Dependence-Driven, Scalable Quantum Circuit Mapping with Affine Abstractions

TL;DR

This work tackles the challenging problem of mapping quantum circuits to near-neighbor hardware by exploiting transitive dependences through affine abstractions, enabling a global, dependence-aware SWAP insertion strategy. It introduces Qlosure, a mapping and routing algorithm that lifts circuits to an affine representation, builds a dependence graph, and uses a layered, look-ahead window with a cost function M(s) to select SWAPs that minimize overall circuit depth and SWAP count. By computing the transitive closure via ISL and weighting gates by downstream impact, Qlosure achieves substantial improvements over state-of-the-art mappers on IBM and Rigetti back-ends across QUEKO and QASMBench circuits, with competitive runtime and scalability. The results demonstrate that dependence-driven, affine abstraction-based mapping can significantly enhance circuit reliability and performance on NISQ devices, offering a scalable path toward more reliable quantum compilation.

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.

Figures (10)

• Figure 1: Qubit mapping example. $q_i$ are logical qubits, $p_j$ are physical ones.
• Figure 2: Mapper comparison: Two circuits are mapped onto the IBM Sherboooke and Rigetti Ankaa-3 QPUs. (i) a 54-qubit circuit (initial depth 900, 9720 two-qubit); and (ii) an 18-qubit circuit (initial depth 1429, 898 two-qubit gates). Metrics of interest are the $\Delta$ (final depth - initial depth) and the SWAP count.
• Figure 3: Qlosure Mapping Pipeline
• Figure 4: Mapping example.
• Figure 5: Mapping time of Qlosure as a function of Quantum Operations (QOPs).