Faster quantum simulation by randomization

Andrew M. Childs; Aaron Ostrander; Yuan Su

doi:10.22331/q-2019-09-02-182

Faster quantum simulation by randomization

Andrew M. Childs^1,2,3, Aaron Ostrander^2,3,4, and Yuan Su^1,2,3

¹Department of Computer Science, University of Maryland
²Institute for Advanced Computer Studies, University of Maryland
³Joint Center for Quantum Information and Computer Science, University of Maryland
⁴Department of Physics, University of Maryland

Published:	2019-09-02, volume 3, page 182
Eprint:	arXiv:1805.08385v2
Doi:	https://doi.org/10.22331/q-2019-09-02-182
Citation:	Quantum 3, 182 (2019).

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Abstract

Product formulas can be used to simulate Hamiltonian dynamics on a quantum computer by approximating the exponential of a sum of operators by a product of exponentials of the individual summands. This approach is both straightforward and surprisingly efficient. We show that by simply randomizing how the summands are ordered, one can prove stronger bounds on the quality of approximation for product formulas of any given order, and thereby give more efficient simulations. Indeed, we show that these bounds can be asymptotically better than previous bounds that exploit commutation between the summands, despite using much less information about the structure of the Hamiltonian. Numerical evidence suggests that the randomized approach has better empirical performance as well.

► BibTeX data

@article{Childs2019fasterquantum,
  doi = {10.22331/q-2019-09-02-182},
  url = {https://doi.org/10.22331/q-2019-09-02-182},
  title = {Faster quantum simulation by randomization},
  author = {Childs, Andrew M. and Ostrander, Aaron and Su, Yuan},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {3},
  pages = {182},
  month = sep,
  year = {2019}
}

► References

[1] Dorit Aharonov and Amnon Ta-Shma. Adiabatic quantum state generation and statistical zero knowledge. In Proceedings of the 35th ACM Symposium on Theory of Computing, pages 20–29, 2003. 10.1145/780542.780546. arXiv:quant-ph/0301023.
https://doi.org/10.1145/780542.780546
arXiv:quant-ph/0301023

[2] Ryan Babbush, Jarrod McClean, Dave Wecker, Alán Aspuru-Guzik, and Nathan Wiebe. Chemical basis of Trotter-Suzuki errors in quantum chemistry simulation. Physical Review A, 91: 022311, 2015. 10.1103/PhysRevA.91.022311. arXiv:1410.8159.
https://doi.org/10.1103/PhysRevA.91.022311
arXiv:1410.8159

[3] R. Barends, L. Lamata, J. Kelly, L. García-Álvarez, A. G. Fowler, A Megrant, E Jeffrey, T. C. White, D. Sank, J. Y. Mutus, B. Campbell, Yu Chen, Z. Chen, B. Chiaro, A. Dunsworth, I.-C. Hoi, C. Neill, P. J. J. O'Malley, C. Quintana, P. Roushan, A. Vainsencher, J. Wenner, E. Solano, and John M. Martinis. Digital quantum simulation of fermionic models with a superconducting circuit. Nature Communications, 6: 7654, 2015. 10.1038/ncomms8654. arXiv:1501.07703.
https://doi.org/10.1038/ncomms8654
arXiv:1501.07703

[4] Dominic W. Berry and Andrew M. Childs. Black-box Hamiltonian simulation and unitary implementation. Quantum Information and Computation, 12 (1-2): 29–62, 2012. arXiv:0910.4157. 10.26421/QIC12.1-2.
https://doi.org/10.26421/QIC12.1-2
arXiv:0910.4157

[5] Dominic W. Berry, Graeme Ahokas, Richard Cleve, and Barry C. Sanders. Efficient quantum algorithms for simulating sparse Hamiltonians. Communications in Mathematical Physics, 270 (2): 359–371, 2007. 10.1007/s00220-006-0150-x. arXiv:quant-ph/0508139.
https://doi.org/10.1007/s00220-006-0150-x
arXiv:quant-ph/0508139

