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arXiv · 2502.06311

Analog classical simulation of closed quantum systems

Ka-Wa Yip
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Abstract

We develop an analog classical simulation algorithm of noiseless quantum dynamics. By formulating the Schr\"{o}dinger equation into a linear system of real-valued ordinary differential equations (ODEs), the probability amplitudes of a complex state vector can be encoded in the continuous physical variables of an analog computer. Our algorithm reveals the full dynamics of complex probability amplitudes. Such real-time simulation is impossible in quantum simulation approaches without collapsing the state vector, and it is relatively computationally expensive for digital classical computers. For a real symmetric time-independent Hamiltonian, the ODEs may be solved by a simple analog mechanical device such as a one-dimensional spring-mass system. Since the underlying dynamics of quantum computers is governed by the Schr\"{o}dinger equation, our findings imply that analog computers can also perform quantum algorithms. We illustrate how to simulate the Schr\"{o}dinger equation in such a paradigm, with an application to quantum approximate optimization algorithm. This may pave the way to emulate quantum algorithms with physical computing devices, including analog, continuous-time circuits.

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Ka-Wa Yip. 2025-02-10. Analog classical simulation of closed quantum systems. https://arxiv.org/abs/2502.06311

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