Efficient quantum circuits based on the quantum natural gradient

Roy, Ananda; Erramilli, Sameer; Konik, Robert M.

doi:10.1103/PhysRevResearch.6.043083

Efficient quantum circuits based on the quantum natural gradient

Journal Article · Sun Nov 03 23:00:00 EST 2024 · Physical Review Research

DOI:https://doi.org/10.1103/PhysRevResearch.6.043083· OSTI ID:2476072

; ; Konik, Robert M.

Efficient preparation of arbitrary entangled quantum states is crucial for quantum computation. This is particularly important for noisy intermediate-scale quantum simulators relying on variational hybrid quantum-classical algorithms. To that end, we propose symmetry-conserving modified quantum approximate optimization algorithm (SCom-QAOA) circuits. The depths of these circuits depend not only on the desired fidelity to the target state but also on the amount of entanglement the state contains. The parameters of the SCom-QAOA circuits are optimized using the quantum natural gradient method based on the Fubini-Study metric. The SCom-QAOA circuit transforms an unentangled state into a ground state of a gapped one-dimensional Hamiltonian with a circuit depth that depends not on the system size but rather on the finite correlation length. In contrast, the circuit depth grows proportionally to the system size for preparing low-lying states of critical one-dimensional systems. Even in the latter case, SCom-QAOA circuits with depth less than the system size were sufficient to generate states with fidelity in excess of 99%, which is relevant for near-term applications. The proposed scheme enlarges the set of the initial states accessible for variational quantum algorithms and widens the scope of investigation of nonequilibrium phenomena in quantum simulators.

Published by the American Physical Society 2024

View Journal Article

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0012704

OSTI ID:: 2476072

Alternate ID(s):: OSTI ID: 2478771

Journal Information:: Physical Review Research, Journal Name: Physical Review Research Journal Issue: 4 Vol. 6; ISSN PPRHAI; ISSN 2643-1564

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

References (54)

