Compilation by stochastic Hamiltonian sparsification

Yingkai Ouyang1, David R. White1, and Earl T. Campbell1,2

1Department of Physics and Astronomy, University of Sheffield, Sheffield, UK
2Riverlane, Cambridge, UK

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Simulation of quantum chemistry is expected to be a principal application of quantum computing. In quantum simulation, a complicated Hamiltonian describing the dynamics of a quantum system is decomposed into its constituent terms, where the effect of each term during time-evolution is individually computed. For many physical systems, the Hamiltonian has a large number of terms, constraining the scalability of established simulation methods. To address this limitation we introduce a new scheme that approximates the actual Hamiltonian with a sparser Hamiltonian containing fewer terms. By stochastically sparsifying weaker Hamiltonian terms, we benefit from a quadratic suppression of errors relative to deterministic approaches. Relying on optimality conditions from convex optimisation theory, we derive an appropriate probability distribution for the weaker Hamiltonian terms, and compare its error bounds with other probability ansatzes for some electronic structure Hamiltonians. Tuning the sparsity of our approximate Hamiltonians allows our scheme to interpolate between two recent random compilers: qDRIFT and randomized first order Trotter. Our scheme is thus an algorithm that combines the strengths of randomised Trotterisation with the efficiency of qDRIFT, and for intermediate gate budgets, outperforms both of these prior methods.

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Cited by

[1] Dominic W. Berry, Andrew M. Childs, Yuan Su, Xin Wang, and Nathan Wiebe, "Time-dependent Hamiltonian simulation withL1-norm scaling", arXiv:1906.07115, Quantum 4, 254 (2020).

[2] Leonardo Novo, "Bridging gaps between random approaches to quantum simulation", Quantum Views 4, 33 (2020).

[3] Vincent E. Elfving, Marta Millaruelo, José A. Gámez, and Christian Gogolin, "Simulating quantum chemistry in the seniority-zero space on qubit-based quantum computers", Physical Review A 103 3, 032605 (2021).

[4] Sam McArdle, Suguru Endo, Alán Aspuru-Guzik, Simon C. Benjamin, and Xiao Yuan, "Quantum computational chemistry", arXiv:1808.10402, Reviews of Modern Physics 92 1, 015003 (2020).

[5] 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).

[6] Yingkai Ouyang, "Quantum storage in quantum ferromagnets", Physical Review B 103 14, 144417 (2021).

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

[8] Yuan Su, Hsin-Yuan Huang, and Earl T. Campbell, "Nearly tight Trotterization of interacting electrons", arXiv:2012.09194.

[9] Hrant Gharibyan, Masanori Hanada, Masazumi Honda, and Junyu Liu, "Toward simulating Superstring/M-theory on a quantum computer", arXiv:2011.06573.

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The above citations are from Crossref's cited-by service (last updated successfully 2021-06-16 02:33:05) and SAO/NASA ADS (last updated successfully 2021-06-16 02:33:06). The list may be incomplete as not all publishers provide suitable and complete citation data.

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