Quantum Algorithmic Measurement

TL;DR

This paper introduces the framework of quantum algorithmic measurements (QUALMs) to analyze experimental quantum physics problems, demonstrating exponential speedups when using coherent quantum samples over traditional methods.

Contribution

The paper develops the QUALM framework and shows it can achieve exponential resource savings in quantum experiments for specific problems.

Findings

Coherent quantum sampling yields exponential speedup.

QUALMs unify quantum algorithms and interactive protocols.

Quantum computers can exponentially reduce experimental resources.

Abstract

We initiate the systematic study of experimental quantum physics from the perspective of computational complexity. To this end, we define the framework of quantum algorithmic measurements (QUALMs), a hybrid of black box quantum algorithms and interactive protocols. We use the QUALM framework to study two important experimental problems in quantum many-body physics: determining whether a system's Hamiltonian is time-independent or time-dependent, and determining the symmetry class of the dynamics of the system. We study abstractions of these problem and show for both cases that if the experimentalist can use her experimental samples coherently (in both space and time), a provable exponential speedup is achieved compared to the standard situation in which each experimental sample is accessed separately. Our work suggests that quantum computers can provide a new type of exponential advantage: exponential savings in resources in quantum experiments.