Maximal entropy approach for quantum state tomography
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.
Rishabh Gupta Rongxin Xia Raphael D. Levine Sabre Kais