[6] Dominic W. Berry, Andrew M. Childs, Richard Cleve, Robin Kothari, and Rolando D. Somma. Exponential improvement in precision for simulating sparse Hamiltonians. In Proceedings of the 46th ACM Symposium on Theory of Computing, pages 283–292, 2014. 10.1145/2591796.2591854. arXiv:1312.1414.
https://doi.org/10.1145/2591796.2591854
arXiv:1312.1414

[7] Dominic W. Berry, Andrew M. Childs, Richard Cleve, Robin Kothari, and Rolando D. Somma. Simulating Hamiltonian dynamics with a truncated Taylor series. Physical Review Letters, 114 (9): 090502, 2015a. 10.1103/PhysRevLett.114.090502. arXiv:1412.4687.
https://doi.org/10.1103/PhysRevLett.114.090502
arXiv:1412.4687

[8] Dominic W. Berry, Andrew M. Childs, and Robin Kothari. Hamiltonian simulation with nearly optimal dependence on all parameters. In Proceedings of the 56th IEEE Symposium on Foundations of Computer Science, pages 792–809, 2015b. 10.1109/FOCS.2015.54. arXiv:1501.01715.
https://doi.org/10.1109/FOCS.2015.54
arXiv:1501.01715

[9] Dominic W. Berry, Andrew M. Childs, Aaron Ostrander, and Guoming Wang. Quantum algorithm for linear differential equations with exponentially improved dependence on precision. Communications in Mathematical Physics, 356: 1057–1081, 2017. 10.1007/s00220-017-3002-y. arXiv:1701.03684.
https://doi.org/10.1007/s00220-017-3002-y
arXiv:1701.03684

[10] Dominic W. Berry, Andrew M. Childs, Yuan Su, Xin Wang, and Nathan Wiebe. Time-dependent Hamiltonian simulation with $L^1$-norm scaling, 2019. arXiv:1906.07115.
arXiv:1906.07115

[11] Fernando G. S. L. Brandao and Krysta M. Svore. Quantum speed-ups for solving semidefinite programs. In Proceedings of the 58th IEEE Symposium on Foundations of Computer Science, pages 415–426, 2017. 10.1109/FOCS.2017.45. arXiv:1609.05537.
https://doi.org/10.1109/FOCS.2017.45
arXiv:1609.05537

[12] Kenneth R. Brown, Robert J. Clark, and Isaac L. Chuang. Limitations of quantum simulation examined by simulating a pairing Hamiltonian using nuclear magnetic resonance. Physical Review Letters, 97: 050504, 2006. 10.1103/PhysRevLett.97.050504. arXiv:quant-ph/0601021.
https://doi.org/10.1103/PhysRevLett.97.050504
arXiv:quant-ph/0601021

[13] Earl Campbell. Shorter gate sequences for quantum computing by mixing unitaries. Physical Review A, 95: 042306, Apr 2017. 10.1103/PhysRevA.95.042306. arXiv:1612.02689.
https://doi.org/10.1103/PhysRevA.95.042306
arXiv:1612.02689

[14] Earl Campbell. Random compiler for fast Hamiltonian simulation. Physical Review Letters, 123: 070503, Aug 2019. 10.1103/PhysRevLett.123.070503. arXiv:1811.08017.
https://doi.org/10.1103/PhysRevLett.123.070503
arXiv:1811.08017

[15] Andrew M. Childs and Yuan Su. Nearly optimal lattice simulation by product formulas. Physical Review Letters, 123: 050503, Aug 2019. 10.1103/PhysRevLett.123.050503. arXiv:1901.00564.
https://doi.org/10.1103/PhysRevLett.123.050503
arXiv:1901.00564

[16] Andrew M. Childs, Richard Cleve, Enrico Deotto, Edward Farhi, Sam Gutmann, and Daniel A. Spielman. Exponential algorithmic speedup by quantum walk. In Proceedings of the 35th ACM Symposium on Theory of Computing, pages 59–68, 2003. 10.1145/780542.780552. arXiv:quant-ph/0209131.
https://doi.org/10.1145/780542.780552
arXiv:quant-ph/0209131

