Tackling the Qubit Mapping Problem with Permutation-Aware Synthesis

TL;DR

This paper introduces a hierarchical qubit mapping and routing algorithm that optimizes quantum circuits by decomposing them into blocks, applying permutation-aware synthesis, and mapping with permutation-aware algorithms, resulting in significantly reduced gate counts compared to existing methods.

Contribution

The paper presents a novel PAS+PAM approach that allows circuit structure modification and hardware-aware optimization, outperforming existing mapping algorithms and commercial compilers in circuit quality.

Findings

Up to 68% fewer gates than Qiskit

Up to 36% fewer gates than TKET

Scales effectively and integrates into existing frameworks

Abstract

We propose a novel hierarchical qubit mapping and routing algorithm. First, a circuit is decomposed into blocks that span an identical number of qubits. In the second stage permutation-aware synthesis (PAS), each block is optimized and synthesized in isolation. In the third stage a permutation-aware mapping (PAM) algorithm maps the blocks to the target device based on the information from the second stage. Our approach is based on the following insights: (1) partitioning the circuit into blocks is beneficial for qubit mapping and routing; (2) with PAS, any block can implement an arbitrary input-output qubit mapping that reduces the gate count; and (3) with PAM, for two adjacent blocks we can select input-output permutations that optimize each block together with the amount of communication required at the block boundary. Whereas existing mapping algorithms preserve the original circuit structure and only introduce "minimal" communication via inserting SWAP or bridge gates, the PAS+PAM approach can additionally change the circuit structure and take full advantage of hardware-connectivity. Our experiments show that we can produce better-quality circuits than existing mapping algorithms or commercial compilers (Qiskit, TKET, BQSKit) with maximum optimization settings. For a combination of benchmarks we produce circuits shorter by up to 68% (18% on average) fewer gates than Qiskit, up to 36% (9% on average) fewer gates than TKET, and up to 67% (21% on average) fewer gates than BQSKit. Furthermore, the approach scales, and it can be seamlessly integrated into any quantum circuit compiler or optimization infrastructure.