An efficient quantum algorithm for the time evolution of parameterized circuits

Stefano Barison, Filippo Vicentini, and Giuseppe Carleo

Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland

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Abstract

We introduce a novel hybrid algorithm to simulate the real-time evolution of quantum systems using parameterized quantum circuits. The method, named "projected – Variational Quantum Dynamics" (p-VQD) realizes an iterative, global projection of the exact time evolution onto the parameterized manifold. In the small time-step limit, this is equivalent to the McLachlan's variational principle. Our approach is efficient in the sense that it exhibits an optimal linear scaling with the total number of variational parameters. Furthermore, it is global in the sense that it uses the variational principle to optimize all parameters at once. The global nature of our approach then significantly extends the scope of existing efficient variational methods, that instead typically rely on the iterative optimization of a restricted subset of variational parameters. Through numerical experiments, we also show that our approach is particularly advantageous over existing global optimization algorithms based on the time-dependent variational principle that, due to a demanding quadratic scaling with parameter numbers, are unsuitable for large parameterized quantum circuits.

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► References

[1] Frank Arute ``Quantum supremacy using a programmable superconducting processor'' Nature 574, 505-510 (2019).
https:/​/​doi.org/​10.1038/​s41586-019-1666-5

[2] LeeAnn M. Sager, Scott E. Smart, and David A. Mazziotti, ``Preparation of an exciton condensate of photons on a 53-qubit quantum computer'' Physical Review Research 2 (2020).
https:/​/​doi.org/​10.1103/​physrevresearch.2.043205

[3] P.W. Shor ``Algorithms for quantum computation: discrete logarithms and factoring'' Proceedings 35th Annual Symposium on Foundations of Computer Science (1994).
https:/​/​doi.org/​10.1109/​sfcs.1994.365700

[4] D. Coppersmith ``An approximate Fourier transform useful in quantum factoring'' (1994).

[5] Giuseppe E Santoroand Erio Tosatti ``Optimization using quantum mechanics: quantum annealing through adiabatic evolution'' Journal of Physics A: Mathematical and General 39, R393–R431 (2006).
https:/​/​doi.org/​10.1088/​0305-4470/​39/​36/​r01

[6] Ivan Kassal, Stephen P. Jordan, Peter J. Love, Masoud Mohseni, and Alán Aspuru-Guzik, ``Polynomial-time quantum algorithm for the simulation of chemical dynamics'' Proceedings of the National Academy of Sciences 105, 18681–18686 (2008).
https:/​/​doi.org/​10.1073/​pnas.0808245105

[7] I. M. Georgescu, S. Ashhab, and Franco Nori, ``Quantum simulation'' Rev. Mod. Phys. 86, 153–185 (2014).
https:/​/​doi.org/​10.1103/​RevModPhys.86.153

[8] Alberto Peruzzo, Jarrod McClean, Peter Shadbolt, Man-Hong Yung, Xiao-Qi Zhou, Peter J. Love, Alán Aspuru-Guzik, and Jeremy L. O’Brien, ``A variational eigenvalue solver on a photonic quantum processor'' Nature Communications 5 (2014).
https:/​/​doi.org/​10.1038/​ncomms5213

[9] Ying Liand Simon C. Benjamin ``Efficient Variational Quantum Simulator Incorporating Active Error Minimization'' Phys. Rev. X 7, 021050 (2017).
https:/​/​doi.org/​10.1103/​PhysRevX.7.021050

[10] Pauline J. Ollitrault, Abhinav Kandala, Chun-Fu Chen, Panagiotis Kl. Barkoutsos, Antonio Mezzacapo, Marco Pistoia, Sarah Sheldon, Stefan Woerner, Jay M. Gambetta, and Ivano Tavernelli, ``Quantum equation of motion for computing molecular excitation energies on a noisy quantum processor'' Physical Review Research 2 (2020).
https:/​/​doi.org/​10.1103/​physrevresearch.2.043140

[11] Mario Motta, Chong Sun, Adrian T. K. Tan, Matthew J. O’Rourke, Erika Ye, Austin J. Minnich, Fernando G. S. L. Brandão, and Garnet Kin-Lic Chan, ``Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution'' Nature Physics 16, 205–210 (2019).
https:/​/​doi.org/​10.1038/​s41567-019-0704-4

[12] M. Cerezo, Andrew Arrasmith, Ryan Babbush, Simon C. Benjamin, Suguru Endo, Keisuke Fujii, Jarrod R. McClean, Kosuke Mitarai, Xiao Yuan, Lukasz Cincio, and Patrick J. Coles, ``Variational Quantum Algorithms'' (2020).
arXiv:2012.09265

