Optimization of Clifford Circuits

Abstract

We study optimal synthesis of Clifford circuits, and apply the results to peep-hole optimization of quantum circuits. We report optimal circuits for all Clifford operations with up to four inputs. We perform peep-hole optimization of Clifford circuits with up to 40 inputs found in the literature, and demonstrate the reduction in the number of gates by about 50%. We extend our methods to the optimal synthesis of linear reversible circuits, partially specified Clifford functions, and optimal Clifford circuits with five inputs up to input/output permutation. The results find their application in randomized benchmarking protocols, quantum error correction, and quantum circuit optimization.

7 pages, 5 figures

References in corpus (5)

• Randomized Benchmarking of Quantum Gates
• Process verification of two-qubit quantum gates by randomized benchmarking
• Randomized Benchmarking of Multi-Qubit Gates
• Randomized benchmarking of single and multi-qubit control in liquid-state NMR quantum information processing
• Linear Depth Stabilizer and Quantum Fourier Transformation Circuits with no Auxiliary Qubits in Finite Neighbor Quantum Architectures

Cited by in corpus (19)

• t$|$ket$⟩$ : A Retargetable Compiler for NISQ Devices
• Polynomial-time T-depth Optimization of Clifford+T circuits via Matroid Partitioning
• Graph-theoretic Simplification of Quantum Circuits with the ZX-calculus
• There and back again: A circuit extraction tale
• Compiling quantum algorithms for architectures with multi-qubit gates
• Exact and practical pattern matching for quantum circuit optimization
• Clifford Circuit Optimization with Templates and Symbolic Pauli Gates
• A deep learning model for noise prediction on near-term quantum devices
• 6-qubit Optimal Clifford Circuits
• HamLib: A library of Hamiltonians for benchmarking quantum algorithms and hardware
• Reinforcement Learning Based Quantum Circuit Optimization via ZX-Calculus
• A Generic Compilation Strategy for the Unitary Coupled Cluster Ansatz
• Quantum Circuit Discovery for Fault-Tolerant Logical State Preparation with Reinforcement Learning
• An Algorithm for Reversible Logic Circuit Synthesis Based on Tensor Decomposition
• Performance comparison of the two reconstruction methods for stabilizer-based quantum secret sharing
• Quantum Theory from Principles, Quantum Software from Diagrams
• Evolutionary-Based Circuit Optimization for Distributed Quantum Computing
• Entanglement boosting: Low-volume logical Bell pair preparation for distributed fault-tolerant quantum computation
• A graph-state based synthesis framework for Clifford isometries