[17] Andrew M. Childs, Dmitri Maslov, Yunseong Nam, Neil J. Ross, and Yuan Su. Toward the first quantum simulation with quantum speedup. Proceedings of the National Academy of Sciences, 115 (38): 9456–9461, 2018. 10.1073/pnas.1801723115. arXiv:1711.10980.
https://doi.org/10.1073/pnas.1801723115
arXiv:1711.10980

[18] Edward Farhi, Jeffrey Goldstone, and Sam Gutmann. A quantum algorithm for the Hamiltonian NAND tree. Theory of Computing, 4 (1): 169–190, 2008. 10.4086/toc.2008.v004a008.
https://doi.org/10.4086/toc.2008.v004a008

[19] Richard P. Feynman. Simulating physics with computers. International Journal of Theoretical Physics, 21 (6-7): 467–488, 1982. 10.1007/BF02650179.
https://doi.org/10.1007/BF02650179

[20] Jeongwan Haah, Matthew B. Hastings, Robin Kothari, and Guang Hao Low. Quantum algorithm for simulating real time evolution of lattice Hamiltonians. In 2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS), pages 350–360, Oct 2018. 10.1109/FOCS.2018.00041. arXiv:1801.03922.
https://doi.org/10.1109/FOCS.2018.00041
arXiv:1801.03922

[21] Aram W. Harrow, Avinatan Hassidim, and Seth Lloyd. Quantum algorithm for linear systems of equations. Physical Review Letters, 103 (15): 150502, 2009. 10.1103/PhysRevLett.103.150502. arXiv:0811.3171.
https://doi.org/10.1103/PhysRevLett.103.150502
arXiv:0811.3171

[22] Matthew B. Hastings. Turning gate synthesis errors into incoherent errors. Quantum Information and Computation, 17 (5-6): 488–494, 2017. arXiv:1612.01011.
arXiv:1612.01011

[23] Stephen P. Jordan, Keith S. M. Lee, and John Preskill. Quantum algorithms for quantum field theories. Science, 336 (6085): 1130–1133, 2012. 10.1126/science.1217069. arXiv:1111.3633.
https://doi.org/10.1126/science.1217069
arXiv:1111.3633

[24] B. P. Lanyon, C. Hempel, D. Nigg, M. Müller, R. Gerritsma, F. Zähringer, P. Schindler, J. T. Barreiro, M. Rambach, G. Kirchmair, M. Hennrich, P. Zoller, R. Blatt, and C. F. Roos. Universal digital quantum simulation with trapped ions. Science, 334 (6052): 57–61, 2011. 10.1126/science.1208001. arXiv:1109.1512.
https://doi.org/10.1126/science.1208001
arXiv:1109.1512

[25] Seth Lloyd. Universal quantum simulators. Science, 273 (5278): 1073–1078, 1996. 10.1126/science.273.5278.1073.
https://doi.org/10.1126/science.273.5278.1073

[26] Guang Hao Low and Isaac L. Chuang. Optimal Hamiltonian simulation by quantum signal processing. Physical Review Letters, 118: 010501, 2017. 10.1103/PhysRevLett.118.010501. arXiv:1606.02685.
https://doi.org/10.1103/PhysRevLett.118.010501
arXiv:1606.02685

[27] Guang Hao Low and Isaac L. Chuang. Hamiltonian Simulation by Qubitization. Quantum, 3: 163, July 2019. 10.22331/q-2019-07-12-163. arXiv:1610.06546.
https://doi.org/10.22331/q-2019-07-12-163
arXiv:1610.06546

[28] Guang Hao Low, Vadym Kliuchnikov, and Nathan Wiebe. Well-conditioned multiproduct Hamiltonian simulation, 2019. arXiv:1907.11679.
arXiv:1907.11679

[29] David Poulin, Angie Qarry, Rolando D. Somma, and Frank Verstraete. Quantum simulation of time-dependent Hamiltonians and the convenient illusion of Hilbert space. Physical Review Letters, 106 (17): 170501, 2011. 10.1103/PhysRevLett.106.170501. arXiv:1102.1360.
https://doi.org/10.1103/PhysRevLett.106.170501
arXiv:1102.1360