[13] Jacob L. Beckey, M. Cerezo, Akira Sone, and Patrick J. Coles, ``Variational Quantum Algorithm for Estimating the Quantum Fisher Information'' (2020).
arXiv:2010.10488v1

[14] Jacob Biamonte, Peter Wittek, Nicola Pancotti, Patrick Rebentrost, Nathan Wiebe, and Seth Lloyd, ``Quantum machine learning'' Nature 549, 195–202 (2017).
https:/​/​doi.org/​10.1038/​nature23474

[15] Sima E. Borujeni, Saideep Nannapaneni, Nam H. Nguyen, Elizabeth C. Behrman, and James E. Steck, ``Quantum circuit representation of Bayesian networks'' (2020).
arXiv:2004.14803

[16] Jonathan Romero, Jonathan P Olson, and Alan Aspuru-Guzik, ``Quantum autoencoders for efficient compression of quantum data'' Quantum Science and Technology 2, 045001 (2017).
https:/​/​doi.org/​10.1088/​2058-9565/​aa8072

[17] Iordanis Kerenidis, Jonas Landman, Alessandro Luongo, and Anupam Prakash, ``q-means: A quantum algorithm for unsupervised machine learning'' Advances in Neural Information Processing Systems 32, 4134–4144 (2019).

[18] Maria Schuldand Nathan Killoran ``Quantum Machine Learning in Feature Hilbert Spaces'' Phys. Rev. Lett. 122, 040504 (2019).
https:/​/​doi.org/​10.1103/​PhysRevLett.122.040504

[19] Maria Schuld, Alex Bocharov, Krysta M. Svore, and Nathan Wiebe, ``Circuit-centric quantum classifiers'' Physical Review A 101 (2020).
https:/​/​doi.org/​10.1103/​physreva.101.032308

[20] Vojtěch Havlíček, Antonio D. Córcoles, Kristan Temme, Aram W. Harrow, Abhinav Kandala, Jerry M. Chow, and Jay M. Gambetta, ``Supervised learning with quantum-enhanced feature spaces'' Nature 567, 209–212 (2019).
https:/​/​doi.org/​10.1038/​s41586-019-0980-2

[21] Mohammad H. Amin, Evgeny Andriyash, Jason Rolfe, Bohdan Kulchytskyy, and Roger Melko, ``Quantum Boltzmann Machine'' Phys. Rev. X 8, 021050 (2018).
https:/​/​doi.org/​10.1103/​PhysRevX.8.021050

[22] Iris Cong, Soonwon Choi, and Mikhail D. Lukin, ``Quantum convolutional neural networks'' Nature Physics 15, 1273–1278 (2019).
https:/​/​doi.org/​10.1038/​s41567-019-0648-8

[23] P. J. J. O'Malley ``Scalable Quantum Simulation of Molecular Energies'' Phys. Rev. X 6, 031007 (2016).
https:/​/​doi.org/​10.1103/​PhysRevX.6.031007

[24] Abhinav Kandala, Antonio Mezzacapo, Kristan Temme, Maika Takita, Markus Brink, Jerry M. Chow, and Jay M. Gambetta, ``Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets'' Nature 549, 242–246 (2017).
https:/​/​doi.org/​10.1038/​nature23879

[25] Bela Bauer, Sergey Bravyi, Mario Motta, and Garnet Kin-Lic Chan, ``Quantum Algorithms for Quantum Chemistry and Quantum Materials Science'' Chemical Reviews 120, 12685–12717 (2020).
https:/​/​doi.org/​10.1021/​acs.chemrev.9b00829

[26] H. F. Trotter ``On the product of semi-groups of operators'' Proc. Amer. Math. Soc. 10, 545–551 (1959).
https:/​/​doi.org/​10.1090/​S0002-9939-1959-0108732-6

[27] Masuo Suzuki ``General theory of fractal path integrals with applications to many‐body theories and statistical physics'' Journal of Mathematical Physics 32, 400–407 (1991).
https:/​/​doi.org/​10.1063/​1.529425

[28] Daniel S. Abramsand Seth Lloyd ``Simulation of Many-Body Fermi Systems on a Universal Quantum Computer'' Phys. Rev. Lett. 79, 2586–2589 (1997).
https:/​/​doi.org/​10.1103/​PhysRevLett.79.2586

