Surface Code Compilation via Edge-Disjoint Paths
We provide an efficient algorithm to compile quantum circuits for fault-tolerant execution. We target surface codes, which form a two-dimensional 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 ancillae in constant depth that can be used to perform these long-range operations. This forms one core part of our edge-disjoint path 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 path 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 swap gates 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 controlled-not (CNOT) gates, and for circuits that implement the multicontrolled X gate CkNOT .
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
- Grant/Contract Number:
- SC0019040; 89233218CNA000001
- OSTI ID:
- 1869727
- Alternate ID(s):
- OSTI ID: 1878073
- Report Number(s):
- LA-UR-22-24266; PQRUAG; 020342
- Journal Information:
- PRX Quantum, Journal Name: PRX Quantum Vol. 3 Journal Issue: 2; ISSN 2691-3399
- Publisher:
- American Physical SocietyCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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