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

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.

arXiv commentAccepted version in Quantum. Additional proof of self-averaging. Updated typo in Fig. 1. 16 + 13 pages, 5 + 2 figures

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Cited by in corpus (6)

• QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems. Part II: bosons, fermions and higher spins
• A Maximum Entropy Principle in Deep Thermalization and in Hilbert-Space Ergodicity
• Constraints on anomalous quartic gauge couplings via $W\gamma jj$ production at the LHC
• Taking snapshots of a quantum thermalization process: emergent classicality in quantum jump trajectories
• Experimental signatures of Hilbert-space ergodicity: Universal bitstring distributions and applications in noise learning
• Model-Independent Simulation Complexity of Complex Quantum Dynamics