[29] G. Ortiz, J. E. Gubernatis, E. Knill, and R. Laflamme, ``Quantum algorithms for fermionic simulations'' Phys. Rev. A 64, 022319 (2001).
https:/​/​doi.org/​10.1103/​PhysRevA.64.022319

[30] Xiao Yuan, Suguru Endo, Qi Zhao, Ying Li, and Simon C. Benjamin, ``Theory of variational quantum simulation'' Quantum 3, 191 (2019).
https:/​/​doi.org/​10.22331/​q-2019-10-07-191

[31] Cristina Cîrstoiu, Zoë Holmes, Joseph Iosue, Lukasz Cincio, Patrick J. Coles, and Andrew Sornborger, ``Variational fast forwarding for quantum simulation beyond the coherence time'' npj Quantum Information 6 (2020).
https:/​/​doi.org/​10.1038/​s41534-020-00302-0

[32] Benjamin Commeau, M. Cerezo, Zoë Holmes, Lukasz Cincio, Patrick J. Coles, and Andrew Sornborger, ``Variational Hamiltonian Diagonalization for Dynamical Quantum Simulation'' (2020).
arXiv:2009.02559

[33] Kishor Bhartiand Tobias Haug ``Quantum Assisted Simulator'' (2020).
arXiv:2011.06911

[34] P. A. M. Dirac ``Note on Exchange Phenomena in the Thomas Atom'' Mathematical Proceedings of the Cambridge Philosophical Society 26, 376–385 (1930).
https:/​/​doi.org/​10.1017/​S0305004100016108

[35] Jacov Frenkel ``Wave Mechanics: Advanced General Theory'' Oxford University Press (1934).

[36] A.D. McLachlan ``A variational solution of the time-dependent Schrodinger equation'' Molecular Physics 8, 39–44 (1964).
https:/​/​doi.org/​10.1080/​00268976400100041

[37] Jutho Haegeman, J. Ignacio Cirac, Tobias J. Osborne, Iztok Pižorn, Henri Verschelde, and Frank Verstraete, ``Time-Dependent Variational Principle for Quantum Lattices'' Phys. Rev. Lett. 107, 070601 (2011).
https:/​/​doi.org/​10.1103/​PhysRevLett.107.070601

[38] Jutho Haegeman, Christian Lubich, Ivan Oseledets, Bart Vandereycken, and Frank Verstraete, ``Unifying time evolution and optimization with matrix product states'' Phys. Rev. B 94, 165116 (2016).
https:/​/​doi.org/​10.1103/​PhysRevB.94.165116

[39] Giuseppe Carleo, Federico Becca, Marco Schiro, and Michele Fabrizio, ``Localization and Glassy Dynamics Of Many-Body Quantum Systems'' Scientific Reports 2, 243 (2012).
https:/​/​doi.org/​10.1038/​srep00243

[40] Giuseppe Carleo, Federico Becca, Laurent Sanchez-Palencia, Sandro Sorella, and Michele Fabrizio, ``Light-cone effect and supersonic correlations in one- and two-dimensional bosonic superfluids'' Phys. Rev. A 89, 031602 (2014).
https:/​/​doi.org/​10.1103/​PhysRevA.89.031602

[41] Michael Kolodrubetz, Dries Sels, Pankaj Mehta, and Anatoli Polkovnikov, ``Geometry and non-adiabatic response in quantum and classical systems'' Physics Reports 697, 1–87 (2017).
https:/​/​doi.org/​10.1016/​j.physrep.2017.07.001

[42] Marin Bukov, Dries Sels, and Anatoli Polkovnikov, ``Geometric Speed Limit of Accessible Many-Body State Preparation'' Phys. Rev. X 9, 011034 (2019).
https:/​/​doi.org/​10.1103/​PhysRevX.9.011034

[43] Marcello Benedetti, Mattia Fiorentini, and Michael Lubasch, ``Hardware-efficient variational quantum algorithms for time evolution'' (2020).
https:/​/​doi.org/​10.1103/​PhysRevResearch.3.033083
arXiv:2009.12361

[44] Lucas Slattery, Benjamin Villalonga, and Bryan K. Clark, ``Unitary Block Optimization for Variational Quantum Algorithms'' (2021).
arXiv:2102.08403

[45] F. Barratt, James Dborin, Matthias Bal, Vid Stojevic, Frank Pollmann, and A. G. Green, ``Parallel quantum simulation of large systems on small NISQ computers'' npj Quantum Information 7 (2021).
https:/​/​doi.org/​10.1038/​s41534-021-00420-3

