non-transitory memory configured to store specific computer-executable instructions and a hardware processor in communication with the non-transitory memory, wherein the hardware processor is configured to execute the specific computer-executable instructions to at least:

receive input data,

prepare the array of qubits based at least in part on the input data;

configure the at least one quantum circuit, based at least in part on the input data, to execute at least a series of quantum operations on the array of qubits to generate final processed qubits;

perform at least a first variational approximation after at least a first sequence of quantum operations of the series of quantum operations, to generate a first variational quantum state based at least in part on the measurement data generated after the first sequence of quantum operations;

execute, using at least the first variational quantum state, at least a second sequence of quantum operations of the series of quantum operations to generate the final processed qubits; and

generate output data using the final processed qubits;

wherein performing the first variational approximation reduces quantum noise arising from performing the quantum computational task and generating the output data compared to quantum noise arising from performing the quantum computational task and generating the output data without performing the first variational approximation.

2 . The quantum computing system of claim 1 , wherein the first variational approximation comprises determining a quantum state of the array of qubits based at least a portion of the measurement data and determining the first variational quantum state by variationally approximating the determined quantum state.

3 . The quantum computing system of claim 1 , wherein the output data has an error less than a threshold error, wherein a number of sequences in the series of quantum operations is determined based at least in part on the threshold error.

4 . The quantum computing system of claim 3 , wherein the quantum computational task comprises quantum amplitude estimation (QAE), the output data comprises an estimated amplitude, and the error comprises an amplitude estimation error.

5 . The quantum computing system of claim 1 , wherein the first variational quantum state comprises a parametrized quantum circuit (PQC) determined using a PQC ansatz.

6 . The quantum computing system of claim 1 , wherein the hardware processor is further configured to perform an adaptive rescaling algorithm to reduce a variational cost of the first variational approximation.

7 . The quantum computing system of claim 1 , wherein the input data comprises a number of quantum operations in the first sequence of quantum operations.

8 . A quantum computing system of claim 1 , wherein a maximum circuit depth of the at least one quantum circuit for performing the quantum computational task is independent of a number of quantum operations in the series of the quantum operations.

9 . The quantum computing system of claim 1 , wherein the first sequence of quantum operations comprises a maximum likelihood amplitude estimation (MLAE).

10 . The quantum computing system of claim 9 , wherein the MLAE is implemented as an iterative process applied to the array of qubits, and an iteration of the iterative process comprises at least the MLAE and the first variational approximation.

11 . A method for operating a computing system comprising a quantum computer having an array of qubits, a non-transitory memory configured to store specific computer-executable instructions, and a hardware processor in communication with the non-transitory memory, the method comprising:

by the hardware processor of the computing system:

receiving input data,

preparing the array of qubits based at least in part on the input data;

configuring a quantum circuit in the quantum computer, based at least in part on the input data, to execute at least a series of quantum operations on the array of qubits to generate final processed qubits;

performing at least a first variational approximation, after at least a first sequence of quantum operations of the series of quantum operations, to generate a first variational quantum state based at least in part on a measured quantum state of the array of qubits after the first sequence of quantum operations;

executing, using the first variational quantum state, at least a second sequence of quantum operations of the series of quantum operations to generate the final processed qubits; and

generating output data using the final processed qubits;

wherein operating the computing system comprises performing a quantum computational task;

wherein performing the quantum computational task comprises at least executing the series of quantum operations; and

wherein performing the first variational approximation reduces quantum noise arising from performing the quantum computational task and generating the output data compared to quantum noise arising from performing the quantum computational task and generating the output data without performing the first variational approximation.

12 . The method of claim 11 , wherein performing the first variational approximation comprises:

determining states of processed qubits to generate measurement data, and

determining a quantum state of the array of qubits based at least a portion of the measurement data and determining the first variational quantum state by variationally approximating the determined quantum state.

13 . The method of claim 11 , wherein the output data has an error less than a threshold error.

14 . The method of claim 13 , wherein performing the quantum computational task comprises performing a quantum amplitude estimation (QAE), the output data comprises an estimated amplitude, and the error comprises an amplitude estimation error.