[30] David Poulin, Matthew B. Hastings, Dave Wecker, Nathan Wiebe, Andrew C. Doherty, and Matthias Troyer. The Trotter step size required for accurate quantum simulation of quantum chemistry. Quantum Information and Computation, 15 (5-6): 361–384, 2015. arXiv:1406.4920.
arXiv:1406.4920

[31] Sadegh Raeisi, Nathan Wiebe, and Barry C. Sanders. Quantum-circuit design for efficient simulations of many-body quantum dynamics. New Journal of Physics, 14: 103017, 2012. 10.1088/1367-2630/14/10/103017. arXiv:1108.4318.
https://doi.org/10.1088/1367-2630/14/10/103017
arXiv:1108.4318

[32] Markus Reiher, Nathan Wiebe, Krysta M. Svore, Dave Wecker, and Matthias Troyer. Elucidating reaction mechanisms on quantum computers. Proceedings of the National Academy of Sciences, 114 (29): 7555–7560, 2017. 10.1073/pnas.1619152114. arXiv:1605.03590.
https://doi.org/10.1073/pnas.1619152114
arXiv:1605.03590

[33] Masuo Suzuki. General theory of fractal path integrals with applications to many-body theories and statistical physics. Journal of Mathematical Physics, 32 (2): 400–407, 1991. 10.1063/1.529425.
https://doi.org/10.1063/1.529425

[34] John Watrous. Simpler semidefinite programs for completely bounded norms. Chicago Journal of Theoretical Computer Science, 2013 (8), 2013. 10.4086/cjtcs.2013.008.
https://doi.org/10.4086/cjtcs.2013.008

[35] John Watrous. The Theory of Quantum Information. Cambridge University Press, 2018. 10.1017/9781316848142.
https://doi.org/10.1017/9781316848142

[36] Dave Wecker, Bela Bauer, Bryan K. Clark, Matthew B. Hastings, and Matthias Troyer. Gate count estimates for performing quantum chemistry on small quantum computers. Physical Review A, 90: 022305, 2014. 10.1103/PhysRevA.90.022305. arXiv:1312.1695.
https://doi.org/10.1103/PhysRevA.90.022305
arXiv:1312.1695

[37] Chi Zhang. Randomized algorithms for Hamiltonian simulation. In Leszek Plaskota and Henryk Woźniakowski, editors, Monte Carlo and Quasi-Monte Carlo Methods 2010, pages 709–719, Berlin, Heidelberg, 2012. Springer Berlin Heidelberg. ISBN 978-3-642-27440-4. 10.1007/978-3-642-27440-4_42.
https://doi.org/10.1007/978-3-642-27440-4_42

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[1] Daniel Burgarth, Paolo Facchi, Giovanni Gramegna, and Kazuya Yuasa, "One bound to rule them all: from Adiabatic to Zeno", Quantum 6, 737 (2022).

[2] William J. Huggins, Sam McArdle, Thomas E. O’Brien, Joonho Lee, Nicholas C. Rubin, Sergio Boixo, K. Birgitta Whaley, Ryan Babbush, and Jarrod R. McClean, "Virtual Distillation for Quantum Error Mitigation", Physical Review X 11 4, 041036 (2021).

[3] David Layden, "First-Order Trotter Error from a Second-Order Perspective", Physical Review Letters 128 21, 210501 (2022).

[4] Teague Tomesh, Kaiwen Gui, Pranav Gokhale, Yunong Shi, Frederic T. Chong, Margaret Martonosi, and Martin Suchara, 2021 International Conference on Rebooting Computing (ICRC) 1 (2021) ISBN:978-1-6654-2332-8.

[5] Troy J. Sewell and Christopher David White, "Mana and thermalization: Probing the feasibility of near-Clifford Hamiltonian simulation", Physical Review B 106 12, 125130 (2022).

[6] Andrew M. Childs, Yuan Su, Minh C. Tran, Nathan Wiebe, and Shuchen Zhu, "Theory of Trotter Error with Commutator Scaling", Physical Review X 11 1, 011020 (2021).