[46] Sheng-Hsuan Lin, Rohit Dilip, Andrew G. Green, Adam Smith, and Frank Pollmann, ``Real- and Imaginary-Time Evolution with Compressed Quantum Circuits'' PRX Quantum 2 (2021).
https:/​/​doi.org/​10.1103/​prxquantum.2.010342

[47] Matthew Otten, Cristian L. Cortes, and Stephen K. Gray, ``Noise-Resilient Quantum Dynamics Using Symmetry-Preserving Ansatzes'' (2019).
arXiv:1910.06284

[48] James Stokes, Josh Izaac, Nathan Killoran, and Giuseppe Carleo, ``Quantum Natural Gradient'' Quantum 4, 269 (2020).
https:/​/​doi.org/​10.22331/​q-2020-05-25-269

[49] Daniel Gottesmanand Isaac Chuang ``Quantum Digital Signatures'' (2001).

[50] Harry Buhrman, Richard Cleve, John Watrous, and Ronald de Wolf, ``Quantum Fingerprinting'' Physical Review Letters 87 (2001).
https:/​/​doi.org/​10.1103/​physrevlett.87.167902

[51] Maria Schuld, Ville Bergholm, Christian Gogolin, Josh Izaac, and Nathan Killoran, ``Evaluating analytic gradients on quantum hardware'' Phys. Rev. A 99, 032331 (2019).
https:/​/​doi.org/​10.1103/​PhysRevA.99.032331

[52] J.C. Spall ``Implementation of the simultaneous perturbation algorithm for stochastic optimization'' IEEE Transactions on Aerospace and Electronic Systems 34, 817–823 (1998).
https:/​/​doi.org/​10.1109/​7.705889

[53] K. Mitarai, M. Negoro, M. Kitagawa, and K. Fujii, ``Quantum circuit learning'' Physical Review A 98 (2018).
https:/​/​doi.org/​10.1103/​physreva.98.032309

[54] Robert M. Parrish, Edward G. Hohenstein, Peter L. McMahon, and Todd J. Martinez, ``Hybrid Quantum/​Classical Derivative Theory: Analytical Gradients and Excited-State Dynamics for the Multistate Contracted Variational Quantum Eigensolver'' (2019).
arXiv:1906.08728

[55] Gavin E. Crooks ``Gradients of parameterized quantum gates using the parameter-shift rule and gate decomposition'' (2019).
arXiv:1905.13311

[56] Andrea Mari, Thomas R. Bromley, and Nathan Killoran, ``Estimating the gradient and higher-order derivatives on quantum hardware'' Physical Review A 103 (2021).
https:/​/​doi.org/​10.1103/​physreva.103.012405

[57] Leonardo Banchiand Gavin E. Crooks ``Measuring Analytic Gradients of General Quantum Evolution with the Stochastic Parameter Shift Rule'' Quantum 5, 386 (2021).
https:/​/​doi.org/​10.22331/​q-2021-01-25-386

[58] M. Cerezo, Akira Sone, Tyler Volkoff, Lukasz Cincio, and Patrick J. Coles, ``Cost function dependent barren plateaus in shallow parametrized quantum circuits'' Nature Communications 12 (2021).
https:/​/​doi.org/​10.1038/​s41467-021-21728-w

[59] Jarrod R. McClean, Sergio Boixo, Vadim N. Smelyanskiy, Ryan Babbush, and Hartmut Neven, ``Barren plateaus in quantum neural network training landscapes'' Nature Communications 9 (2018).
https:/​/​doi.org/​10.1038/​s41467-018-07090-4

[60] Tobias Haugand M. S. Kim ``Optimal training of variational quantum algorithms without barren plateaus'' (2021).
arXiv:2104.14543

[61] Edward Grant, Leonard Wossnig, Mateusz Ostaszewski, and Marcello Benedetti, ``An initialization strategy for addressing barren plateaus in parametrized quantum circuits'' Quantum 3, 214 (2019).
https:/​/​doi.org/​10.22331/​q-2019-12-09-214

[62] Carlos Bravo-Prieto, Ryan LaRose, M. Cerezo, Yigit Subasi, Lukasz Cincio, and Patrick J. Coles, ``Variational Quantum Linear Solver'' (2020).
arXiv:1909.05820

[63] Héctor Abraham et al. ``Qiskit: An Open-source Framework for Quantum Computing'' (2019).
https:/​/​doi.org/​10.5281/​zenodo.2562110

