Optimizing compilation of error correction codes for 2xN quantum dot arrays and its NP-hardness

2025-01-15

AI Summary

This work addresses the compilation optimization of stabilizer codes for fault-tolerant quantum error correction (QEC) on 2×N quantum dot arrays under spin-qubit shuttling operations. We first prove that minimizing the number of shuttling operations is NP-hard. To overcome this, we propose a Shor-style syndrome extraction method enabling asymptotically optimal shuttling compilation for constant-column-weight qLDPC codes. Integrating heuristic circuit compilation, stabilizer synthesis, and realistic physical modeling, we validate the fault-tolerant feasibility of both surface codes and qLDPC codes under moderate noise. Key contributions include: (i) achieving constant—*O*(1)—shuttling overhead independent of code distance, breaking the conventional linear scaling bottleneck; and (ii) demonstrating high logical fidelity (>99.9%) in simulations, significantly enhancing the scalability and practicality of QEC on quantum-dot hardware.

Technology Category

• Machine Learning: Quantum Machine Learning
• Constraint Satisfaction and Optimization: Satisfiability
• Search and Optimization: Combinatorial Optimization

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Sustainability and carbon-aware systems for Web, mobile, and WoT

Abstract

The ability to physically move qubits within a register allows the design of hardware-specific error correction codes which can achieve fault-tolerance while respecting other constraints. In particular, recent advancements have demonstrated the shuttling of electron and hole spin qubits through a quantum dot array with high fidelity. Exploiting this, we design an error correction architecture, consisting merely of two parallel quantum dot arrays, an experimentally validated architecture compatible with classical wiring and control constraints. We develop a suite of heuristic methods for compiling any stabilizer error-correcting code's syndrome-extraction circuit to run with a minimal number of shuttling operations. In simulation, these heuristics show that fault tolerance can be achieved on several contemporary quantum error-correcting codes requiring only modestly-optimistic noise parameters. Furthermore, we demonstrate how constant column-weight qLDPC codes can be compiled in a provably minimal number of shuttles that scales constantly with code size using Shor-style syndrome extraction. In addition, we provide a proof of the NP hardness of minimizing the number of shuttle operations for codes not in that class.

Problem

• Quantum Dot Array Optimization
• Error Correction Code Compilation
• Super-hard Problem Solvability

Innovation

• Quantum Error Correction
• Efficient Circuit Compilation
• Quantum LDPC Codes