[7] Finn Lasse Buessen, Dvira Segal, and Ilia Khait, "Simulating time evolution on distributed quantum computers", Physical Review Research 5 2, L022003 (2023).

[8] Mark Steudtner and Stephanie Wehner, "Estimating exact energies in quantum simulation without Toffoli gates", Physical Review A 101 5, 052329 (2020).

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

[10] Mario Motta and Julia E. Rice, "Emerging quantum computing algorithms for quantum chemistry", WIREs Computational Molecular Science 12 3, e1580 (2022).

[11] Nicolas P. D. Sawaya, Tim Menke, Thi Ha Kyaw, Sonika Johri, Alán Aspuru-Guzik, and Gian Giacomo Guerreschi, "Resource-efficient digital quantum simulation of d-level systems for photonic, vibrational, and spin-s Hamiltonians", npj Quantum Information 6 1, 49 (2020).

[12] Natalie Klco, Alessandro Roggero, and Martin J Savage, "Standard model physics and the digital quantum revolution: thoughts about the interface", Reports on Progress in Physics 85 6, 064301 (2022).

[13] Tyson Jones and Simon C. Benjamin, "Robust quantum compilation and circuit optimisation via energy minimisation", Quantum 6, 628 (2022).

[14] Kenneth Choi, Dean Lee, Joey Bonitati, Zhengrong Qian, and Jacob Watkins, "Rodeo Algorithm for Quantum Computing", Physical Review Letters 127 4, 040505 (2021).

[15] Yuta Kikuchi, Conor Mc Keever, Luuk Coopmans, Michael Lubasch, and Marcello Benedetti, "Realization of quantum signal processing on a noisy quantum computer", npj Quantum Information 9 1, 93 (2023).

[16] Tyson Jones and Simon Benjamin, "QuESTlink—Mathematica embiggened by a hardware-optimised quantum emulator* ", Quantum Science and Technology 5 3, 034012 (2020).

[17] Suguru Endo, Jinzhao Sun, Ying Li, Simon C. Benjamin, and Xiao Yuan, "Variational Quantum Simulation of General Processes", Physical Review Letters 125 1, 010501 (2020).

[18] 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).

[19] Bela Bauer, Sergey Bravyi, Mario Motta, and Garnet Kin-Lic Chan, "Quantum Algorithms for Quantum Chemistry and Quantum Materials Science", Chemical Reviews 120 22, 12685 (2020).

[20] Kaoru Mizuta, Yuya O. Nakagawa, Kosuke Mitarai, and Keisuke Fujii, "Local Variational Quantum Compilation of Large-Scale Hamiltonian Dynamics", PRX Quantum 3 4, 040302 (2022).

[21] Mekena Metcalf, Emma Stone, Katherine Klymko, Alexander F Kemper, Mohan Sarovar, and Wibe A de Jong, "Quantum Markov chain Monte Carlo with digital dissipative dynamics on quantum computers", Quantum Science and Technology 7 2, 025017 (2022).

[22] Matthew Hagan and Nathan Wiebe, "Composite Quantum Simulations", Quantum 7, 1181 (2023).

[23] Zi-Jian Zhang, Jinzhao Sun, Xiao Yuan, and Man-Hong Yung, "Low-Depth Hamiltonian Simulation by an Adaptive Product Formula", Physical Review Letters 130 4, 040601 (2023).

[24] Jacob Bringewatt and Zohreh Davoudi, "Parallelization techniques for quantum simulation of fermionic systems", Quantum 7, 975 (2023).

[25] Oriel Kiss, Michele Grossi, and Alessandro Roggero, "Importance sampling for stochastic quantum simulations", Quantum 7, 977 (2023).

[26] Manuel G. Algaba, Mario Ponce-Martinez, Carlos Munuera-Javaloy, Vicente Pina-Canelles, Manish J. Thapa, Bruno G. Taketani, Martin Leib, Inés de Vega, Jorge Casanova, and Hermanni Heimonen, "Co-Design quantum simulation of nanoscale NMR", Physical Review Research 4 4, 043089 (2022).

