Long-time simulations with high fidelity on quantum hardware

TL;DR

This paper demonstrates long-time, high-fidelity quantum simulations on current hardware using a novel fsVFF algorithm that significantly reduces resource requirements and extends simulation duration beyond previous methods.

Contribution

Introduction of the fsVFF algorithm enabling longer, more accurate quantum simulations by reducing circuit complexity and resource demands.

Findings

Achieved over 600 time steps with fidelity ≥ 0.9 on real quantum hardware.

Extended simulation duration by a factor of 150 compared to traditional Trotter methods.

Validated the noise resilience and scalability of the fsVFF algorithm.

Abstract

Moderate-size quantum computers are now publicly accessible over the cloud, opening the exciting possibility of performing dynamical simulations of quantum systems. However, while rapidly improving, these devices have short coherence times, limiting the depth of algorithms that may be successfully implemented. Here we demonstrate that, despite these limitations, it is possible to implement long-time, high fidelity simulations on current hardware. Specifically, we simulate an XY-model spin chain on the Rigetti and IBM quantum computers, maintaining a fidelity of at least 0.9 for over 600 time steps. This is a factor of 150 longer than is possible using the iterated Trotter method. Our simulations are performed using a new algorithm that we call the fixed state Variational Fast Forwarding (fsVFF) algorithm. This algorithm decreases the circuit depth and width required for a quantum simulation by finding an approximate diagonalization of a short time evolution unitary. Crucially, fsVFF only requires finding a diagonalization on the subspace spanned by the initial state, rather than on the total Hilbert space as with previous methods, substantially reducing the required resources. We further demonstrate the viability of fsVFF through large numerical implementations of the algorithm, as well as an analysis of its noise resilience and the scaling of simulation errors.