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.
Highlights
The ability to control and manipulate microscopic systems at the single particle level is an essential requirement for many quantum technologies
In this work we show that the equilibration dynamics [12,13,14,15,16,17,18] of a quantum system can be used to extract such information on the dimension of the Hilbert space of a quantum device, in terms of the effective number of states that contribute to the dynamics of a local observable
The results shown above demonstrate how the chaotic dynamics of thermalization may be exploited in order to gain information on the complexity of the unitary quantum dynamics of a system
Summary
The ability to control and manipulate microscopic systems at the single particle level is an essential requirement for many quantum technologies. The size of a quantum computer or simulator is often given in terms of number of qubits, such that the Hilbert space dimension is 2N for N qubits This is a measure that ignores the effect of disorder or the possible lack of connectivity between different zones in the device. We note that this is arranged such that our key findings can be understood from sections 2 and 3, with the detailed calculations presented later in the text
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