Quantum Algorithm For Simulating Hamiltonian Dynamics With An Off-diagonal Series Expansion

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Amir Kalev¹ and Itay Hen^2,3

¹Information Sciences Institute, University of Southern California, Arlington, VA 22203, USA
²Information Sciences Institute, University of Southern California, Marina del Rey, CA 90292, USA
³Department of Physics and Astronomy, and Center for Quantum Information Science & Technology,University of Southern California, Los Angeles, California 90089, USA

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Abstract

We propose an efficient quantum algorithm for simulating the dynamics of general Hamiltonian systems. Our technique is based on a power series expansion of the time-evolution operator in its off-diagonal terms. The expansion decouples the dynamics due to the diagonal component of the Hamiltonian from the dynamics generated by its off-diagonal part, which we encode using the linear combination of unitaries technique. Our method has an optimal dependence on the desired precision and, as we illustrate, generally requires considerably fewer resources than the current state-of-the-art. We provide an analysis of resource costs for several sample models.

Popular summary

Simulating the dynamics of quantum many-body systems is a central challenge in Physics, Chemistry and the Material Sciences as well as in other areas of science and technology. While for classical algorithms this task is in general intractable, quantum circuits offer a way around the classical bottlenecks by way of `circuitizing’ the time evolution of the system in question. However, present-day quantum computing devices allow for the programming of only small and noisy quantum circuits, a state of matters that places severe constraints on the types of applications these devices may be used for in practice. The qubit and gate costs of circuitization procedures have therefore rightfully become key factors in determining the feasibility of any potential application and increasingly more efficient algorithms are continuously being devised. We propose a novel approach to resource-efficient Hamiltonian dynamics simulations on quantum circuits that we argue offers certain advantages, which directly translate to a shorter algorithm runtime, over state-of-the-art quantum simulation algorithms. We accomplish this by utilizing a series expansion of the quantum time-evolution operator in its off-diagonal elements wherein the operator is expanded around its diagonal component. This expansion allows one to effectively integrate out the diagonal component of the evolution, thereby reducing the overall gate and qubit complexities of the algorithm as compared to existing methods.

► BibTeX data

@article{Kalev2021quantumalgorithm, doi = {10.22331/q-2021-04-08-426}, url = {https://doi.org/10.22331/q-2021-04-08-426}, title = {Quantum {A}lgorithm for {S}imulating {H}amiltonian {D}ynamics with an {O}ff-diagonal {S}eries {E}xpansion}, author = {Kalev, Amir and Hen, Itay}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{“{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {5}, pages = {426}, month = apr, year = {2021}<br /> }

► References

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Cited by

[1] Amir Kalev and Itay Hen, “An integral-free representation of the Dyson series using divided differences”, arXiv:2010.09888.

[2] Yi-Hsiang Chen, Amir Kalev, and Itay Hen, “A quantum algorithm for time-dependent Hamiltonian simulation by permutation expansion”, arXiv:2103.15334.

[3] Efekan Kökcü, Thomas Steckmann, J. K. Freericks, Eugene F. Dumitrescu, and Alexander F. Kemper, “Fixed Depth Hamiltonian Simulation via Cartan Decomposition”, arXiv:2104.00728.

The above citations are from SAO/NASA ADS (last updated successfully 2021-04-10 13:00:28). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref’s cited-by service no data on citing works was found (last attempt 2021-04-10 13:00:26).

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.

Source: https://quantum-journal.org/papers/q-2021-04-08-426/

Time Stamp: April 8, 2021

Quantum Algorithm for Simulating Hamiltonian Dynamics with an Off-diagonal Series Expansion

Republished By Plato

Abstract

Popular summary

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► References

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