Randomized benchmarking of single and multi-qubit control in liquid-state NMR quantum information processing

TL;DR

This paper applies randomized benchmarking to liquid-state NMR quantum information processing, quantifying control errors for single and multi-qubit gates, and discusses potential improvements to reduce these errors.

Contribution

It demonstrates the implementation of randomized benchmarking in liquid-state NMR QIP and extends the protocol to multi-qubit systems, providing experimental error estimates.

Findings

Single-qubit error per gate: 1.3e-4

Two-qubit error rate: 4.7e-3

Errors are not limited by decoherence

Abstract

Being able to quantify the level of coherent control in a proposed device implementing a quantum information processor (QIP) is an important task for both comparing different devices and assessing a device's prospects with regards to achieving fault-tolerant quantum control. We implement in a liquid-state nuclear magnetic resonance QIP the randomized benchmarking protocol presented by Knill et al (PRA 77: 012307 (2008)). We report an error per randomized $\frac{\pi}{2}$ pulse of $1.3 \pm 0.1 \times 10^{-4}$ with a single qubit QIP and show an experimentally relevant error model where the randomized benchmarking gives a signature fidelity decay which is not possible to interpret as a single error per gate. We explore and experimentally investigate multi-qubit extensions of this protocol and report an average error rate for one and two qubit gates of $4.7 \pm 0.3 \times 10^{-3}$ for a three qubit QIP. We estimate that these error rates are still not decoherence limited and thus can be improved with modifications to the control hardware and software.