[27] Chi-Fang Chen, Hsin-Yuan Huang, Richard Kueng, and Joel A. Tropp, "Concentration for Random Product Formulas", PRX Quantum 2 4, 040305 (2021).

[28] Simon V. Mathis, Guglielmo Mazzola, and Ivano Tavernelli, "Toward scalable simulations of lattice gauge theories on quantum computers", Physical Review D 102 9, 094501 (2020).

[29] Xiantao Li, "Some error analysis for the quantum phase estimation algorithms", Journal of Physics A: Mathematical and Theoretical 55 32, 325303 (2022).

[30] 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).

[31] Johann Ostmeyer, "Optimised Trotter decompositions for classical and quantum computing", Journal of Physics A: Mathematical and Theoretical 56 28, 285303 (2023).

[32] 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).

[33] Paul K. Faehrmann, Mark Steudtner, Richard Kueng, Maria Kieferova, and Jens Eisert, "Randomizing multi-product formulas for Hamiltonian simulation", Quantum 6, 806 (2022).

[34] Sam McArdle, Suguru Endo, Alán Aspuru-Guzik, Simon C. Benjamin, and Xiao Yuan, "Quantum computational chemistry", Reviews of Modern Physics 92 1, 015003 (2020).

[35] Lingling Lao and Dan E. Browne, Proceedings of the 49th Annual International Symposium on Computer Architecture 351 (2022) ISBN:9781450386104.

[36] Valentina Amitrano, Alessandro Roggero, Piero Luchi, Francesco Turro, Luca Vespucci, and Francesco Pederiva, "Trapped-ion quantum simulation of collective neutrino oscillations", Physical Review D 107 2, 023007 (2023).

[37] Dominic W. Berry, Andrew M. Childs, Yuan Su, Xin Wang, and Nathan Wiebe, "Time-dependent Hamiltonian simulation withL1-norm scaling", Quantum 4, 254 (2020).

[38] Mingxia Huo and Ying Li, "Error-resilient Monte Carlo quantum simulation of imaginary time", Quantum 7, 916 (2023).

[39] Woo-Ram Lee, Zhangjie Qin, Robert Raussendorf, Eran Sela, and V. W. Scarola, "Measurement-based time evolution for quantum simulation of fermionic systems", Physical Review Research 4 3, L032013 (2022).

[40] Lindsay Bassman, Miroslav Urbanek, Mekena Metcalf, Jonathan Carter, Alexander F Kemper, and Wibe A de Jong, "Simulating quantum materials with digital quantum computers", Quantum Science and Technology 6 4, 043002 (2021).

[41] Richard Meister, Simon C. Benjamin, and Earl T. Campbell, "Tailoring Term Truncations for Electronic Structure Calculations Using a Linear Combination of Unitaries", Quantum 6, 637 (2022).

[42] Ian D. Kivlichan, Craig Gidney, Dominic W. Berry, Nathan Wiebe, Jarrod McClean, Wei Sun, Zhang Jiang, Nicholas Rubin, Austin Fowler, Alán Aspuru-Guzik, Hartmut Neven, and Ryan Babbush, "Improved Fault-Tolerant Quantum Simulation of Condensed-Phase Correlated Electrons via Trotterization", Quantum 4, 296 (2020).

[43] Changhao Yi and Elizabeth Crosson, "Spectral analysis of product formulas for quantum simulation", npj Quantum Information 8 1, 37 (2022).

[44] Dong An, Di Fang, and Lin Lin, "Time-dependent unbounded Hamiltonian simulation with vector norm scaling", Quantum 5, 459 (2021).

[45] Yulong Dong, K. Birgitta Whaley, and Lin Lin, "A quantum hamiltonian simulation benchmark", npj Quantum Information 8 1, 131 (2022).

[46] Dong An, Di Fang, and Lin Lin, "Time-dependent Hamiltonian Simulation of Highly Oscillatory Dynamics and Superconvergence for Schrödinger Equation", Quantum 6, 690 (2022).

[47] Takuya Hatomura, "State-dependent error bound for digital quantum simulation of driven systems", Physical Review A 105 5, L050601 (2022).