[64] J. Demmel ``On condition numbers and the distance to the nearest ill-posed problem'' Numerische Mathematik 51, 251–289 (1987).
https:/​/​doi.org/​10.1007/​BF01400115

[65] Guifré Vidal ``Efficient Simulation of One-Dimensional Quantum Many-Body Systems'' Physical Review Letters 93, 040502 (2004).
https:/​/​doi.org/​10.1103/​PhysRevLett.93.040502

[66] A. J. Daley, C. Kollath, U. Schollwock, and G. Vidal, ``Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces'' Journal of Statistical Mechanics-Theory and Experiment P04005 (2004).
https:/​/​doi.org/​10.1088/​1742-5468/​2004/​04/​P04005

[67] Steven R. Whiteand Adrian E. Feiguin ``Real-Time Evolution Using the Density Matrix Renormalization Group'' Physical Review Letters 93, 076401 (2004).
https:/​/​doi.org/​10.1103/​PhysRevLett.93.076401

[68] Giuseppe Carleoand Matthias Troyer ``Solving the quantum many-body problem with artificial neural networks'' Science 355, 602–606 (2017).
https:/​/​doi.org/​10.1126/​science.aag2302

[69] Markus Schmittand Markus Heyl ``Quantum Many-Body Dynamics in Two Dimensions with Artificial Neural Networks'' Physical Review Letters 125, 100503 (2020) Publisher: American Physical Society.
https:/​/​doi.org/​10.1103/​PhysRevLett.125.100503

[70] Stefano Barison ``Github repository'' (2021).
https:/​/​github.com/​StefanoBarison/​p-VQD

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[1] Kaito Wada, Rudy Raymond, Yu-ya Ohnishi, Eriko Kaminishi, Michihiko Sugawara, Naoki Yamamoto, and Hiroshi C. Watanabe, "Simulating time evolution with fully optimized single-qubit gates on parametrized quantum circuits", Physical Review A 105 6, 062421 (2022).

[2] Stefano Barison, Filippo Vicentini, Ignacio Cirac, and Giuseppe Carleo, "Variational dynamics as a ground-state problem on a quantum computer", Physical Review Research 4 4, 043161 (2022).

[3] Shi-Xin Zhang and Shuai Yin, "Universal imaginary-time critical dynamics on a quantum computer", Physical Review B 109 13, 134309 (2024).

[4] Jonathan Wei Zhong Lau, Kian Hwee Lim, Harshank Shrotriya, and Leong Chuan Kwek, "NISQ computing: where are we and where do we go?", AAPPS Bulletin 32 1, 27 (2022).

[5] Rebecca Erbanni, Kishor Bharti, Leong-Chuan Kwek, and Dario Poletti, "NISQ algorithm for the matrix elements of a generic observable", SciPost Physics 15 4, 180 (2023).

[6] Baptiste Anselme Martin, Thomas Ayral, François Jamet, Marko J. Rančić, and Pascal Simon, "Combining matrix product states and noisy quantum computers for quantum simulation", Physical Review A 109 6, 062437 (2024).

[7] Pooja Siwach, Kaytlin Harrison, and A. Baha Balantekin, "Collective neutrino oscillations on a quantum computer with hybrid quantum-classical algorithm", Physical Review D 108 8, 083039 (2023).

[8] Alexander Miessen, Pauline J. Ollitrault, Francesco Tacchino, and Ivano Tavernelli, "Quantum algorithms for quantum dynamics", Nature Computational Science 3 1, 25 (2022).

[9] James Dborin, Vinul Wimalaweera, F. Barratt, Eric Ostby, Thomas E. O’Brien, and A. G. Green, "Simulating groundstate and dynamical quantum phase transitions on a superconducting quantum computer", Nature Communications 13 1, 5977 (2022).

[10] Benedikt Fauseweh and Jian-Xin Zhu, "Quantum computing Floquet energy spectra", Quantum 7, 1063 (2023).

[11] Phillip W. K. Jensen, Peter D. Johnson, and Alexander A. Kunitsa, "Near-term quantum algorithm for computing molecular and materials properties based on recursive variational series methods", Physical Review A 108 2, 022422 (2023).

[12] Refik Mansuroglu, Felix Fischer, and Michael J. Hartmann, "Problem-specific classical optimization of Hamiltonian simulation", Physical Review Research 5 4, 043035 (2023).

[13] Yu-Qin Chen, Shi-Xin Zhang, Chang-Yu Hsieh, and Shengyu Zhang, "Non-Hermitian ground-state-searching algorithm enhanced by a variational toolbox", Physical Review A 107 4, 042418 (2023).

