Multi-qubit Lattice Surgery Scheduling

TL;DR

This paper introduces a scheduling method for multi-qubit lattice surgery in fault-tolerant quantum computing, optimizing gate sequences to reduce circuit length and execution time.

Contribution

It proposes a novel earliest-available-first scheduling approach using Steiner trees to improve multi-qubit gate efficiency in quantum circuits.

Findings

Significant reduction in circuit length after transpilation.

Improved expected circuit execution time over serial execution.

Method demonstrates scalability and performance on various circuits.

Abstract

Fault-tolerant quantum computation using two-dimensional topological quantum error correcting codes can benefit from multi-qubit long-range operations. By using simple commutation rules, a quantum circuit can be transpiled into a sequence of solely non-Clifford multi-qubit gates. Prior work on fault-tolerant compilation avoids optimal scheduling of such gates since they reduce the parallelizability of the circuit. We observe that the reduced parallelization potential is outweighed by the significant reduction in the number of gates. We therefore devise a method for scheduling multi-qubit lattice surgery using an earliest-available-first policy, solving the associated forest packing problem using a representation of the multi-qubit gates as Steiner trees. Our extensive testing on random and application-inspired circuits demonstrates the method's scalability and performance. We show that the transpilation significantly reduces the circuit length on the set of circuits tested, and that the resulting circuit of multi-qubit gates has a further reduction in the expected circuit execution time compared to serial execution.