Simulating physics with computers Feynman, Richard P. International Journal of Theoretical Physics, Vol. 21, Issue 6-7 https://doi.org/10.1007/BF02650179	journal	June 1982
Circuit complexity in quantum field theory Jefferson, Robert A.; Myers, Robert C. Journal of High Energy Physics, Vol. 2017, Issue 10 https://doi.org/10.1007/JHEP10(2017)107	journal	October 2017
Complexity of mixed Gaussian states from Fisher information geometry Di Giulio, Giuseppe; Tonni, Erik Journal of High Energy Physics, Vol. 2020, Issue 12 https://doi.org/10.1007/JHEP12(2020)101	journal	December 2020
On the universality of the quantum approximate optimization algorithm Morales, M. E. S.; Biamonte, J. D.; Zimborás, Z. Quantum Information Processing, Vol. 19, Issue 9 https://doi.org/10.1007/s11128-020-02748-9	journal	August 2020
Mixer-phaser Ansätze for quantum optimization with hard constraints LaRose, Ryan; Rieffel, Eleanor; Venturelli, Davide Quantum Machine Intelligence, Vol. 4, Issue 2 https://doi.org/10.1007/s42484-022-00069-x	journal	June 2022
Geometry and non-adiabatic response in quantum and classical systems Kolodrubetz, Michael; Sels, Dries; Mehta, Pankaj Physics Reports, Vol. 697 https://doi.org/10.1016/j.physrep.2017.07.001	journal	June 2017
The Variational Quantum Eigensolver: A review of methods and best practices Tilly, Jules; Chen, Hongxiang; Cao, Shuxiang Physics Reports, Vol. 986 https://doi.org/10.1016/j.physrep.2022.08.003	journal	November 2022
Probing many-body dynamics on a 51-atom quantum simulator Bernien, Hannes; Schwartz, Sylvain; Keesling, Alexander Nature, Vol. 551, Issue 7682 https://doi.org/10.1038/nature24622	journal	November 2017
Multimode quantum interference of photons in multiport integrated devices Peruzzo, Alberto; Laing, Anthony; Politi, Alberto Nature Communications, Vol. 2, Issue 1 https://doi.org/10.1038/ncomms1228	journal	March 2011
Noise-induced barren plateaus in variational quantum algorithms Wang, Samson; Fontana, Enrico; Cerezo, M. Nature Communications, Vol. 12, Issue 1 https://doi.org/10.1038/s41467-021-27045-6	journal	November 2021
Ising meson spectroscopy on a noisy digital quantum simulator Lamb, Christopher; Tang, Yicheng; Davis, Robert Nature Communications, Vol. 15, Issue 1 https://doi.org/10.1038/s41467-024-50206-2	journal	July 2024
Simulating quantum many-body dynamics on a current digital quantum computer Smith, Adam; Kim, M. S.; Pollmann, Frank npj Quantum Information, Vol. 5, Issue 1 https://doi.org/10.1038/s41534-019-0217-0	journal	November 2019
Alignment between initial state and mixer improves QAOA performance for constrained optimization He, Zichang; Shaydulin, Ruslan; Chakrabarti, Shouvanik npj Quantum Information, Vol. 9, Issue 1 https://doi.org/10.1038/s41534-023-00787-5	journal	November 2023
A divide-and-conquer algorithm for quantum state preparation Araujo, Israel F.; Park, Daniel K.; Petruccione, Francesco Scientific Reports, Vol. 11, Issue 1 https://doi.org/10.1038/s41598-021-85474-1	journal	March 2021
Confinement and entanglement dynamics on a digital quantum computer Vovrosh, Joseph; Knolle, Johannes Scientific Reports, Vol. 11, Issue 1 https://doi.org/10.1038/s41598-021-90849-5	journal	June 2021
Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems Verstraete, F.; Murg, V.; Cirac, J. I. Advances in Physics, Vol. 57, Issue 2 https://doi.org/10.1080/14789940801912366	journal	March 2008
Evolution of entanglement entropy in one-dimensional systems Calabrese, Pasquale; Cardy, John Journal of Statistical Mechanics: Theory and Experiment, Vol. 2005, Issue 04 https://doi.org/10.1088/1742-5468/2005/04/P04010	journal	April 2005
An area law for one-dimensional quantum systems Hastings, M. B. Journal of Statistical Mechanics: Theory and Experiment, Vol. 2007, Issue 08 https://doi.org/10.1088/1742-5468/2007/08/P08024	journal	August 2007