[14] Matija Medvidović and Dries Sels, "Variational Quantum Dynamics of Two-Dimensional Rotor Models", PRX Quantum 4 4, 040302 (2023).

[15] James Stokes, Brian Chen, and Shravan Veerapaneni, "Numerical and geometrical aspects of flow-based variational quantum Monte Carlo", Machine Learning: Science and Technology 4 2, 021001 (2023).

[16] Duc Tuan Hoang, Friederike Metz, Andreas Thomasen, Tran Duong Anh-Tai, Thomas Busch, and Thomás Fogarty, "Variational quantum algorithm for ergotropy estimation in quantum many-body batteries", Physical Review Research 6 1, 013038 (2024).

[17] Alessandro Sinibaldi, Clemens Giuliani, Giuseppe Carleo, and Filippo Vicentini, "Unbiasing time-dependent Variational Monte Carlo by projected quantum evolution", Quantum 7, 1131 (2023).

[18] R Carobene, S Barison, and A Giachero, "Sequence of penalties method to study excited states using VQE", Quantum Science and Technology 8 3, 035014 (2023).

[19] Julien Gacon, Jannes Nys, Riccardo Rossi, Stefan Woerner, and Giuseppe Carleo, "Variational quantum time evolution without the quantum geometric tensor", Physical Review Research 6 1, 013143 (2024).

[20] Zhu Cao, "Deep Ising Born Machine", Advanced Quantum Technologies 6 7, 2300033 (2023).

[21] Lento Nagano, Aniruddha Bapat, and Christian W. Bauer, "Quench dynamics of the Schwinger model via variational quantum algorithms", Physical Review D 108 3, 034501 (2023).

[22] Christa Zoufal, David Sutter, and Stefan Woerner, "Error bounds for variational quantum time evolution", Physical Review Applied 20 4, 044059 (2023).

[23] Sanket Sharma, T. Papenbrock, and L. Platter, "Scattering phase shifts from a quantum computer", Physical Review C 109 6, L061001 (2024).

[24] Avin Seneviratne, Peter L. Walters, and Fei Wang, "Exact Non-Markovian Quantum Dynamics on the NISQ Device Using Kraus Operators", ACS Omega 9 8, 9666 (2024).

[25] Pauline J Ollitrault, Sven Jandura, Alexander Miessen, Irene Burghardt, Rocco Martinazzo, Francesco Tacchino, and Ivano Tavernelli, "Quantum algorithms for grid-based variational time evolution", Quantum 7, 1139 (2023).

[26] Daniel Bultrini and Oriol Vendrell, "Mixed quantum-classical dynamics for near term quantum computers", Communications Physics 6 1, 328 (2023).

[27] Erik Lötstedt, Takanori Nishi, and Kaoru Yamanouchi, Advances In Atomic, Molecular, and Optical Physics 73, 33 (2024) ISBN:9780443314582.

[28] Michael R. Geller, Zoë Holmes, Patrick J. Coles, and Andrew Sornborger, "Experimental quantum learning of a spectral decomposition", Physical Review Research 3 3, 033200 (2021).

[29] Kishor Bharti, Tobias Haug, Vlatko Vedral, and Leong-Chuan Kwek, "Noisy intermediate-scale quantum algorithm for semidefinite programming", Physical Review A 105 5, 052445 (2022).

[30] Stefan H. Sack, Raimel A. Medina, Alexios A. Michailidis, Richard Kueng, and Maksym Serbyn, "Avoiding Barren Plateaus Using Classical Shadows", PRX Quantum 3 2, 020365 (2022).

[31] Michael R. Geller, Andrew Arrasmith, Zoë Holmes, Bin Yan, Patrick J. Coles, and Andrew Sornborger, "Quantum simulation of operator spreading in the chaotic Ising model", Physical Review E 105 3, 035302 (2022).

[32] Tianchen Zhao, Chuhao Sun, Asaf Cohen, James Stokes, and Shravan Veerapaneni, "Quantum-inspired variational algorithms for partial differential equations: application to financial derivative pricing", Quantitative Finance 24 1, 1 (2024).

[33] Conor Mc Keever and Michael Lubasch, "Towards Adiabatic Quantum Computing Using Compressed Quantum Circuits", PRX Quantum 5 2, 020362 (2024).

[34] Lindsay Bassman Oftelie, Katherine Klymko, Diyi Liu, Norm M. Tubman, and Wibe A. de Jong, "Computing Free Energies with Fluctuation Relations on Quantum Computers", Physical Review Letters 129 13, 130603 (2022).

