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Ergodicity probes: using time-fluctuations to measure the Hilbert space dimension

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posted on 2023-06-09, 20:12 authored by Charlie Nation, Diego Porras
Quantum devices, such as quantum simulators, quantum annealers, and quantum computers, may be exploited to solve problems beyond what is tractable with classical computers. This may be achieved as the Hilbert space available to perform such `calculations' is far larger than that which may be classically simulated. In practice, however, quantum devices have imperfections, which may limit the accessibility to the whole Hilbert space. We thus determine that the dimension of the space of quantum states that are available to a quantum device is a meaningful measure of its functionality, though unfortunately this quantity cannot be directly experimentally determined. Here we outline an experimentally realisable approach to obtaining the required Hilbert space dimension of such a device to compute its time evolution, by exploiting the thermalization dynamics of a probe qubit. This is achieved by obtaining a fluctuation-dissipation theorem for high-temperature chaotic quantum systems, which facilitates the extraction of information on the Hilbert space dimension via measurements of the decay rate, and time-fluctuations.

History

Publication status

  • Published

File Version

  • Accepted version

Journal

Quantum

ISSN

2521-327X

Publisher

Quantum

Volume

3

Page range

207

Department affiliated with

  • Physics and Astronomy Publications

Research groups affiliated with

  • Atomic, Molecular and Optical Physics Research Group Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2020-01-10

First Open Access (FOA) Date

2020-01-10

First Compliant Deposit (FCD) Date

2020-01-09

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