[Paper Review] Quantum Circuit Transformation Based on Subgraph Isomorphism and Tabu Search

Hui Jiang, Yuxin Deng+1 more|arXiv (Cornell University)|Apr 12, 2021

Quantum Computing Algorithms and Architecture27 references5 citations

TL;DR

This paper proposes a two-stage quantum circuit transformation method combining Complementary Subgraph Isomorphism and Complement (CSIC) for initial mapping and Tabu Search-based Adjustment (TSA) for dynamic optimization. CSIC reduces auxiliary gates by 22.43% and circuit depth by 8.46% on average compared to wghtgraph, while TSA demonstrates superior scalability in mapping refinement.

ABSTRACT

The goal of quantum circuit transformation is to construct mappings from logical quantum circuits to physical ones in an acceptable amount of time, and in the meantime to introduce as few auxiliary gates as possible. We present an effective approach to constructing the mappings. It consists of two key steps: one makes use of a combined subgraph isomorphism and complement (CSIC) to initialize a mapping, the other dynamically adjusts the mapping by using Tabu search-based adjustment (TSA). Our experiments show that, compared with the very recent method wghtgraph considered in the literature, CSIC can save 22.43% of auxiliary gates and reduce the depth of output circuits by 8.46% on average in the initialization of the mapping, and TSA has a better scalability than many state-of-the-art algorithms for adjusting mappings.

Motivation & Objective

• To develop an efficient quantum circuit mapping technique that minimizes auxiliary gates and circuit depth.
• To address the challenge of mapping logical quantum circuits to physical architectures within acceptable timeframes.
• To improve scalability and optimization quality in quantum circuit transformation compared to existing state-of-the-art methods.
• To reduce resource overhead in NISQ-era quantum computing by minimizing ancilla qubit usage and circuit depth.

Proposed method

• The method uses Complementary Subgraph Isomorphism and Complement (CSIC) to initialize a logical-to-physical qubit mapping by identifying optimal substructure matches.
• CSIC leverages subgraph isomorphism with complement graph analysis to enhance mapping quality during initialization.
• A Tabu Search-based Adjustment (TSA) mechanism dynamically refines the initial mapping to further reduce circuit depth and auxiliary gate count.
• TSA employs memory-based search strategies to avoid local optima and improve scalability across diverse circuit architectures.
• The approach integrates both static initialization and iterative improvement phases to balance speed and optimization quality.
• The method is evaluated against the recent wghtgraph approach to benchmark performance in gate count and circuit depth reduction.

Experimental results

Research questions

• RQ1 Can a combined subgraph isomorphism and complement technique (CSIC) significantly reduce auxiliary gate count in quantum circuit initialization?
• RQ2 How does the performance of CSIC compare to wghtgraph in terms of auxiliary gate usage and circuit depth?
• RQ3 To what extent can Tabu Search-based Adjustment (TSA) improve mapping quality and scalability in quantum circuit transformation?
• RQ4 Does the integration of CSIC and TSA lead to better overall optimization than standalone methods?
• RQ5 How scalable is the proposed two-stage approach across diverse quantum circuit benchmarks?

Key findings

• CSIC reduces the average number of auxiliary gates by 22.43% compared to the wghtgraph method during initial mapping.
• CSIC reduces circuit depth by an average of 8.46% compared to wghtgraph in the initialization phase.
• The Tabu Search-based Adjustment (TSA) mechanism demonstrates better scalability than many state-of-the-art algorithms for mapping refinement.
• The two-stage approach—CSIC for initialization and TSA for refinement—achieves superior optimization in both gate count and depth.
• The method maintains high performance across diverse quantum circuits, indicating strong generalization and robustness.
• The integration of CSIC and TSA results in a more efficient and scalable solution for quantum circuit mapping in NISQ devices.