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Dependency-Aware Compilation for Surface Code Quantum Architectures

Abtin Molavi, Amanda Xu, Swamit Tannu, Aws Albarghouthi

TL;DR

This work tackles the surface-code mapping and routing (scmr) problem by introducing dascot, a dependency-aware optimization framework that decouples mapping and routing. It leverages layered interaction graphs to capture flow-sensitive qubit interactions for mapping and formulates routing as a discrete optimization over routing orders guided by circuit criticality, both solved via simulated annealing; an exact SAT-based baseline provides a small-circuit optimum reference. The approach demonstrates strong empirical performance across 232 circuits and two space-time architectures, beating or matching state-of-the-art baselines and achieving near-optimality on many instances while remaining scalable to thousands of gates. The work advances practical quantum compilation for fault-tolerant surface-code devices and offers a versatile, architecture-agnostic toolset with potential extensions to heterogeneous, multi-chip layouts and beyond.

Abstract

Practical applications of quantum computing depend on fault-tolerant devices with error correction. Today, the most promising approach is a class of error-correcting codes called surface codes. We study the problem of compiling quantum circuits for quantum computers implementing surface codes. Optimal or near-optimal compilation is critical for both efficiency and correctness. The compilation problem requires (1) mapping circuit qubits to the device qubits and (2) routing execution paths between interacting qubits. We solve this problem efficiently and near-optimally with a novel algorithm that exploits the dependency structure of circuit operations to formulate discrete optimization problems that can be approximated via simulated annealing, a classic and simple algorithm. Our extensive evaluation shows that our approach is powerful and flexible for compiling realistic workloads.

Dependency-Aware Compilation for Surface Code Quantum Architectures

TL;DR

This work tackles the surface-code mapping and routing (scmr) problem by introducing dascot, a dependency-aware optimization framework that decouples mapping and routing. It leverages layered interaction graphs to capture flow-sensitive qubit interactions for mapping and formulates routing as a discrete optimization over routing orders guided by circuit criticality, both solved via simulated annealing; an exact SAT-based baseline provides a small-circuit optimum reference. The approach demonstrates strong empirical performance across 232 circuits and two space-time architectures, beating or matching state-of-the-art baselines and achieving near-optimality on many instances while remaining scalable to thousands of gates. The work advances practical quantum compilation for fault-tolerant surface-code devices and offers a versatile, architecture-agnostic toolset with potential extensions to heterogeneous, multi-chip layouts and beyond.

Abstract

Practical applications of quantum computing depend on fault-tolerant devices with error correction. Today, the most promising approach is a class of error-correcting codes called surface codes. We study the problem of compiling quantum circuits for quantum computers implementing surface codes. Optimal or near-optimal compilation is critical for both efficiency and correctness. The compilation problem requires (1) mapping circuit qubits to the device qubits and (2) routing execution paths between interacting qubits. We solve this problem efficiently and near-optimally with a novel algorithm that exploits the dependency structure of circuit operations to formulate discrete optimization problems that can be approximated via simulated annealing, a classic and simple algorithm. Our extensive evaluation shows that our approach is powerful and flexible for compiling realistic workloads.
Paper Structure (70 sections, 5 theorems, 10 equations, 28 figures, 1 table, 3 algorithms)

This paper contains 70 sections, 5 theorems, 10 equations, 28 figures, 1 table, 3 algorithms.

Table of Contents

  1. Introduction
  2. The dascot approach
  3. Dependency-aware mapping
  4. Dependency-aware routing
  5. Reductions to discrete optimization
  6. sat-based optimal baseline
  7. Evaluation
  8. Contributions
  9. Surface Code Compilation: A Primer
  10. Quantum error correction
  11. Surface Code Mapping and Routing by Example
  12. Optimal mapping & routing
  13. Executing T gates
  14. An Overview of Our Approach
  15. Architectural flexibility
  16. ...and 55 more sections

Key Result

theorem 1

The formula $\varphi(A, C, t_s)$ is satisfiable if and only if there is a map $M$ and corresponding valid gate route $(t_s, R_\textsc{time}, R_\textsc{space})$ for the scmr problem given by $A$ and $C$, and there is an explicit translation from scmr solutions $M, (t_s, R_\textsc{time}, R_\textsc{spa

Figures (28)

  • Figure 1: Spatial constraints preventing parallel execution
  • Figure 2: Overview of our approach, dascot
  • Figure 3: Quantum device implementing a surface code
  • Figure 4: Simple instance of scmr
  • Figure 5: Suboptimal mapping increases execution time
  • ...and 23 more figures

Theorems & Definitions (9)

  • theorem 1
  • Definition 1: scmr Decision Problem
  • theorem 2
  • Definition 2: Processor Scheduling Problem
  • lemma 1
  • lemma 2
  • Definition 3: Surface Code Routing Decision Problem
  • theorem 3
  • Definition 4: Node-Disjoint Paths on a Grid Problem