Maximal entropy approach for quantum state tomography

TL;DR

This paper introduces a maximal entropy-based method for quantum state tomography that reconstructs quantum states with high fidelity using partial measurement data, addressing noise and limitations in current quantum devices.

Contribution

It proposes a novel maximal entropy approach for quantum tomography that effectively handles incomplete data and noise in NISQ quantum devices.

Findings

Reconstructs quantum states with high fidelity from partial data

Addresses noise and measurement limitations in quantum tomography

Provides a practical inference method for quantum states

Abstract

Quantum computation has been growing rapidly in both theory and experiments. In particular, quantum computing devices with a large number of qubits have been developed by IBM, Google, IonQ, and others. The current quantum computing devices are noisy intermediate-scale quantum $($NISQ$)$ devices, and so approaches to validate quantum processing on these quantum devices are needed. One of the most common ways of validation for an n-qubit quantum system is quantum tomography, which tries to reconstruct a quantum system's density matrix by a complete set of observables. However, the inherent noise in the quantum systems and the intrinsic limitations poses a critical challenge to precisely know the actual measurement operators which make quantum tomography impractical in experiments. Here, we propose an alternative approach to quantum tomography, based on the maximal information entropy, that can predict the values of unknown observables based on the available mean measurement data. This can then be used to reconstruct the density matrix with high fidelity even though the results for some observables are missing. Of additional contexts, a practical approach to the inference of the quantum mechanical state using only partial information is also needed.