Variational quantum anomaly detection: Unsupervised mapping of phase diagrams on a physical quantum computer

Korbinian Kottmann,Friederike Metz,Niccolò Baldelli,Joana Fraxanet

doi:10.1103/physrevresearch.3.043184

Abstract

One of the most promising applications of quantum computing is simulating quantum many-body systems. However, there is still a need for methods to efficiently investigate these systems in a native way, capturing their full complexity. Here, we propose variational quantum anomaly detection, an unsupervised quantum machine learning algorithm to analyze quantum data from quantum simulation. The algorithm is used to extract the phase diagram of a system with no prior physical knowledge and can be performed end-to-end on the same quantum device that the system is simulated on. We showcase its capabilities by mapping out the phase diagram of the one-dimensional extended Bose Hubbard model with dimerized hoppings, which exhibits a symmetry protected topological phase. Further, we show that it can be used with readily accessible devices nowadays and perform the algorithm on a real quantum computer.

Highlights

Since the discovery of Shor’s algorithm [1], there have been many attempts to leverage the power of quantum computers to outperform classical computers [2]
Note that in previous works, where the same task has been tackled with classical machine learning techniques, it has been shown that a single ground state was sufficient to successfully train the model [44]
This feature stems from the fact that ground states within the same phase share similar properties and there is very little variance when changing the physical parameters inside one phase

Summary

INTRODUCTION

Since the discovery of Shor’s algorithm [1], there have been many attempts to leverage the power of quantum computers to outperform classical computers [2]. There are several proposals for algorithms on these devices [9,10] such as the variational quantum eigensolver (VQE) [11], the quantum approximate optimization algorithm [12], or the quantum autoencoder [13,14], which employ parameterized circuits that are optimized through a classical feedback loop typically with gradient-based methods [15,16,17] These approaches can suffer from so-called barren plateaus, the phenomenon of an exponentially vanishing gradient of the loss function [18]. Our quantum anomaly detection (QAD) scheme belongs to the category of variational quantum algorithms where the circuit learns characteristic features of the input state [38] This can in principle be leveraged for obtaining physical insights of the system from training [39] and is in con-. VQAD allows us to perform anomaly detection directly on a quantum computer, and, with programmable devices readily available, we demonstrate it experimentally on a real device

PROPOSAL

Simulations with ideal quantum data

Experiments on a real quantum computer

OUTLOOK