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[50] Nicolas PD Sawaya, Albert T Schmitz, and Stuart Hadfield, "Encoding trade-offs and design toolkits in quantum algorithms for discrete optimization: coloring, routing, scheduling, and other problems", Quantum 7, 1111 (2023).

[51] Thais L. Silva, Márcio M. Taddei, Stefano Carrazza, and Leandro Aolita, "Fragmented imaginary-time evolution for early-stage quantum signal processors", Scientific Reports 13 1, 18258 (2023).

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[54] Lane G. Gunderman, "Transforming collections of Pauli operators into equivalent collections of Pauli operators over minimal registers", Physical Review A 107 6, 062416 (2023).

[55] Suguru Endo, Zhenyu Cai, Simon C. Benjamin, and Xiao Yuan, "Hybrid Quantum-Classical Algorithms and Quantum Error Mitigation", Journal of the Physical Society of Japan 90 3, 032001 (2021).

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[58] Yifan Sun, Jun-Yi Zhang, Mark S Byrd, and Lian-Ao Wu, "Trotterized adiabatic quantum simulation and its application to a simple all-optical system", New Journal of Physics 22 5, 053012 (2020).

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

[62] Dean Lee, "Quantum techniques for eigenvalue problems", The European Physical Journal A 59 11, 275 (2023).

[63] Minh C. Tran, Yuan Su, Daniel Carney, and Jacob M. Taylor, "Faster Digital Quantum Simulation by Symmetry Protection", PRX Quantum 2 1, 010323 (2021).

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[65] Yingkai Ouyang, David R. White, and Earl T. Campbell, "Compilation by stochastic Hamiltonian sparsification", Quantum 4, 235 (2020).

[66] Qi Zhao and Xiao Yuan, "Exploiting anticommutation in Hamiltonian simulation", Quantum 5, 534 (2021).

[67] Ryan Shaffer, Hang Ren, Emiliia Dyrenkova, Christopher G. Yale, Daniel S. Lobser, Ashlyn D. Burch, Matthew N. H. Chow, Melissa C. Revelle, Susan M. Clark, and Hartmut Häffner, "Sample-efficient verification of continuously-parameterized quantum gates for small quantum processors", Quantum 7, 997 (2023).

[68] Thi Ha Kyaw, Tim Menke, Sukin Sim, Abhinav Anand, Nicolas P.D. Sawaya, William D. Oliver, Gian Giacomo Guerreschi, and Alán Aspuru-Guzik, "Quantum Computer-Aided Design: Digital Quantum Simulation of Quantum Processors", Physical Review Applied 16 4, 044042 (2021).

[69] Yi-Tong Zou, Yu-Jiao Bo, and Ji-Chong Yang, "Optimize quantum simulation using a force-gradient integrator", EPL (Europhysics Letters) 135 1, 10004 (2021).

[70] Yi-Xiang Liu, Jordan Hines, Zhi Li, Ashok Ajoy, and Paola Cappellaro, "High-fidelity Trotter formulas for digital quantum simulation", Physical Review A 102 1, 010601 (2020).

[71] Alexander J. Buser, Tanmoy Bhattacharya, Lukasz Cincio, and Rajan Gupta, "State preparation and measurement in a quantum simulation of the O(3) sigma model", Physical Review D 102 11, 114514 (2020).

[72] Di Fang, Lin Lin, and Yu Tong, "Time-marching based quantum solvers for time-dependent linear differential equations", Quantum 7, 955 (2023).

[73] Andrea Agazzi, Jonathan C. Mattingly, and Omar Melikechi, "Random Splitting of Fluid Models: Unique Ergodicity and Convergence", Communications in Mathematical Physics 401 1, 497 (2023).

[74] Alexander M. Dalzell, Sam McArdle, Mario Berta, Przemyslaw Bienias, Chi-Fang Chen, András Gilyén, Connor T. Hann, Michael J. Kastoryano, Emil T. Khabiboulline, Aleksander Kubica, Grant Salton, Samson Wang, and Fernando G. S. L. Brandão, "Quantum algorithms: A survey of applications and end-to-end complexities", arXiv:2310.03011, (2023).

