A quantum hamiltonian simulation benchmark

TL;DR

This paper introduces a simplified quantum circuit for Hamiltonian simulation called the minimal QSVT circuit, along with a scalable benchmark metric, QUES, to evaluate quantum performance and explore classical hardness under noise.

Contribution

It proposes a minimal QSVT circuit with reduced qubit and gate requirements and introduces QUES, a scalable, verifiable benchmark for quantum evolution.

Findings

QUES relates to circuit fidelity under noise.

Optimal simulation time is approximately 4.81 units.

Potential for noisy quantum devices to demonstrate classical hardness.

Abstract

Hamiltonian simulation is one of the most important problems in quantum computation, and quantum singular value transformation (QSVT) is an efficient way to simulate a general class of Hamiltonians. However, the QSVT circuit typically involves multiple ancilla qubits and multi-qubit control gates. In order to simulate a certain class of $n$-qubit random Hamiltonians, we propose a drastically simplified quantum circuit that we refer to as the minimal QSVT circuit, which uses only one ancilla qubit and no multi-qubit controlled gates. We formulate a simple metric called the quantum unitary evolution score (QUES), which is a scalable quantum benchmark and can be verified without any need for classical computation. Under the globally depolarized noise model, we demonstrate that QUES is directly related to the circuit fidelity, and the potential classical hardness of an associated quantum circuit sampling problem. Under the same assumption, theoretical analysis suggests there exists an `optimal' simulation time $t^{\text{opt}}\approx 4.81$, at which even a noisy quantum device may be sufficient to demonstrate the potential classical hardness.