Composite Quantum Simulations

Matthew Hagan¹ and Nathan Wiebe^2,3,4

¹Department of Physics, University of Toronto, Toronto ON, Canada
²Department of Computer Science, University of Toronto, Toronto ON, Canada
³Pacific Northwest National Laboratory, Richland Wa, USA
⁴Canadian Institute for Advanced Study, Toronto ON, Canada

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Abstract

In this paper we provide a framework for combining multiple quantum simulation methods, such as Trotter-Suzuki formulas and QDrift into a single Composite channel that builds upon older coalescing ideas for reducing gate counts. The central idea behind our approach is to use a partitioning scheme that allocates a Hamiltonian term to the Trotter or QDrift part of a channel within the simulation. This allows us to simulate small but numerous terms using QDrift while simulating the larger terms using a high-order Trotter-Suzuki formula. We prove rigorous bounds on the diamond distance between the Composite channel and the ideal simulation channel and show under what conditions the cost of implementing the Composite channel is asymptotically upper bounded by the methods that comprise it for both probabilistic partitioning of terms and deterministic partitioning. Finally, we discuss strategies for determining partitioning schemes as well as methods for incorporating different simulation methods within the same framework.

► BibTeX data

@article{Hagan2023compositequantum, doi = {10.22331/q-2023-11-14-1181}, url = {https://doi.org/10.22331/q-2023-11-14-1181}, title = {Composite {Q}uantum {S}imulations}, author = {Hagan, Matthew and Wiebe, Nathan}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{“{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {7}, pages = {1181}, month = nov, year = {2023}<br /> }

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Cited by

[1] 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).

[2] Etienne Granet and Henrik Dreyer, “Continuous Hamiltonian dynamics on noisy digital quantum computers without Trotter error”, arXiv:2308.03694, (2023).

[3] Almudena Carrera Vazquez, Daniel J. Egger, David Ochsner, and Stefan Woerner, “Well-conditioned multi-product formulas for hardware-friendly Hamiltonian simulation”, Quantum 7, 1067 (2023).

[4] Matthew Pocrnic, Matthew Hagan, Juan Carrasquilla, Dvira Segal, and Nathan Wiebe, “Composite QDrift-Product Formulas for Quantum and Classical Simulations in Real and Imaginary Time”, arXiv:2306.16572, (2023).

[5] Nicholas H. Stair, Cristian L. Cortes, Robert M. Parrish, Jeffrey Cohn, and Mario Motta, “Stochastic quantum Krylov protocol with double-factorized Hamiltonians”, Physical Review A 107 3, 032414 (2023).

[6] Gumaro Rendon, Jacob Watkins, and Nathan Wiebe, “Improved Accuracy for Trotter Simulations Using Chebyshev Interpolation”, arXiv:2212.14144, (2022).

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

[8] Maximilian Amsler, Peter Deglmann, Matthias Degroote, Michael P. Kaicher, Matthew Kiser, Michael Kühn, Chandan Kumar, Andreas Maier, Georgy Samsonidze, Anna Schroeder, Michael Streif, Davide Vodola, and Christopher Wever, “Quantum-enhanced quantum Monte Carlo: an industrial view”, arXiv:2301.11838, (2023).

[9] Alireza Tavanfar, S. Alipour, and A. T. Rezakhani, “Does Quantum Mechanics Breed Larger, More Intricate Quantum Theories? The Case for Experience-Centric Quantum Theory and the Interactome of Quantum Theories”, arXiv:2308.02630, (2023).

[10] Pei Zeng, Jinzhao Sun, Liang Jiang, and Qi Zhao, “Simple and high-precision Hamiltonian simulation by compensating Trotter error with linear combination of unitary operations”, arXiv:2212.04566, (2022).

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

[12] Lea M. Trenkwalder, Eleanor Scerri, Thomas E. O’Brien, and Vedran Dunjko, “Compilation of product-formula Hamiltonian simulation via reinforcement learning”, arXiv:2311.04285, (2023).

The above citations are from SAO/NASA ADS (last updated successfully 2023-11-14 11:17:33). The list may be incomplete as not all publishers provide suitable and complete citation data.

Could not fetch Crossref cited-by data during last attempt 2023-11-14 11:17:32: Could not fetch cited-by data for 10.22331/q-2023-11-14-1181 from Crossref. This is normal if the DOI was registered recently.

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.

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Abstract

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