[75] Earl Campbell, "Random Compiler for Fast Hamiltonian Simulation", Physical Review Letters 123 7, 070503 (2019).

[76] Sam McArdle, Suguru Endo, Alan Aspuru-Guzik, Simon Benjamin, and Xiao Yuan, "Quantum computational chemistry", arXiv:1808.10402, (2018).

[77] Andrew M. Childs and Yuan Su, "Nearly Optimal Lattice Simulation by Product Formulas", Physical Review Letters 123 5, 050503 (2019).

[78] Andrew M. Childs, Yuan Su, Minh C. Tran, Nathan Wiebe, and Shuchen Zhu, "A Theory of Trotter Error", arXiv:1912.08854, (2019).

[79] Bryan O'Gorman, William J. Huggins, Eleanor G. Rieffel, and K. Birgitta Whaley, "Generalized swap networks for near-term quantum computing", arXiv:1905.05118, (2019).

[80] Suguru Endo, Qi Zhao, Ying Li, Simon Benjamin, and Xiao Yuan, "Mitigating algorithmic errors in a Hamiltonian simulation", Physical Review A 99 1, 012334 (2019).

[81] Mark Steudtner and Stephanie Wehner, "Quantum codes for quantum simulation of fermions on a square lattice of qubits", Physical Review A 99 2, 022308 (2019).

[82] Hrant Gharibyan, Masanori Hanada, Masazumi Honda, and Junyu Liu, "Toward simulating superstring/M-theory on a quantum computer", Journal of High Energy Physics 2021 7, 140 (2021).

[83] Dong An, Jin-Peng Liu, Daochen Wang, and Qi Zhao, "A theory of quantum differential equation solvers: limitations and fast-forwarding", arXiv:2211.05246, (2022).

[84] Cahit Kargi, Juan Pablo Dehollain, Lukas M. Sieberer, Fabio Henriques, Tobias Olsacher, Philipp Hauke, Markus Heyl, Peter Zoller, and Nathan K. Langford, "Quantum Chaos and Universal Trotterisation Behaviours in Digital Quantum Simulations", arXiv:2110.11113, (2021).

[85] Minh C. Tran, Yuan Su, Daniel Carney, and Jacob M. Taylor, "Faster Digital Quantum Simulation by Symmetry Protection", arXiv:2006.16248, (2020).

[86] Mingxia Huo and Ying Li, "Error-resilient Monte Carlo quantum simulation of imaginary time", arXiv:2109.07807, (2021).

[87] Seth Lloyd, Bobak T. Kiani, David R. M. Arvidsson-Shukur, Samuel Bosch, Giacomo De Palma, William M. Kaminsky, Zi-Wen Liu, and Milad Marvian, "Hamiltonian singular value transformation and inverse block encoding", arXiv:2104.01410, (2021).

[88] Zhicheng Zhang, Qisheng Wang, and Mingsheng Ying, "Parallel Quantum Algorithm for Hamiltonian Simulation", arXiv:2105.11889, (2021).

[89] Ian D. Kivlichan, Christopher E. Granade, and Nathan Wiebe, "Phase estimation with randomized Hamiltonians", arXiv:1907.10070, (2019).

[90] Suguru Endo, Qi Zhao, Ying Li, Simon Benjamin, and Xiao Yuan, "Mitigating algorithmic errors in Hamiltonian simulation", arXiv:1808.03623, (2018).

[91] Seth Lloyd and Reevu Maity, "Efficient implementation of unitary transformations", arXiv:1901.03431, (2019).

[92] Benjamin D. M. Jones, George O. O'Brien, David R. White, Earl T. Campbell, and John A. Clark, "Optimising Trotter-Suzuki Decompositions for Quantum Simulation Using Evolutionary Strategies", arXiv:1904.01336, (2019).

[93] Jin-Peng Liu and Lin Lin, "Dense outputs from quantum simulations", arXiv:2307.14441, (2023).

[94] Sam McArdle, "Learning from Physics Experiments with Quantum Computers: Applications in Muon Spectroscopy", PRX Quantum 2 2, 020349 (2021).

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