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

Understand

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.