Verifiable measurement-based quantum random sampling with trapped ions

TL;DR

This paper demonstrates a scalable, verifiable quantum random sampling method using a trapped-ion quantum processor, advancing the practical verification of quantum advantage in measurement-based quantum computing.

Contribution

It introduces an experimentally feasible approach for verifiable quantum random sampling with measurement-based quantum computation on trapped ions, including state fidelity estimation and noise analysis.

Findings

Successfully sampled from 4x4 qubit cluster states

Developed a method to recycle qubits for larger entangled states

Compared verification results with cross-entropy benchmarking

Abstract

Quantum computers are now on the brink of outperforming their classical counterparts. One way to demonstrate the advantage of quantum computation is through quantum random sampling performed on quantum computing devices. However, existing tools for verifying that a quantum device indeed performed the classically intractable sampling task are either impractical or not scalable to the quantum advantage regime. The verification problem thus remains an outstanding challenge. Here, we experimentally demonstrate efficiently verifiable quantum random sampling in the measurement-based model of quantum computation on a trapped-ion quantum processor. We create and sample from random cluster states, which are at the heart of measurement-based computing, up to a size of 4 x 4 qubits. By exploiting the structure of these states, we are able to recycle qubits during the computation to sample from entangled cluster states that are larger than the qubit register. We then efficiently estimate the fidelity to verify the prepared states -- in single instances and on average -- and compare our results to cross-entropy benchmarking. Finally, we study the effect of experimental noise on the certificates. Our results and techniques provide a feasible path toward a verified demonstration of a quantum advantage.