Fidelity Witnesses for Fermionic Quantum Simulations

Gluza M, Kliesch M, Eisert J, Aolita L (2018)

Publication Type: Journal article

Publication year: 2018

Journal

Physical Review Letters American Physical Society

Book Volume: 120

Article Number: 190501

Journal Issue: 19

DOI: 10.1103/PhysRevLett.120.190501

Abstract

The experimental interest and developments in quantum spin-1/2 chains has increased uninterruptedly over the past decade. In many instances, the target quantum simulation belongs to the broader class of noninteracting fermionic models, constituting an important benchmark. In spite of this class being analytically efficiently tractable, no direct certification tool has yet been reported for it. In fact, in experiments, certification has almost exclusively relied on notions of quantum state tomography scaling very unfavorably with the system size. Here, we develop experimentally friendly fidelity witnesses for all pure fermionic Gaussian target states. Their expectation value yields a tight lower bound to the fidelity and can be measured efficiently. We derive witnesses in full generality in the Majorana-fermion representation and apply them to experimentally relevant spin-1/2 chains. Among others, we show how to efficiently certify strongly out-of-equilibrium dynamics in critical Ising chains. At the heart of the measurement scheme is a variant of importance sampling specially tailored to overlaps between covariance matrices. The method is shown to be robust against finite experimental-state infidelities.

Involved external institutions

Freie Universität Berlin DE Germany (DE) University of Gdańsk / Uniwersytet Gdański PL Poland (PL) Universidade Federal do Rio de Janeiro (UFRJ) / Federal University of Rio de Janeiro BR Brazil (BR)

How to cite

APA:

Gluza, M., Kliesch, M., Eisert, J., & Aolita, L. (2018). Fidelity Witnesses for Fermionic Quantum Simulations. Physical Review Letters, 120(19). https://doi.org/10.1103/PhysRevLett.120.190501

MLA:

Gluza, M., et al. "Fidelity Witnesses for Fermionic Quantum Simulations." Physical Review Letters 120.19 (2018).

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