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Published June 2015 | Published
Journal Article Open

Practical variational tomography for critical one-dimensional systems

Abstract

We improve upon a recently introduced efficient quantum state reconstruction procedure targeted to states well approximated by the multiscale entanglement renormalization ansatz (MERA), e.g., ground states of critical models. We show how to numerically select a subset of experimentally accessible measurements which maximize information extraction about renormalized particles, thus dramatically reducing the required number of physical measurements. We numerically estimate the number of measurements required to characterize the ground state of the critical one-dimensional Ising (resp. XX) model and find that MERA tomography on 16-qubit (resp. 24-qubit) systems requires the same experimental effort as brute-force tomography on 8 qubits. We derive a bound computable from experimental data which certifies the distance between the experimental and reconstructed states.

Additional Information

© 2015 American Physical Society. Received 10 December 2014; revised manuscript received 13 May 2015; published 30 June 2015. J.Y.L. acknowledges support from the Summer Undergraduate Research Fellowship (SURF) program at the California Institute of Technology. O.L.C. acknowledges funding provided by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center with support of the Gordon and Betty Moore Foundation (Grants No. PHY-0803371 and No. PHY-1125565) and the Fonds de recherche Québec - Nature et Technologies (FRQNT). Both authors would like to thank Glen Evenbly for insightful discussions and numerical help and John Preskill for helpful comments throughout the project.

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Published - PhysRevA.91.062128.pdf

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August 20, 2023
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