On the Hardness of Measuring Magic

TL;DR

This paper introduces Pauli instability as a measure of magic in quantum computers, demonstrates its experimental measurement on IBM's quantum processor, and proves the intractability of measuring extensive magic, highlighting limitations in assessing quantum computational resources.

Contribution

It proposes a new measure of magic called Pauli instability and analyzes its practical and theoretical limitations in large-scale quantum systems.

Findings

Measuring extensive magic is computationally intractable.

Pauli instability can be experimentally measured on current quantum hardware.

Measuring magic may only be feasible when quantum computers do not offer speed-ups.

Abstract

Quantum computers promise to solve computational problems significantly faster than classical computers. These 'speed-ups' are achieved by utilizing a resource known as magic. Measuring the amount of magic used by a device allows us to quantify its potential computational power. Without this property, quantum computers are no faster than classical computers. Whether magic can be accurately measured on large-scale quantum computers has remained an open problem. To address this question, we introduce Pauli instability as a measure of magic and experimentally measure it on the IBM Eagle quantum processor. We prove that measuring large (i.e., extensive) quantities of magic is intractable. Our results suggest that one may only measure magic when a quantum computer does not provide a speed-up. We support our conclusions with both theoretical and experimental evidence. Our work illustrates the capabilities and limitations of quantum technology in measuring one of the most important resources in quantum computation.