Mixed Quantum-Semiclassical Simulation

• URL: http://arxiv.org/abs/2308.16147v1
• Date: Wed, 30 Aug 2023 17:02:33 GMT
• Title: Mixed Quantum-Semiclassical Simulation
• Authors: Javier Gonzalez-Conde, Andrew T. Sornborger
• Abstract summary: We study the quantum simulation of mixed quantum-semiclassical (MQS) systems, of fundamental interest in many areas of physics. A basic question for these systems is whether quantum algorithms of MQS systems would be valuable at all, when one could instead study the full quantum-quantum system.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study the quantum simulation of mixed quantum-semiclassical (MQS) systems, of fundamental interest in many areas of physics, such as molecular scattering and gravitational backreaction. A basic question for these systems is whether quantum algorithms of MQS systems would be valuable at all, when one could instead study the full quantum-quantum system. We study MQS simulations in the context where a semiclassical system is encoded in a Koopman-von Neumann (KvN) Hamiltonian and a standard quantum Hamiltonian describes the quantum system. In this case, because KvN and quantum Hamiltonians are constructed with the same operators on a Hilbert space, standard theorems guaranteeing simulation efficiency apply. We show that, in this context, $\textit{many-body}$ MQS particle simulations give only nominal improvements in qubit resources over quantum-quantum simulations due to logarithmic scaling in the ratio, $S_q/S_c$, of actions between quantum and semiclassical systems. However, $\textit{field}$ simulations can give improvements proportional to the ratio of quantum to semiclassical actions, $S_q/S_c$. Of particular note, due to the ratio $S_q/S_c \sim 10^{-18}$ of particle and gravitational fields, this approach could be important for semiclassical gravity. We demonstrate our approach in a model of gravitational interaction, where a harmonic oscillator mediates the interaction between two spins. In particular, we demonstrate a lack of distillable entanglement generation between spins due to classical mediators, a distinct difference in dynamics relative to the fully quantum case.

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