Resilience-Runtime Tradeoff Relations for Quantum Algorithms

TL;DR

This paper reveals a fundamental tradeoff in quantum algorithm design, showing that minimizing operations can increase noise sensitivity, and introduces a framework to optimize algorithm resilience against various noise types.

Contribution

It develops a framework to analyze the resilience of quantum algorithms to different noises and establishes a tradeoff relation between operation count and noise robustness.

Findings

Minimizing quantum operations can increase noise sensitivity.

Algorithms can be resilient to some noises but vulnerable to others.

Framework helps identify optimal compilations for noise robustness.

Abstract

A leading approach to algorithm design aims to minimize the number of operations in an algorithm's compilation. One intuitively expects that reducing the number of operations may decrease the chance of errors. This paradigm is particularly prevalent in quantum computing, where gates are hard to implement and noise rapidly decreases a quantum computer's potential to outperform classical computers. Here, we find that minimizing the number of operations in a quantum algorithm can be counterproductive, leading to a noise sensitivity that induces errors when running the algorithm in non-ideal conditions. To show this, we develop a framework to characterize the resilience of an algorithm to perturbative noises (including coherent errors, dephasing, and depolarizing noise). Some compilations of an algorithm can be resilient against certain noise sources while being unstable against other noises. We condense these results into a tradeoff relation between an algorithm's number of operations and its noise resilience. We also show how this framework can be leveraged to identify compilations of an algorithm that are better suited to withstand certain noises.