Adaptive Quantum State Tomography with Active Learning

Abstract

Recently, tremendous progress has been made in the field of quantum science and technologies: different platforms for quantum simulation as well as quantum computing, ranging from superconducting qubits to neutral atoms, are starting to reach unprecedentedly large systems. In order to benchmark these systems and gain physical insights, the need for efficient tools to characterize quantum states arises. The exponential growth of the Hilbert space with system size renders a full reconstruction of the quantum state prohibitively demanding in terms of the number of necessary measurements. Here we propose and implement an efficient scheme for quantum state tomography using active learning. Based on a few initial measurements, the active learning protocol proposes the next measurement basis, designed to yield the maximum information gain. For a fixed total number of measurements and basis configurations, our algorithm maximizes the information one can obtain about the quantum state under consideration. We apply the active learning quantum state tomography scheme to reconstruct different multi-qubit states with varying degree of entanglement as well as to ground states of a kinetically constrained spin chain. In all cases, we obtain a significantly improved reconstruction as compared to a reconstruction based on the exact same number of measurements, but with randomly chosen basis configurations. Our scheme is highly relevant to gain physical insights in quantum many-body systems as well as for the characterization of quantum devices, and paves the way for benchmarking and probing large quantum systems.

Learning Quantum Phases of Matter Using a Basis-Enhanced Born Machine

“…The naive approach would be to include data from three orthogonal bases (x, y, and z) in training, although this may include redundant information. Another approach would involve using information about the training data sets' Shannon entropies for basis selection, either prior to learning or adaptively as in [75]. A few global bases that are experimentally easily accessible could be considered as candidates, and the Shannon entropy of each could be estimated from a small amount of data.…”

“…These results stress the importance of using a priori knowledge about the Hamiltonian to select the training bases. When this knowledge is not available, an active learning strategy like that employed by [75] could be adapted for Born machines.…”

Confinement induced frustration in a one-dimensional Z2 lattice gauge theory

“…More specifically we used the pyten module of the SYTEN [22]. In order to carry out the calculations we map the original model equation ( 1) to a spin-1/2 model by using the Gauss law constraint [25,27,28]. More precisely, we use the constraint Ĝj = +1 in order to write nj =…”

“…Here L is the number of Z 2 gauge and electric fields-link variables. Such mapping was already implemented in references [25,27,28]. Similar model was also considered to study quantum scared states [36][37][38].…”

“…We propose the static structure factor as a simple probe which could be used in such experiments, since it could be readily obtained from snapshots. Recent developments in advanced state tomography reconstruction schemes [28] could also be used to gain even better insights into our model within existing experiments.…”