NISQ Algorithm for Hamiltonian Simulation via Truncated Taylor Series

TL;DR

This paper introduces the truncated Taylor quantum simulator (TTQS), a NISQ algorithm for Hamiltonian simulation that avoids classical-quantum feedback loops and the barren plateau problem, unifying existing approaches and demonstrating practical tests on current quantum hardware.

Contribution

The paper proposes TTQS, a novel NISQ algorithm for Hamiltonian simulation that unifies and improves upon existing methods, with a classical optimization step based on QCQP and semidefinite relaxation.

Findings

Successfully tested on toy examples on cloud quantum computers.

Provides a systematic approach to enhance accuracy.

Unifies Hamiltonian ground state and simulation algorithms.

Abstract

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 (TTQS), 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.