15 . The method of claim 11 , wherein the first variational quantum state comprises a parametrized quantum circuit (PQC) determined using a PQC ansatz.

16 . The method of claim 11 , further comprising performing an adaptive rescaling algorithm to reduce a variational cost of the first variational approximation.

17 . The method of claim 11 , wherein the input data comprises a number of quantum operations in the first sequence of quantum operations.

18 . The method of claim 11 , wherein a maximum circuit depth of the quantum circuit for performing the quantum computational task is independent of a number of quantum operations in the series of the quantum operations.

19 . The method of claim 11 wherein the first sequence of quantum operations comprises a maximum likelihood amplitude estimation (MLAE).

20 . A non-transitory computer-readable storage medium comprising specific computer-readable instructions executable on data processing hardware, wherein the specific computer-readable instructions, when executed the data processing hardware, implement the method of claim 11 .

Assignments (2)
CHANGE OF NAME Recorded Oct 30, 2023
From: CAMBRIDGE QUANTUM COMPUTING LIMITED
To: QUANTINUUM LTD
Reel/Frame 065396/0682 →
ASSIGNMENT OF ASSIGNOR'S INTEREST Recorded Nov 30, 2022
From: ROSENKRANZ, MATTHIAS; LUBASCH, MICHAEL; FIORENTINI, MATTIA; PLEKHANOV, KIRILL
To: CAMBRIDGE QUANTUM COMPUTING LIMITED
Reel/Frame 061929/0220 →
Priority Claims (1)
GB 2112786 · Sep 8, 2021 · national
Continuity (1)
Related Publication 20230385677A1 · Nov 30, 2023
References Cited (62)
US 6449580B1 · Bardetsky · 2002 [cited by examiner]
US 11558069B1 · Sparrow · 2023 [cited by examiner]
US 20210044305A1 · Niu · 2021 [cited by examiner]
US 20210049493A1 · Vivoli · 2021 [cited by examiner]
WO WO2020168158A1 · 2020 [cited by examiner]
WO WO2021050541A1 · 2021 [cited by examiner]
Aaronson et al., 2020, Quantum approximate counting, simpilied, in Symposium on Simplicity in Algorithms (SIAM, 2020) pp. 24-32. [cited by applicant]
Aharonov et al., 2009, A polynomial quantum algorithm for approximating the Jones polynomial, Algorithmica 55:395-421. [cited by applicant]
Amaro et al., Jun. 18, 2021, Filtering variational quantum algorithms for combinatorial optimization, arXiv:2106.10055v1, 12 pp. [cited by applicant]
Arouna, 2004, Adaptative Monte Carlo Method, a Variance Reduction Technique, Monte Carlo Methods Appl. 10, 1. [cited by applicant]
Banchi et al., Jan. 19, 2021, Measuring analytic gradients of general quantum evolution with the stochastic parameter shift rule, arXiv:2015/10299v2 [quant-ph], 14 pp. [cited by applicant]
Benedetti et al., 2019, Parameterized quantum circuits as machine learning models, Quantum Sci. Technol. 4:043001, 20 pp. [cited by applicant]
Benedetti et al., 2021, Hardware efficient variational quantum algorithms for time evolution, Phys. Rev. Research 3, 033083. [cited by applicant]
Benedetti et al., Mar. 11, 2021, Variational inference with a quantum computer, arXiv:2103.06720v1 [quant-ph], 17 pp. [cited by applicant]
Bharti et al., Oct. 12, 2020, Iterative quantum assisted Eigensolver, arXiv:2010.05638v1 [quant-ph], 10 pp. [cited by applicant]
Bharti et al., Oct. 6, 2021, Noisy intermediate-scale quantum (NISQ) algorithms, arXiv:2101.08448 [quant-ph], 91 pp. [cited by applicant]
