Quantum Mixed State Compiling

TL;DR

This paper introduces a variational quantum algorithm for efficiently learning and compressing mixed quantum states, suitable for near-term quantum hardware, and demonstrates its effectiveness on various states including noise-induced states.

Contribution

It generalizes previous pure state learning algorithms to mixed states using two ansätze, enabling state compression and principal component analysis on quantum hardware.

Findings

Effective for learning random and thermal states

Enables state compression based on rank approximation

Demonstrated on quantum hardware for noise-induced states

Abstract

The task of learning a quantum circuit to prepare a given mixed state is a fundamental quantum subroutine. We present a variational quantum algorithm (VQA) to learn mixed states which is suitable for near-term hardware. Our algorithm represents a generalization of previous VQAs that aimed at learning preparation circuits for pure states. We consider two different ans\"{a}tze for compiling the target state; the first is based on learning a purification of the state and the second on representing it as a convex combination of pure states. In both cases, the resources required to store and manipulate the compiled state grow with the rank of the approximation. Thus, by learning a lower rank approximation of the target state, our algorithm provides a means of compressing a state for more efficient processing. As a byproduct of our algorithm, one effectively learns the principal components of the target state, and hence our algorithm further provides a new method for principal component analysis. We investigate the efficacy of our algorithm through extensive numerical implementations, showing that typical random states and thermal states of many body systems may be learnt this way. Additionally, we demonstrate on quantum hardware how our algorithm can be used to study hardware noise-induced states.