Polyhedral Classical Simulators for Quantum Computation

• URL: http://arxiv.org/abs/2510.07540v1
• Date: Wed, 08 Oct 2025 20:55:55 GMT
• Title: Polyhedral Classical Simulators for Quantum Computation
• Authors: Cihan Okay,
• Abstract summary: We introduce polyhedral classical simulators, a framework for classical simulation grounded in polyhedral geometry.<n>We show how this framework unifies and extends existing simu- lation methods while at the same time providing a geometric roadmap for pushing the boundary of efficient classical simulation further.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum advantage in computation refers to the existence of computational tasks that can be performed efficiently on a quantum computer but cannot be efficiently simulated on any classical computer. Identifying the precise boundary of efficient classical simulability is a central challenge and motivates the development of new simulation paradigms. In this paper, we introduce polyhedral classical simulators, a framework for classical simulation grounded in polyhedral geometry. This framework encompasses well-known methods such as the Gottesman-Knill algorithm, while also extending naturally to more recent models of quantum computation, including those based on magic states and measurement-based quantum computation. We show how this framework unifies and extends existing simu- lation methods while at the same time providing a geometric roadmap for pushing the boundary of efficient classical simulation further.

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