Bonyadi et al., 2017, Particle Swarm Optimization for Single Objective Continuous Space Problems: A Review, Evol. Comput. 25(1):1-54. [cited by applicant]
Bouland et al., Nov. 12, 2020, Prospects and challenges of quantum finance, arXiv:2011.06492v1 [q-fin.CP], 49 pp. [cited by applicant]
Brassard et al., 1997, An exact quantum polynomial-time algorithm for Simon's problem, Proceedings of the Fifth Israeli Symposium on Theory of Computing and Systems (IEEE, 1997) pp. 12-23. [cited by applicant]
Brassard et al., 2002, Quantum amplitude amplification and estimation, Contemp. Math. 305, 53. [cited by applicant]
Braun et al., Mar. 9, 2021, A Quantum Algorithm for the Sensitivity Analysis of Business Risks, arXiv:2103.05475v1 [quant-ph], 21 pp. [cited by applicant]
Cerezo et al., 2021, Cost function dependent barren plateaus in shallow parameterized quantum circuits, Nat. Commun, 12:1791. [cited by applicant]
Cerezo et al., Dec. 16, 2020, Variational Quantum Algorithms, arXiv:2012.09265 [quant-ph], 29 pp. [cited by applicant]
Egger et al., 2020, Quantum Computing for Finance: State-of-the-Art and Future Prospects, IEEE Trans. Quantum Eng. 1:1-24. [cited by applicant]
Giurgica-Tiron et al., Dec. 6, 2020, Low depth algorithms for quantum amplitude estimation, arXiv:2012.03348v1 [quant-ph], 27 pp. [cited by applicant]
Grinko et al., 2021, Iterative quantum amplitude estimation, npj Quantum Inf. 7:52, 6 pp. [cited by applicant]
Grover, May 11, 1998, Quantum computers can search rapidly by using almost any transformation, Phys. Rev. Lett. 80(19):4329-4332. [cited by applicant]
Hazan et al., May 2014, Beyond convexity: Stochastic quasi-convex optimization, arXiv:1507.02030v2 [cs.LG], 23 pp. [cited by applicant]
Herbert, Dec. 10, 2021, Quantum Monte-Carlo Integration: The Full Advantage in Minimal Circuit Depth, arXiv:2105.09100 [quant-ph], 17 pp. [cited by applicant]
Kassal et al., Dec. 2, 2008, Polynomial-time quantum algorithm for the simulation of chemical dynamics, Proc. Natl. Acad. Sci. USA 105(48):18681-18686. [cited by applicant]
Kennedy et al., 1995, Particle swarm optimization, in Proceedings of ICNN'95—International Conference on Neural Networks, 4:1942-1948. [cited by applicant]
Kerenidis et al., 2019, q-means: A quantum algorithm for unsupervised machine learning, 33rd Conference on Neural Information Processing Systems (NeurIPS 2019), Vancouver, Canada, 11 pp. [cited by applicant]
Kingma et al., Dec. 22, 2014, Adam: A Method for Stochastic Optimization, arXiv:1412.6980v1 [cs.LG], 9 pp. [cited by applicant]
Klymko et al., Apr. 7, 2021, Real time evolution for ultracompact Hamiltonian eigenstates on quantum hardware, arXiv:2103.08563v3 [quant-ph], 19 pp. [cited by applicant]
Knill et al., 2007, Optimal quantum measurements of expectation values of observables, Phys. Rev. A 75, 012328, 13 pp. [cited by applicant]
Lau et al., Aug. 15, 2021, Noisy intermediate scale quantum simulation of time dependent Hamiltonians, arXiv:2101/07677v2 [quant-ph], 15 pp. [cited by applicant]
Li et al., Jan. 19, 2017, Hybrid Quantum-Classical Approach to Quantum Optimal Control, arXiv:1608.00677v4 [quant-ph], 8 pp. [cited by applicant]
Liu et al., Dec. 13, 2020, An efficient adaptive variational quantum solver of the Schrodinger equation based on reduced density matrices, arXiv:2012.07047v1 [quant-ph], 27 pp. [cited by applicant]
