Abstract
Current algorithms for quantum state tomography (QST) are costly both on the experimental front, requiring measurement of many copies of the state, and on the classical computational front, needing a long time to analyze the gathered data. Here, we introduce neural adaptive quantum state tomography (NAQT), a fast, flexible machine-learning-based algorithm for QST that adapts measurements and provides orders of magnitude faster processing while retaining state-of-the-art reconstruction accuracy. As in other adaptive QST schemes, measurement adaptation makes use of the information gathered from previous measured copies of the state to perform a targeted sensing of the next copy, maximizing the information gathered from that next copy. Our NAQT approach allows for a rapid and seamless integration of measurement adaptation and statistical inference, using a neural-network replacement of the standard Bayes’ update, to obtain the best estimate of the state. Our algorithm, which falls into the machine learning subfield of “meta-learning” (in effect “learning to learn” about quantum states), does not require any ansatz about the form of the state to be estimated. Despite this generality, it can be retrained within hours on a single laptop for a two-qubit situation, which suggests a feasible time-cost when extended to larger systems and potential speed-ups if provided with additional structure, such as a state ansatz.
Highlights
Quantum state tomography (QST) is the task of estimating the density matrix of an unknown quantum state, through repeated measurements of the source, assumed to put out identical copies of the state
Neural adaptive quantum tomography we describe a family of functions, with trainable parameters
The “secret sauce” here is the incredible expressive power of neural networks as functional approximators; our resampling step uses them to learn an effective heuristic for state perturbations directly from data, sidestepping adaptive bayesian quantum tomography (ABQT)’s computationally expensive resampling step
Summary
Quantum state tomography (QST) is the task of estimating the density matrix of an unknown quantum state, through repeated measurements of the source, assumed to put out identical copies of the state. This procedure can be used to characterize quantum states, and processes acting on quantum states, and is an indispensable subroutine in quantum information processing tasks 10 as adaptive bayesian quantum tomography (ABQT). These methods were later experimentally implemented in refs. The adaptation criterion, following Bayesian principles, relies on a merit function that requires an average over the posterior distribution on the state space
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