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NISQ Algorithm for Hamiltonian Simulation via Truncated Taylor Series

by Jonathan Wei Zhong Lau, Tobias Haug, Leong Chuan Kwek, Kishor Bharti

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): Jonathan Wei Zhong Lau · Hai-Rui Wei
Submission information
Preprint Link: scipost_202105_00027v3  (pdf)
Date accepted: 2022-02-28
Date submitted: 2022-02-15 02:34
Submitted by: Lau, Jonathan Wei Zhong
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Quantum Physics
Approaches: Theoretical, Computational


Simulating the dynamics of many-body quantum systems is believed to be one of the first fields that quantum computers can show a quantum advantage over classical computers. Noisy intermediate-scale quantum (NISQ) algorithms aim at effectively using the currently available quantum hardware. For quantum simulation, various types of NISQ algorithms have been proposed with individual advantages as well as challenges. In this work, we propose a new algorithm, truncated Taylor quantum simulator (TQS), that shares the advantages of existing algorithms and alleviates some of the shortcomings. Our algorithm does not have any classical-quantum feedback loop and bypasses the barren plateau problem by construction. The classical part in our hybrid quantum-classical algorithm corresponds to a quadratically constrained quadratic program (QCQP) with a single quadratic equality constraint, which admits a semidefinite relaxation. The QCQP based classical optimization was recently introduced as the classical step in quantum assisted eigensolver (QAE), a NISQ algorithm for the Hamiltonian ground state problem. Thus, our work provides a conceptual unification between the NISQ algorithms for the Hamiltonian ground state problem and the Hamiltonian simulation. We recover differential equation-based NISQ algorithms for Hamiltonian simulation such as quantum assisted simulator (QAS) and variational quantum simulator (VQS) as particular cases of our algorithm. We test our algorithm on some toy examples on current cloud quantum computers. We also provide a systematic approach to improve the accuracy of our algorithm.

Published as SciPost Phys. 12, 122 (2022)

Author comments upon resubmission

We would like to thank you again for considering our submission titled “NISQ Algorithm for Hamiltonian
Simulation via Truncated Taylor Series” for publication in Scipost. We would also like to extend our gratitude
to the referees for their second round of valuable feedback and reports. We have addressed their comments, point by point, in
the manuscript submitted to scipost below, and edited the manuscript accordingly. We hope that the improved manuscript is fit for publication in Scipost.

List of changes

We have given a point-by-point reply to the questions in the manuscript submitted to scipost.

Reports on this Submission

Anonymous Report 1 on 2022-2-15 (Invited Report)


I read the revised manuscript and in particular the changes made by the authors. My reamining questions and comments have been adressed. In particular the paragraph on page 7 adresses now limitations in terms of reachable time scales, which was one of my main concerns.

Also other questions like the connection of the proposed method to Krylov time evolution have been clarified.

I thus have no further objections to publication of this manuscript.

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