Maximal entropy approach for quantum state tomography

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.

27 pages, 6 figures, submitted to PRX Quantum

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• Quantum Machine Learning for Chemistry and Physics
• Convergence of reconstructed density matrix to a pure state using maximal entropy approach
• Variational Approach to Quantum State Tomography based on Maximal Entropy Formalism
• Quantum Gram-Schmidt Processes and Their Application to Efficient State Read-out for Quantum Algorithms
• Simulating noisy quantum channels via quantum state preparation algorithms
• Hamiltonian learning from time dynamics using variational algorithms
• Dimension reduction and redundancy removal through successive Schmidt decompositions
• Principle of Information Increase: An Operational Perspective of Information Gain in the Foundations of Quantum Theory
• Random Projection using Random Quantum Circuits