Variational Quantum Circuits for Quantum State Tomography

TL;DR

This paper introduces a variational quantum circuit approach for quantum state tomography that efficiently reconstructs quantum states with polynomial measurements, suitable for near-term quantum devices.

Contribution

It presents a novel variational quantum circuit method for quantum state tomography that reduces measurement complexity and is feasible for near-term quantum hardware.

Findings

Successfully simulated tomography of a quantum spin chain ground state

Requires polynomial measurements regardless of entanglement complexity

Compatible with near-term quantum computing platforms

Abstract

Quantum state tomography is a key process in most quantum experiments. In this work, we employ quantum machine learning for state tomography. Given an unknown quantum state, it can be learned by maximizing the fidelity between the output of a variational quantum circuit and this state. The number of parameters of the variational quantum circuit grows linearly with the number of qubits and the circuit depth, so that only polynomial measurements are required, even for highly-entangled states. After that, a subsequent classical circuit simulator is used to transform the information of the target quantum state from the variational quantum circuit into a familiar format. We demonstrate our method by performing numerical simulations for the tomography of the ground state of a one-dimensional quantum spin chain, using a variational quantum circuit simulator. Our method is suitable for near-term quantum computing platforms, and could be used for relatively large-scale quantum state tomography for experimentally relevant quantum states.