[35] Maurits S. J. Tepaske, David J. Luitz, and Dominik Hahn, "Optimal compression of constrained quantum time evolution", Physical Review B 109 20, 205134 (2024).

[36] I-Chi Chen, Benjamin Burdick, Yongxin Yao, Peter P. Orth, and Thomas Iadecola, "Error-mitigated simulation of quantum many-body scars on quantum computers with pulse-level control", Physical Review Research 4 4, 043027 (2022).

[37] Maurits S. J. Tepaske, Dominik Hahn, and David J. Luitz, "Optimal compression of quantum many-body time evolution operators into brickwall circuits", SciPost Physics 14 4, 073 (2023).

[38] Leonardo Ratini, Chiara Capecci, and Leonardo Guidoni, "Natural Orbitals and Sparsity of Quantum Mutual Information", Journal of Chemical Theory and Computation 20 9, 3535 (2024).

[39] Tasneem M Watad and Netanel H Lindner, "Variational quantum algorithms for simulation of Lindblad dynamics", Quantum Science and Technology 9 2, 025015 (2024).

[40] Alexander Miessen, Pauline J. Ollitrault, and Ivano Tavernelli, "Quantum algorithms for quantum dynamics: A performance study on the spin-boson model", Physical Review Research 3 4, 043212 (2021).

[41] Reinis Irmejs, Mari-Carmen Bañuls, and J. Ignacio Cirac, "Quantum simulation of Z2 lattice gauge theory with minimal resources", Physical Review D 108 7, 074503 (2023).

[42] Alberto Baiardi, Matthias Christandl, and Markus Reiher, "Quantum Computing for Molecular Biology**", ChemBioChem 24 13, e202300120 (2023).

[43] Gian Gentinetta, Friederike Metz, and Giuseppe Carleo, "Overhead-constrained circuit knitting for variational quantum dynamics", Quantum 8, 1296 (2024).

[44] Leonardo Ratini, Chiara Capecci, and Leonardo Guidoni, "Optimization strategies in WAHTOR algorithm for quantum computing empirical ansatz: a comparative study", Electronic Structure 5 4, 045006 (2023).

[45] Lucas Slattery, Benjamin Villalonga, and Bryan K. Clark, "Unitary block optimization for variational quantum algorithms", Physical Review Research 4 2, 023072 (2022).

[46] Nikita Astrakhantsev, Sheng-Hsuan Lin, Frank Pollmann, and Adam Smith, "Time evolution of uniform sequential circuits", Physical Review Research 5 3, 033187 (2023).

[47] Noah F. Berthusen, Thaís V. Trevisan, Thomas Iadecola, and Peter P. Orth, "Quantum dynamics simulations beyond the coherence time on noisy intermediate-scale quantum hardware by variational Trotter compression", Physical Review Research 4 2, 023097 (2022).

[48] Conor Mc Keever and Michael Lubasch, "Classically optimized Hamiltonian simulation", Physical Review Research 5 2, 023146 (2023).

[49] Chenfeng Cao, Zheng An, Shi-Yao Hou, D. L. Zhou, and Bei Zeng, "Quantum imaginary time evolution steered by reinforcement learning", Communications Physics 5 1, 57 (2022).

[50] Pavel P. Popov, Michael Meth, Maciej Lewestein, Philipp Hauke, Martin Ringbauer, Erez Zohar, and Valentin Kasper, "Variational quantum simulation of U(1) lattice gauge theories with qudit systems", Physical Review Research 6 1, 013202 (2024).

[51] Yaswitha Gujju, Atsushi Matsuo, and Rudy Raymond, "Quantum machine learning on near-term quantum devices: Current state of supervised and unsupervised techniques for real-world applications", Physical Review Applied 21 6, 067001 (2024).

[52] Shi-Xin Zhang, Chang-Yu Hsieh, Shengyu Zhang, and Hong Yao, "Neural predictor based quantum architecture search", Machine Learning: Science and Technology 2 4, 045027 (2021).

[53] Sergey Bravyi, Oliver Dial, Jay M. Gambetta, Darío Gil, and Zaira Nazario, "The future of quantum computing with superconducting qubits", Journal of Applied Physics 132 16, 160902 (2022).

[54] Francesco Libbi, Jacopo Rizzo, Francesco Tacchino, Nicola Marzari, and Ivano Tavernelli, "Effective calculation of the Green's function in the time domain on near-term quantum processors", Physical Review Research 4 4, 043038 (2022).

