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Description
Over the past years, numerous quantum circuit architectures have been proposed to achieve quantum advantage on noisy quantum devices. However, many widely studied (parameterized) quantum circuits have been shown to be efficiently classically simulable, motivating the development of classical surrogate models for reproducing circuit dynamics. Beyond classical simulability, a natural question arises: Is it more (time/memory) efficient to run quantum algorithms via classical surrogates or directly on quantum hardware?
In this work, we address this question by we comparing the efficiency of Quantum Simulation and (Quantum-Enhanced) Classical Simulation using three resource metrics: (i) quantum sample complexity (number of quantum measurements), (ii) classical time complexity (number of classical operations), and (iii) quantum time complexity (circuit depth). We further estimate the corresponding wall-clock runtimes for both approaches with different circuit architecture, and discuss their relative efficiency depending on the underlying algorithm and the characteristics of the quantum hardware.
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