Measurement Optimization Of Variational Quantum Simulation By Classical Shadow And Derandomization

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Kouhei Nakaji^1,4, Suguru Endo², Yuichiro Matsuzaki¹, and Hideaki Hakoshima³

¹Device Technology Research Institute, National Institute of Advanced Industrial Science and Technology (AIST),1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan.
²NTT Computer and Data Science laboratories, NTT corporation, Musashino, Tokyo 180-8585, Japan
³Center for Quantum Information and Quantum Biology, Osaka University, 1-2 Machikaneyama, Toyonaka, Osaka 560-0043, Japan.
⁴Current address: Department of Computer Science, University of Toronto, Toronto, Ontario, Canada

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Abstract

Simulating large quantum systems is the ultimate goal of quantum computing. Variational quantum simulation (VQS) gives us a tool to achieve the goal in near-term devices by distributing the computation load to both classical and quantum computers. However, as the size of the quantum system becomes large, the execution of VQS becomes more and more challenging. One of the most severe challenges is the drastic increase in the number of measurements; for example, the number of measurements tends to increase by the fourth power of the number of qubits in a quantum simulation with a chemical Hamiltonian. This work aims to dramatically decrease the number of measurements in VQS by recently proposed shadow-based strategies such as classical shadow and derandomization. Even though previous literature shows that shadow-based strategies successfully optimize measurements in the variational quantum optimization (VQO), how to apply them to VQS was unclear due to the gap between VQO and VQS in measuring observables. In this paper, we bridge the gap by changing the way of measuring observables in VQS and propose an algorithm to optimize measurements in VQS by shadow-based strategies. Our theoretical analysis not only reveals the advantage of using our algorithm in VQS but theoretically supports using shadow-based strategies in VQO, whose advantage has only been given numerically. Additionally, our numerical experiment shows the validity of using our algorithm with a quantum chemical system.

Featured image: The evolutions of the infidelity due to the shot noise for each measurement strategy: the conventional measurement strategy (naive), classical shadow, largest degree first grouping (ldf grouping), and derandomization. The left figure results from the real-time evolution with ${rm H}_2$ molecule Hamiltonian. The right figure results from the imaginary-time evolution with ${rm LiH}$ molecule Hamiltonian.

Popular summary

Simulating large quantum systems is the ultimate goal of quantum computing. Variational Quantum Simulation (VQS) is a promising quantum algorithm to realize quantum simulation in the near-term quantum computer. However, executing VQS becomes increasingly challenging as the quantum system grows in size, with one of the most severe challenges being the significant increase in the number of required measurements. To address this issue, we proposed an algorithm to optimize measurements in VQS using measurement optimization techniques like classical shadow and derandomization by changing the way of measuring observables in VQS. We demonstrated the validity of the algorithm using numerical experiments with quantum chemical systems. Additionally, we theoretically revealed the advantage of using shadow-based strategies, such as classical shadow and derandomization, not only in VQS but also in Variational Quantum Optimization (VQO). This study has significant implications for measurement optimization in general variational quantum algorithms.

► BibTeX data

@article{Nakaji2023measurement, doi = {10.22331/q-2023-05-04-995}, url = {https://doi.org/10.22331/q-2023-05-04-995}, title = {Measurement optimization of variational quantum simulation by classical shadow and derandomization}, author = {Nakaji, Kouhei and Endo, Suguru and Matsuzaki, Yuichiro and Hakoshima, Hideaki}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{“{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {7}, pages = {995}, month = may, year = {2023}<br /> }

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Cited by

[1] Benchen Huang, Nan Sheng, Marco Govoni, and Giulia Galli, “Quantum simulations of Fermionic Hamiltonians with efficient encoding and ansatz schemes”, arXiv:2212.01912, (2022).

The above citations are from SAO/NASA ADS (last updated successfully 2023-05-06 01:00:39). 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 2023-05-06 01:00:37).

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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Source: https://quantum-journal.org/papers/q-2023-05-04-995/

Time Stamp: May 4, 2023

Measurement optimization of variational quantum simulation by classical shadow and derandomization

Republished By Plato

Abstract

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