Lattice Surgery Compilation Beyond the Surface Code

Abstract

Large-scale fault-tolerant quantum computation requires compiling logical circuits into physical operations tailored to a given architecture. Prior work addressing this challenge has mostly focused on the surface code and lattice surgery schemes. In this work, we broaden the scope by considering lattice surgery compilation for topological codes beyond the surface code. We begin by defining a code substrate - a blueprint for implementing topological codes and lattice surgery. We then abstract from the microscopic details and rephrase the compilation task as a mapping and routing problem on a macroscopic routing graph, potentially subject to substrate-specific constraints. We explore specific substrates and codes, including the color code and the folded surface code, providing detailed microscopic constructions. For the color code, we present numerical simulations analyzing how design choices at the microscopic and macroscopic levels affect the depth of compiled logical $\mathrm{CNOT}+\mathrm{T}$ circuits. An open-source code is available on GitHub https://github.com/cda-tum/mqt-qecc.

12 pages, 11 figures

References in corpus (30)

• Surface codes: Towards practical large-scale quantum computation
• Quantum information with Rydberg atoms
• Circuit Quantum Electrodynamics
• Universal Quantum Computation with ideal Clifford gates and noisy ancillas
• Many-Body Physics with Individually-Controlled Rydberg Atoms
• Topological Quantum Distillation
• Surface code quantum computing by lattice surgery
• High-threshold and low-overhead fault-tolerant quantum memory
• A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery
• Demonstration of fault-tolerant universal quantum gate operations
• Unfolding the color code
• Sparse Blossom: correcting a million errors per core second with minimum-weight matching
• Quantum "hyperbicycle" low-density parity check codes with finite rate
• Triangular color codes on trivalent graphs with flag qubits
• Combining Topological Hardware and Topological Software: Color Code Quantum Computing with Topological Superconductor Networks
• Surface code compilation via edge-disjoint paths
• Anyon condensation and the color code
• Code Deformation and Lattice Surgery Are Gauge Fixing
• The MQT Handbook: A Summary of Design Automation Tools and Software for Quantum Computing
• Mapping of Lattice Surgery-based Quantum Circuits on Surface Code Architectures
• Scaling and logic in the color code on a superconducting quantum processor
• Transversal Clifford gates on folded surface codes
• Fault-tolerance thresholds for the surface code with fabrication errors
• Optimization of Lattice Surgery is NP-Hard
• Lattice Surgery Translation for Quantum Computation
• Efficient color code decoders in $d\ge 2$ dimensions from toric code decoders
• A High Performance Compiler for Very Large Scale Surface Code Computations
• Shortest node-disjoint paths on random graphs
• Color code decoder with improved scaling for correcting circuit-level noise
• Snakes and Ladders: Adapting the surface code to defects