Surface code compilation via edge-disjoint paths

TL;DR

This paper introduces EDPC, an efficient algorithm for surface code quantum circuit compilation that leverages edge-disjoint paths to enable constant-depth long-range operations, significantly improving circuit depth performance.

Contribution

The paper presents a novel EDPC algorithm that uses edge-disjoint paths for efficient surface code compilation, enabling parallel long-range Clifford and non-Clifford operations with improved depth guarantees.

Findings

EDPC achieves quadratic depth improvement over sequential methods.

EDPC provides the best asymptotic worst-case performance guarantees.

Implementation shows significant performance gains for parallel CNOT and multi-controlled X circuits.

Abstract

We provide an efficient algorithm to compile quantum circuits for fault-tolerant execution. We target surface codes, which form a 2D grid of logical qubits with nearest-neighbor logical operations. Embedding an input circuit's qubits in surface codes can result in long-range two-qubit operations across the grid. We show how to prepare many long-range Bell pairs on qubits connected by edge-disjoint paths of ancillas in constant depth that can be used to perform these long-range operations. This forms one core part of our Edge-Disjoint Paths Compilation (EDPC) algorithm, by easily performing many parallel long-range Clifford operations in constant depth. It also allows us to establish a connection between surface code compilation and several well-studied edge-disjoint paths problems. Similar techniques allow us to perform non-Clifford single-qubit rotations far from magic state distillation factories. In this case, we can easily find the maximum set of paths by a max-flow reduction, which forms the other major part of EDPC. EDPC has the best asymptotic worst-case performance guarantees on the circuit depth for compiling parallel operations when compared to related compilation methods based on swaps and network coding. EDPC also shows a quadratic depth improvement over sequential Pauli-based compilation for parallel rotations requiring magic resources. We implement EDPC and find significantly improved performance for circuits built from parallel cnots, and for circuits which implement the multi-controlled $X$ gate.