Reducing 2-QuBit Gate Count for ZX-Calculus based Quantum Circuit Optimization

Abstract

In the near term, programming quantum computers will remain severely limited by low quantum volumes. Therefore, it is desirable to implement quantum circuits with the fewest resources possible. For the common Clifford+T circuits, most research is focused on reducing the number of T gates, since they are an order of magnitude more expensive than Clifford gates in quantum error corrected encoding schemes. However, this optimization sometimes leads to more 2-qubit gates, which, even though they are less expensive in terms of fault-tolerance, contribute significantly to the overall circuit cost. Approaches based on the ZX-calculus have recently gained some popularity in the field, but reduction of 2-qubit gates is not their focus. In this work, we present an alternative for improving 2-qubit gate count of a quantum circuit with the ZX-calculus by using heuristics in ZX-diagram simplification. Our approach maintains the good reduction of the T gate count provided by other strategies based on ZX-calculus, thus serving as an extension for other optimization algorithms. Our results show that combining the available ZX-calculus-based optimizations with our algorithms can reduce the number of 2-qubit gates by as much as 40% compared to current approaches using ZX-calculus. Additionally, we improve the results of the best currently available optimization technique of Nam et. al for some circuits by up to 15%.

arXiv commentIn Proceedings QPL 2022, arXiv:2311.08375

References in corpus (15)

• A variational eigenvalue solver on a quantum processor
• Quantum algorithm for solving linear systems of equations
• A Quantum Approximate Optimization Algorithm
• t$|$ket$⟩$ : A Retargetable Compiler for NISQ Devices
• Interacting Quantum Observables: Categorical Algebra and Diagrammatics
• Polynomial-time T-depth Optimization of Clifford+T circuits via Matroid Partitioning
• Automated optimization of large quantum circuits with continuous parameters
• Magic State Distillation: Not as Costly as You Think
• Graph-theoretic Simplification of Quantum Circuits with the ZX-calculus
• Quantum computation with realistic magic state factories
• Reducing T-count with the ZX-calculus
• PyZX: Large Scale Automated Diagrammatic Reasoning
• A Verified Optimizer for Quantum Circuits
• There and back again: A circuit extraction tale
• Circuit Extraction for ZX-diagrams can be #P-hard

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