X Y mixers: Analytical and numerical results for the quantum alternating operator ansatz Wang, Zhihui; Rubin, Nicholas C.; Dominy, Jason M. Physical Review A, Vol. 101, Issue 1 https://doi.org/10.1103/PhysRevA.101.012320	journal	January 2020
Parameter concentrations in quantum approximate optimization Akshay, V.; Rabinovich, D.; Campos, E. Physical Review A, Vol. 104, Issue 1 https://doi.org/10.1103/PhysRevA.104.L010401	journal	July 2021
Quantum circuits with uniformly controlled one-qubit gates Bergholm, Ville; Vartiainen, Juha J.; Möttönen, Mikko Physical Review A, Vol. 71, Issue 5 https://doi.org/10.1103/PhysRevA.71.052330	journal	May 2005
Quantum circuits for strongly correlated quantum systems Verstraete, Frank; Cirac, J. Ignacio; Latorre, José I. Physical Review A, Vol. 79, Issue 3 https://doi.org/10.1103/PhysRevA.79.032316	journal	March 2009
Quantum-state preparation with universal gate decompositions Plesch, Martin; Brukner, Časlav Physical Review A, Vol. 83, Issue 3 https://doi.org/10.1103/PhysRevA.83.032302	journal	March 2011
Classifying and measuring geometry of a quantum ground state manifold Kolodrubetz, Michael; Gritsev, Vladimir; Polkovnikov, Anatoli Physical Review B, Vol. 88, Issue 6 https://doi.org/10.1103/PhysRevB.88.064304	journal	August 2013
Compression of correlation matrices and an efficient method for forming matrix product states of fermionic Gaussian states Fishman, Matthew T.; White, Steven R. Physical Review B, Vol. 92, Issue 7 https://doi.org/10.1103/PhysRevB.92.075132	journal	August 2015
Entropy Scaling and Simulability by Matrix Product States Schuch, Norbert; Wolf, Michael M.; Verstraete, Frank Physical Review Letters, Vol. 100, Issue 3 https://doi.org/10.1103/PhysRevLett.100.030504	journal	January 2008
Class of Quantum Many-Body States That Can Be Efficiently Simulated Vidal, G. Physical Review Letters, Vol. 101, Issue 11 https://doi.org/10.1103/PhysRevLett.101.110501	journal	September 2008
Entanglement of Low-Energy Excitations in Conformal Field Theory Alcaraz, Francisco Castilho; Berganza, Miguel Ibáñez; Sierra, Germán Physical Review Letters, Vol. 106, Issue 20 https://doi.org/10.1103/PhysRevLett.106.201601	journal	May 2011
Lattice Supersymmetry and Order-Disorder Coexistence in the Tricritical Ising Model O’Brien, Edward; Fendley, Paul Physical Review Letters, Vol. 120, Issue 20 https://doi.org/10.1103/PhysRevLett.120.206403	journal	May 2018
Training Variational Quantum Algorithms Is NP-Hard Bittel, Lennart; Kliesch, Martin Physical Review Letters, Vol. 127, Issue 12 https://doi.org/10.1103/PhysRevLett.127.120502	journal	September 2021
Preparation of Matrix Product States with Log-Depth Quantum Circuits Malz, Daniel; Styliaris, Georgios; Wei, Zhi-Yuan Physical Review Letters, Vol. 132, Issue 4 https://doi.org/10.1103/PhysRevLett.132.040404	journal	January 2024
Simulation of Many-Body Fermi Systems on a Universal Quantum Computer Abrams, Daniel S.; Lloyd, Seth Physical Review Letters, Vol. 79, Issue 13 https://doi.org/10.1103/PhysRevLett.79.2586	journal	September 1997
Information-Theoretic Differential Geometry of Quantum Phase Transitions Zanardi, Paolo; Giorda, Paolo; Cozzini, Marco Physical Review Letters, Vol. 99, Issue 10 https://doi.org/10.1103/PhysRevLett.99.100603	journal	September 2007
Avoiding local minima in variational quantum eigensolvers with the natural gradient optimizer Wierichs, David; Gogolin, Christian; Kastoryano, Michael Physical Review Research, Vol. 2, Issue 4 https://doi.org/10.1103/PhysRevResearch.2.043246	journal	November 2020
Preparation and verification of tensor network states Cruz, Esther; Baccari, Flavio; Tura, Jordi Physical Review Research, Vol. 4, Issue 2 https://doi.org/10.1103/PhysRevResearch.4.023161	journal	May 2022
Finite-depth scaling of infinite quantum circuits for quantum critical points Jobst, Bernhard; Smith, Adam; Pollmann, Frank Physical Review Research, Vol. 4, Issue 3 https://doi.org/10.1103/PhysRevResearch.4.033118	journal	August 2022