Low et al., 2014, Quantum inference on Bayesian networks, Phys. Rev. A 89:062315, pp. 1-7. [cited by applicant]
Mitarai et al., 2018, Quantum circuit learning, Phys. Rev. A 98, 032309. [cited by applicant]
Montanaro, 2015, Quantum speedup of Monte Carlo methods, Proc. Math. Phys. Eng. Sci. 471. [cited by applicant]
Nakanishi et al., 2020, Sequential minimal optimization for quantum-classical hybrid algorithms, Phys. Rev. Research 2:043158, pp. 1-10. [cited by applicant]
Orus et al., 2019, Quantum computing for _nance: Overview and prospects, Rev. Phys. 4, 100028. [cited by applicant]
Ostaszewski et al., Jan. 27, 2021, Structure optimization for parameterized quantum circuits, arXiv:1905.09692v2 [quant-ph], 13 pp. [cited by applicant]
Parrish et al., 2019, Quantum Filter Diagonalization: Quantum Eigendecomposition without Full Quantum Phase Estimation, arXiv:1909.08925 =v1 [quant-ph], 10 pp. [cited by applicant]
Parrish et al., Apr. 5, 2019, A Jacobi Diagonalization and Anderson Acceleration Algorithm For Variational Quantum Algorithm Parameter Optimization, arXiv:1904.03206v1 [quant-ph], 31 pp. [cited by applicant]
Plekhanov et al., Feb. 28, 2022, Variational quantum amplitude estimation, arXiv:2109.03687v2 [quant-ph], 11 p. [cited by applicant]
Pogorelov et al., Jun. 7, 2021, A compact ion-trap quantum computing demonstrator, arXiv:2101.11390v3 [quant-ph], 22 pp. [cited by applicant]
Press et al., 1992, Numerical Recipes in C: The Art of Scientific Computing, Second Ed., Cambridge University Press, New York, USA (TOC). [cited by applicant]
Rebentrost et al., 2018, Quantum computational finance: Monte Carlo pricing of financial derivatives, Phys. Rev. A 98, 022321. [cited by applicant]
Schuld et al., 2019, Evaluating analytic gradients on quantum hardware, Phys. Rev. A 99, 032331. [cited by applicant]
Stair et al., 2020, A Multireference Quantum Krylov Algorithm for Strongly Correlated Electrons, J. Chem. Theory Comput. 16:2236-2245. [cited by applicant]
Stamatopoulos et al., Jul. 2, 2020, Option Pricing using Quantum Computers, arXiv:1905.02666v5 [quant-ph], 20 pp. [cited by applicant]
Suzuki et al., 2020, Amplitude estimation without phase estimation, Quantum Inf. Process. 19:75, 17 pp. [cited by applicant]
Suzuki et al., 2021, Normalized Gradient Descent for Variational Quantum Algorithms, arXiv:2106.10981v1 [quant-ph], 9 pp. [cited by applicant]
Tanaka et al., Oct. 11, 2021, Amplitude estimation via maximum likelihood on noisy quantum computer, arXiv:2006.16223v3 [quant-ph], 28 pp. [cited by applicant]
van den Berg et al., Sep. 5, 2020, Circuit optimization of Hamiltonian simulation by simultaneous diagonalization of Pauli clusters, arXiv:2003.13599v1 [quant-ph], 28 pp. [cited by applicant]
Vidal et al., Dec. 31, 2018, Calculus on parameterized quantum circuits, arXiv:1812.06323v2 [quant-ph]. [cited by applicant]
Wiebe et al., 2016, Quantum Deep Learning, Quantum Info. Comput. 16(7&8):0541-0587. [cited by applicant]
Wiebe et al., Jul. 18, 2014, Quantum Algorithms for Nearest-Neighbor Methods for Supervised and Unsupervised Learning, Quantum Information and Computation, 15(3&4):0316-0356. [cited by applicant]
Woerner et al., 2019, Quantum risk analysis, npj Quantum Inf. 5:15, 8 pp. [cited by applicant]
Extended European search report dated Jan. 16, 2023 in application No. 22194462.2, 9 pp. [cited by applicant]