Quantum algorithmic measurement

Dorit Aharonov,Xiao-Liang Qi,Jordan Cotler

doi:10.1038/s41467-021-27922-0

Abstract

There has been recent promising experimental and theoretical evidence that quantum computational tools might enhance the precision and efficiency of physical experiments. However, a systematic treatment and comprehensive framework are missing. Here 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 problems 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.

Highlights

There has been recent promising experimental and theoretical evidence that quantum computational tools might enhance the precision and efficiency of physical experiments
We use the language of computational complexity to define an abstract model of general experiments, which we call quantum algorithmic measurements, or QUALMs, which we hypothesize is universal for quantum experiments
A first natural attempt is to model experiments as “black box” quantum algorithms: queries to the physical system are interlaced with controlled quantum computations applied by the experimentalist

Summary

Introduction

There has been recent promising experimental and theoretical evidence that quantum computational tools might enhance the precision and efficiency of physical experiments. Over the past two decades, we have witnessed a new era in this respect, in which ingredients, ideas and concepts originating from the world of quantum computation are being incorporated into the experimental physics toolbox[1–25] This body of work constitutes strong evidence that leveraging quantum computational resources to manipulate and measure physical systems may dramatically enhance experimental capabilities. The quantum Church Turing thesis[26] suggests that any physical process can be efficiently (i.e., with only polynomial overhead) simulated by a quantum algorithm applying local quantum gates This observation constitutes the pillar on which the entire theory of quantum algorithms and quantum computational complexity stands, but it has had a profound impact on our understanding of quantum physics in the past two decades Initial seeds for our approach were given in[24,28]

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