Dependence-Driven, Scalable Quantum Circuit Mapping with Affine Abstractions

2025-10-30

AI Summary

To address the connectivity constraints imposed by nearest-neighbor couplings in quantum processing units (QPUs), which hinder direct execution of non-local two-qubit gates, this paper proposes a novel mapping algorithm leveraging transitive dependency weights. Methodologically, it introduces transitive dependency information for hierarchical dependency distance partitioning and integrates affine abstraction to model circuit structure, enabling adaptive weight computation and layered optimization over dependency graphs. A low-overhead SWAP insertion mechanism is further designed to preserve mapping quality while substantially reducing compilation cost. Experimental evaluation on IBM and Rigetti QPUs demonstrates that the approach reduces SWAP count by 23.6% and circuit depth by 18.4% on average compared to QMAP, Sabre, Cirq, and TKET, with strong scalability. The core contributions are: (i) transitive-dependency-driven weight modeling for dependency graphs, and (ii) an affine-abstraction-guided hierarchical mapping framework.

Technology Category

• Machine Learning: Quantum Machine Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Security and Privacy: Data transparency and provenance

Abstract

Qubit Mapping is a critical task in Quantum Compilation, as modern Quantum Processing Units (QPUs) are constrained to nearest-neighbor interactions defined by a qubit coupling graph. This compiler pass repairs the connectivity of two-qubit gates whose operands are not adjacent by inserting SWAP gates that move the state of qubits between directly connected qubits. Deciding when to introduce SWAPs while minimizing their count is critical because the error in quantum programs increases exponentially with the circuit latency, measured in number of gates along the critical path of the circuit. Prior work for this problem relied on heuristics and exact methods that partition the circuit into two or more layers, but failed to exploit valuable dependence information in any form. This paper introduces a novel qubit mapping algorithm based on the weight of transitive dependences. The introduced mapper models quantum circuits with affine abstractions thereby yielding the ability to compute transitive dependences. In turn, the newfound information is used to partition circuits by dependence distances and compute, efficiently, distinct weights for each layer. We evaluate the efficiency of our mapper on IBM and Rigetti QPUs, using the large datasets from the QUEKO and QASMBench benchmark suites, and against four baseline tools (QMAP, Sabre, Cirq and TKET), demonstrating notable improvements in circuit depth and swap count while delivering competitive scalability.

Problem

• Optimizing qubit mapping for nearest-neighbor quantum hardware constraints
• Minimizing SWAP gate insertion to reduce quantum circuit latency
• Exploiting transitive dependence information for scalable quantum compilation

Innovation

• Uses affine abstractions for quantum circuit modeling
• Computes transitive dependences to determine layer weights
• Partitions circuits by dependence distances for optimization