Simulating Hamiltonian dynamics in a programmable photonic quantum processor using linear combinations of unitary operations

TL;DR

This paper demonstrates an improved multi-product Trotterization algorithm for simulating Hamiltonian dynamics, implemented experimentally on a silicon photonic quantum processor, achieving higher precision and near-deterministic success.

Contribution

The paper introduces a modified multi-product Trotterization combined with amplitude amplification, enabling more accurate and reliable quantum simulations on photonic hardware.

Findings

Higher simulation precision than traditional Trotterizations

Near-deterministic success probability achieved

Experimental validation on a four-qubit silicon photonic quantum processor

Abstract

Simulating the dynamic evolutions of physical and molecular systems in a quantum computer is of fundamental interest in many applications. Its implementation requires efficient quantum simulation algorithms. The Lie-Trotter-Suzuki approximation algorithm, also well known as the Trotterization, is a basic algorithm in quantum dynamic simulation. A multi-product algorithm that is a linear combination of multiple Trotterizations has been proposed to improve the approximation accuracy. Implementing such multi-product Trotterization in quantum computers however remains experimentally challenging and its success probability is limited. Here, we modify the multi-product Trotterization and combine it with the oblivious amplitude amplification to simultaneously reach a high simulation precision and high success probability. We experimentally implement the modified multi-product algorithm in an integrated-photonics programmable quantum simulator in silicon, which allows the initialization, manipulation and measurement of four-qubit states and a sequence of linearly combined controlled-unitary gates, to emulate the dynamics of a coupled electron and nuclear spins system. Theoretical and experimental results are in good agreement, and they both show the modified multi-product algorithm can simulate Hamiltonian dynamics with a higher precision than conventional Trotterizations and a nearly deterministic success probability. We certificate the multi-product algorithm in a small-scale quantum simulator based on linear combinations of operations, and this work promises the practical implementations of quantum dynamics simulations.