Precise measurement of quantum observables with neural-network estimators

Giacomo Torlai,Guglielmo Mazzola,Giuseppe Carleo,Antonio Mezzacapo

doi:10.1103/physrevresearch.2.022060

Giacomo Torlai, Guglielmo Mazzola + Show 2 more

Open Access

https://doi.org/10.1103/physrevresearch.2.022060

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Abstract

The measurement precision of modern quantum simulators is intrinsically constrained by the limited set of measurements that can be efficiently implemented on hardware. This fundamental limitation is particularly severe for quantum algorithms where complex quantum observables are to be precisely evaluated. To achieve precise estimates with current methods, prohibitively large amounts of sample statistics are required in experiments. Here, we propose to reduce the measurement overhead by integrating artificial neural networks with quantum simulation platforms. We show that unsupervised learning of single-qubit data allows the trained networks to accommodate measurements of complex observables, otherwise costly using traditional post-processing techniques. The effectiveness of this hybrid measurement protocol is demonstrated for quantum chemistry Hamiltonians using both synthetic and experimental data. Neural-network estimators attain high-precision measurements with a drastic reduction in the amount of sample statistics, without requiring additional quantum resources.

Highlights

The measurement process in quantum mechanics has farreaching implications, ranging from the fundamental interpretation of quantum theory [1] to the design of quantum hardware [2]
In order to suppress the uncertainty arising from a suboptimal measurement apparatus, massive amounts of sample statistics need to be generated by the quantum device [6]
We have introduced a procedure to measure complex observables in quantum hardware

Summary

INTRODUCTION

The measurement process in quantum mechanics has farreaching implications, ranging from the fundamental interpretation of quantum theory [1] to the design of quantum hardware [2]. With the increasing stream of quantum data produced in laboratories, it is natural to expect further synergy between machine learning and experimental quantum hardware In this Rapid Communication, we propose to integrate neural networks with quantum simulators to increase the measurement precision of quantum observables. Using unsupervised learning on single-qubit data to learn approximately the quantum state underlying the hardware, neural networks can be deployed to generate estimators free of intrinsic quantum noise. This comes at the cost of a systematic bias from the imperfect quantum state reconstruction. Opens up opportunities for quantum simulation on near-term quantum hardware [28]

NEURAL-NETWORK ESTIMATORS

RESULTS

CONCLUSIONS