Abstract
Bayesian inference is a powerful paradigm for quantum state tomography, treating uncertainty in meaningful and informative ways. Yet the numerical challenges associated with sampling from complex probability distributions hampers Bayesian tomography in practical settings. In this article, we introduce an improved, self-contained approach for Bayesian quantum state estimation. Leveraging advances in machine learning and statistics, our formulation relies on highly efficient preconditioned Crank–Nicolson sampling and a pseudo-likelihood. We theoretically analyze the computational cost, and provide explicit examples of inference for both actual and simulated datasets, illustrating improved performance with respect to existing approaches.
Highlights
Quantum state tomography (QST) is of fundamental importance in quantum information processing, where realization of computational advantages rests critically on the quality of the underlying quantum resources
The Hilbert space of a collection of qubits grows exponentially with the number of particles, as does the number of independent quantities needed to fully characterize ρ. Such exponential scaling is the source of the unique computational power inherent in quantum information, and QST cannot be used for characterizing large-scale QIP systems of the future, at least in their entirety
Linear inversion—the first method considered in quantum information processing, linear inversion tomography relies on the fact that measurement outcome probabilities are linear functions of the individual elements comprising ρ [1]
Summary
Quantum state tomography (QST) is of fundamental importance in quantum information processing, where realization of computational advantages rests critically on the quality of the underlying quantum resources. The Hilbert space of a collection of qubits grows exponentially with the number of particles, as does the number of independent quantities needed to fully characterize ρ Such exponential scaling is the source of the unique computational power inherent in quantum information, and QST cannot be used for characterizing large-scale QIP systems of the future, at least in their entirety. There remains demand for efficient and informative QST techniques that make the most of available resources and push limits on system size. In this vein, Bayesian methods offer exciting promise. Our method represents an improvement over previous Bayesian QST approaches and should provide a valuable tool for comprehensive, yet numerically efficient, state estimation
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