Qubit-count optimization using ZX-calculus

• URL: http://arxiv.org/abs/2407.10171v1
• Date: Sun, 14 Jul 2024 11:58:53 GMT
• Title: Qubit-count optimization using ZX-calculus
• Authors: Vivien Vandaele,
• Abstract summary: We show how to optimize the number of qubits in a quantum circuit while preserving the number of non-Clifford gates. One of our approaches consists in reversing the gadgetization of Hadamard gates, which is a procedure used by some $T$-counts. We also show how this method can be used to efficiently optimize the number of qubits in a quantum circuit by using the ZX-calculus as an intermediate representation.
• Score: 3.129187821625805
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose several methods for optimizing the number of qubits in a quantum circuit while preserving the number of non-Clifford gates. One of our approaches consists in reversing, as much as possible, the gadgetization of Hadamard gates, which is a procedure used by some $T$-count optimizers to circumvent Hadamard gates at the expense of additional qubits. We prove the NP-hardness of this problem and we present an algorithm for solving it. We also propose a more general approach to optimize the number of qubits by showing how it relates to the problem of finding a minimal-width path-decomposition of the graph associated with a given ZX-diagram. This approach can be used to optimize the number of qubits for any computational model that can natively be depicted in ZX-calculus, such as the Pauli Fusion computational model which can represent lattice surgery operations. We also show how this method can be used to efficiently optimize the number of qubits in a quantum circuit by using the ZX-calculus as an intermediate representation.

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