[55] Refik Mansuroglu, Timo Eckstein, Ludwig Nützel, Samuel A Wilkinson, and Michael J Hartmann, "Variational Hamiltonian simulation for translational invariant systems via classical pre-processing", Quantum Science and Technology 8 2, 025006 (2023).

[56] Benedikt Fauseweh, "Quantum many-body simulations on digital quantum computers: State-of-the-art and future challenges", Nature Communications 15 1, 2123 (2024).

[57] Tobias Haug and M. S. Kim, "Natural parametrized quantum circuit", Physical Review A 106 5, 052611 (2022).

[58] Maurits S. J. Tepaske and David J. Luitz, "Compressed quantum error mitigation", Physical Review B 107 20, L201114 (2023).

[59] David Linteau, Stefano Barison, Netanel H. Lindner, and Giuseppe Carleo, "Adaptive projected variational quantum dynamics", Physical Review Research 6 2, 023130 (2024).

[60] José D. Guimarães, Mikhail I. Vasilevskiy, and Luís S. Barbosa, "Digital quantum simulation of non-perturbative dynamics of open systems with orthogonal polynomials", Quantum 8, 1242 (2024).

[61] Kian Hwee Lim, Tobias Haug, Leong Chuan Kwek, and Kishor Bharti, "Fast-forwarding with NISQ processors without feedback loop", Quantum Science and Technology 7 1, 015001 (2022).

[62] Lindsay Bassman Oftelie, Connor Powers, and Wibe A. De Jong, "ArQTiC: A Full-stack Software Package for Simulating Materials on Quantum Computers", ACM Transactions on Quantum Computing 3 3, 1 (2022).

[63] Kishor Bharti, Alba Cervera-Lierta, Thi Ha Kyaw, Tobias Haug, Sumner Alperin-Lea, Abhinav Anand, Matthias Degroote, Hermanni Heimonen, Jakob S. Kottmann, Tim Menke, Wai-Keong Mok, Sukin Sim, Leong-Chuan Kwek, and Alán Aspuru-Guzik, "Noisy intermediate-scale quantum algorithms", Reviews of Modern Physics 94 1, 015004 (2022).

[64] Takanori Nishi and Kaoru Yamanouchi, "Simulation of a spin-boson model by iterative optimization of a parametrized quantum circuit", AVS Quantum Science 6 2, 023801 (2024).

[65] Jonathan Wei Zhong Lau, Tobias Haug, Leong Chuan Kwek, and Kishor Bharti, "NISQ Algorithm for Hamiltonian simulation via truncated Taylor series", SciPost Physics 12 4, 122 (2022).

[66] Yong-Xin Yao, Niladri Gomes, Feng Zhang, Cai-Zhuang Wang, Kai-Ming Ho, Thomas Iadecola, and Peter P. Orth, "Adaptive Variational Quantum Dynamics Simulations", PRX Quantum 2 3, 030307 (2021).

[67] Tobias Haug and M. S. Kim, "Optimal training of variational quantum algorithms without barren plateaus", arXiv:2104.14543, (2021).

[68] Mario Motta and Julia Rice, "Emerging quantum computing algorithms for quantum chemistry", arXiv:2109.02873, (2021).

[69] Paolo P. Mazza, Dominik Zietlow, Federico Carollo, Sabine Andergassen, Georg Martius, and Igor Lesanovsky, "Machine learning time-local generators of open quantum dynamics", Physical Review Research 3 2, 023084 (2021).

[70] Yu-Qin Chen, Shi-Xin Zhang, Chang-Yu Hsieh, and Shengyu Zhang, "A non-Hermitian Ground State Searching Algorithm Enhanced by Variational Toolbox", arXiv:2210.09007, (2022).

[71] Rouven Koch and Jose L. Lado, "Neural network enhanced hybrid quantum many-body dynamical distributions", Physical Review Research 3 3, 033102 (2021).

[72] Antoine Michel, "Quantum simulation for strongly interacting fermions with neutral atoms array: towards the simulation of materials of interest", arXiv:2406.13343, (2024).

[73] Sara Santos, Xinyu Song, and Vincenzo Savona, "Low-Rank Variational Quantum Algorithm for the Dynamics of Open Quantum Systems", arXiv:2403.05908, (2024).

The above citations are from Crossref's cited-by service (last updated successfully 2024-07-15 11:18:39) and SAO/NASA ADS (last updated successfully 2024-07-15 11:18:40). The list may be incomplete as not all publishers provide suitable and complete citation data.