Surface code compilation via edge-disjoint paths

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.

48 pages, 20 figures. Published version in PRX Quantum. Includes new comparison table, tightened Theorem 3.3/3.4, and source code

References in corpus (33)

• Fault-tolerant quantum computation by anyons
• Surface codes: Towards practical large-scale quantum computation
• Universal Quantum Computation with ideal Clifford gates and noisy ancillas
• Quantum Computing with Very Noisy Devices
• Elucidating Reaction Mechanisms on Quantum Computers
• How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits
• Scalable Designs for Quasiparticle-Poisoning-Protected Topological Quantum Computation with Majorana Zero Modes
• Surface code quantum computing by lattice surgery
• A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery
• Quantum codes on a lattice with boundary
• Quantum computing with nearest neighbor interactions and error rates over 1%
• Soundness and completeness of quantum root-mean-square errors
• Novel constructions for the fault-tolerant Toffoli gate
• Topological and subsystem codes on low-degree graphs with flag qubits
• Quantum network communication -- the butterfly and beyond
• On the capacities of bipartite Hamiltonians and unitary gates
• Poking holes and cutting corners to achieve Clifford gates with the surface code
• The surface code with a twist
• Universal quantum computing with twist-free and temporally encoded lattice surgery
• Fault-Tolerant Postselected Quantum Computation: Schemes
• Quantum network coding for quantum repeaters
• Optimized Surface Code Communication in Superconducting Quantum Computers
• General Scheme for Perfect Quantum Network Coding with Free Classical Communication
• Controlled-NOT for multiparticle qubits and topological quantum computation based on parity measurements
• Mapping of Lattice Surgery-based Quantum Circuits on Surface Code Architectures
• Braiding by Majorana Tracking and Long-Range CNOT Gates with Color Codes
• Quantum computing by color-code lattice surgery
• Optimization of the surface code design for Majorana-based qubits
• Advantages and limitations of quantum routing
• Quantum linear network coding for entanglement distribution in restricted architectures
• Bounds on stabilizer measurement circuits and obstructions to local implementations of quantum LDPC codes
• Flexible layout of surface code computations using AutoCCZ states
• Advantages of a modular high-level quantum programming framework

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