Efficient Classical Simulation of Clifford Circuits from Framed Wigner Functions

• URL: http://arxiv.org/abs/2307.16688v1
• Date: Mon, 31 Jul 2023 14:02:33 GMT
• Title: Efficient Classical Simulation of Clifford Circuits from Framed Wigner Functions
• Authors: Guedong Park, Hyukjoon Kwon, and Hyunseok Jeong
• Abstract summary: Wigner function formalism serves as crucial tool for simulating continuous-variable and odd-prime dimensional quantum circuits. We introduce a novel classical simulation method for non-adaptive Clifford circuits based on the framed Wigner function.
• Score: 4.282159812965446
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The Wigner function formalism serves as a crucial tool for simulating continuous-variable and odd-prime dimensional quantum circuits, as well as assessing their classical hardness. However, applying such a formalism to qubit systems is limited due to the negativity in the Wigner function induced by Clifford operations. In this work, we introduce a novel classical simulation method for non-adaptive Clifford circuits based on the framed Wigner function, an extended form of the qubit Wigner function characterized by a binary-valued frame function. Our approach allows for updating phase space points under Clifford circuits without inducing negativity in the Wigner function by switching to a suitable frame when applying each Clifford gate. By leveraging this technique, we establish a sufficient condition for efficient classical simulation of Clifford circuits even with non-stabilizer inputs, where direct application of the Gottesmann-Knill tableau method is not feasible. We further develop a graph-theoretical approach to identify classically simulatable marginal outcomes of Clifford circuits and explore the number of simulatable qubits of log-depth circuits. We also present the Born probability estimation scheme using the framed Wigner function and discuss its precision. Our approach opens new avenues for quasi-probability simulation of quantum circuits, thereby expanding the boundary of classically simulatable circuits.

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