6-qubit Optimal Clifford Circuits

Abstract

Clifford group lies at the core of quantum computation -- it underlies quantum error correction, its elements can be used to perform magic state distillation and they form randomized benchmarking protocols, Clifford group is used to study quantum entanglement, and more. The ability to utilize Clifford group elements in practice relies heavily on the efficiency of their circuit-level implementation. Finding short circuits is a hard problem; despite Clifford group being finite, its size grows quickly with the number of qubits $n$, limiting known optimal implementations to $n=4$ qubits. For $n=6$, the number of Clifford group elements is about $2.1\cdot 10^{23}$. In this paper, we report a set of algorithms, along with their C/C++ implementation, that implicitly synthesize optimal circuits for all 6-qubit Clifford group elements by storing a subset of the latter in a database of size 2.1TB (1KB=1024B). We demonstrate how to extract arbitrary optimal 6-qubit Clifford circuit in $0.0009358$ and $0.0006274$ seconds using consumer- and enterprise-grade computers (hardware) respectively, while relying on this database.

23 pages

References in corpus (3)

• Randomized Benchmarking of Quantum Gates
• Robust randomized benchmarking of quantum processes
• Pseudo-randomness and Learning in Quantum Computation

Cited by in corpus (11)

• Clifford Circuit Optimization with Templates and Symbolic Pauli Gates
• Depth optimization of CZ, CNOT, and Clifford circuits
• Error Mitigation for Deep Quantum Optimization Circuits by Leveraging Problem Symmetries
• Automated Synthesis of Fault-Tolerant State Preparation Circuits for Quantum Error Correction Codes
• Fundamental limits on quantum cloning from the no-signalling principle
• Quantum Circuit Discovery for Fault-Tolerant Logical State Preparation with Reinforcement Learning
• An Algorithm for Reversible Logic Circuit Synthesis Based on Tensor Decomposition
• A Rubik's Cube inspired approach to Clifford synthesis
• Resource-efficient shadow tomography using equatorial stabilizer measurements
• A graph-state based synthesis framework for Clifford isometries
• Limits of Clifford Disentangling in Tensor Network States