Efficient Variational Quantum Simulator Incorporating Active Error Minimization Li, Ying; Benjamin, Simon C. Physical Review X, Vol. 7, Issue 2 https://doi.org/10.1103/PhysRevX.7.021050	journal	June 2017
Low-Rank Quantum State Preparation Araujo, Israel F.; Blank, Carsten; Araújo, Ismael C. S. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, Vol. 43, Issue 1 https://doi.org/10.1109/tcad.2023.3297972	journal	January 2024
Witnessing eigenstates for quantum simulation of Hamiltonian spectra Santagati, Raffaele; Wang, Jianwei; Gentile, Antonio A. Science Advances, Vol. 4, Issue 1 https://doi.org/10.1126/sciadv.aap9646	journal	January 2018
Evidence of scaling advantage for the quantum approximate optimization algorithm on a classically intractable problem Shaydulin, Ruslan; Li, Changhao; Chakrabarti, Shouvanik Science Advances, Vol. 10, Issue 22 https://doi.org/10.1126/sciadv.adm6761	journal	May 2024
Quantum Computation as Geometry Nielsen, M. A. Science, Vol. 311, Issue 5764 https://doi.org/10.1126/science.1121541	journal	February 2006
Parameter Transfer for Quantum Approximate Optimization of Weighted MaxCut Shaydulin, Ruslan; Lotshaw, Phillip C.; Larson, Jeffrey ACM Transactions on Quantum Computing, Vol. 4, Issue 3 https://doi.org/10.1145/3584706	journal	April 2023
Natural Gradient Works Efficiently in Learning Amari, Shun-ichi Neural Computation, Vol. 10, Issue 2 https://doi.org/10.1162/089976698300017746	journal	February 1998
QGOpt: Riemannian optimization for quantum technologies Luchnikov, Ilia; Ryzhov, Alexander; Filippov, Sergey SciPost Physics, Vol. 10, Issue 3 https://doi.org/10.21468/SciPostPhys.10.3.079	journal	March 2021
Integrability and complexity in quantum spin chains Craps, Ben; De Clerck, Marine; Evnin, Oleg SciPost Physics, Vol. 16, Issue 2 https://doi.org/10.21468/SciPostPhys.16.2.041	journal	February 2024
Efficient variational simulation of non-trivial quantum states Ho, Wen Wei; Hsieh, Timothy H. SciPost Physics, Vol. 6, Issue 3 https://doi.org/10.21468/SciPostPhys.6.3.029	journal	January 2019
Entanglement spreading in non-equilibrium integrable systems Calabrese, Pasquale SciPost Physics Lecture Notes https://doi.org/10.21468/SciPostPhysLectNotes.20	journal	December 2020
Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy) Hauschild, Johannes; Pollmann, Frank SciPost Physics Lecture Notes https://doi.org/10.21468/SciPostPhysLectNotes.5	journal	October 2018
Quantum Natural Gradient Stokes, James; Izaac, Josh; Killoran, Nathan Quantum, Vol. 4 https://doi.org/10.22331/q-2020-05-25-269	journal	May 2020
Quantum Circuits for Sparse Isometries Malvetti, Emanuel; Iten, Raban; Colbeck, Roger Quantum, Vol. 5 https://doi.org/10.22331/q-2021-03-15-412	journal	March 2021
Simultaneous Perturbation Stochastic Approximation of the Quantum Fisher Information Gacon, Julien; Zoufal, Christa; Carleo, Giuseppe Quantum, Vol. 5 https://doi.org/10.22331/q-2021-10-20-567	journal	October 2021
The Quantum Approximate Optimization Algorithm and the Sherrington-Kirkpatrick Model at Infinite Size Farhi, Edward; Goldstone, Jeffrey; Gutmann, Sam Quantum, Vol. 6 https://doi.org/10.22331/q-2022-07-07-759	journal	July 2022
From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz Hadfield, Stuart; Wang, Zhihui; O'Gorman, Bryan Algorithms, Vol. 12, Issue 2 https://doi.org/10.3390/a12020034	journal	February 2019
Constraint Preserving Mixers for the Quantum Approximate Optimization Algorithm Fuchs, Franz Georg; Lye, Kjetil Olsen; Møll Nilsen, Halvor Algorithms, Vol. 15, Issue 6 https://doi.org/10.3390/a15060202	journal	June 2022

Similar Records

Feedback-based quantum algorithms for ground state preparation

Journal Article · Wed Sep 25 00:00:00 EDT 2024 · Physical Review Research · OSTI ID:2473490

Efficient state preparation for the Schwinger model with a theta term

Journal Article · Thu Apr 24 00:00:00 EDT 2025 · Physical Review. D. · OSTI ID:2562697

Efficient quantum circuits based on the quantum natural gradient

Citation Formats

References (54)

Similar Records

Related Subjects