Surface code compilation via edge-disjoint paths

• URL: http://arxiv.org/abs/2110.11493v2
• Date: Fri, 1 Jul 2022 19:55:32 GMT
• Title: Surface code compilation via edge-disjoint paths
• Authors: Michael Beverland and Vadym Kliuchnikov and Eddie Schoute
• Abstract summary: We show how to prepare many long-range pairs on qubits connected by edge-disjoint paths of ancillas in constant depth. This forms one core part of our Edge-Disjoint Paths Compilation algorithm. We find significantly improved performance for circuits built from parallel cnots, and for circuits which implement the multi-controlled $X$ gate.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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