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

Nation, Charlie and Porras, Diego (2019) Ergodicity probes: using time-fluctuations to measure the Hilbert space dimension. Quantum, 3. p. 207. ISSN 2521-327X

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Abstract

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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Physics and Astronomy
Research Centres and Groups: Atomic, Molecular and Optical Physics Research Group
Subjects: Q Science > QC Physics > QC0170 Atomic physics. Constitution and properties of matter Including molecular physics, relativity, quantum theory, and solid state physics > QC0174.12 Quantum theory. Quantum mechanics
Q Science > QC Physics > QC0170 Atomic physics. Constitution and properties of matter Including molecular physics, relativity, quantum theory, and solid state physics > QC0174.8 Statistical physics
Depositing User: Charlie Nation
Date Deposited: 10 Jan 2020 10:21
Last Modified: 10 Jan 2020 10:30
URI: http://sro.sussex.ac.uk/id/eprint/89275

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