[Paper Review] Circuit Transformations for Quantum Architectures

Andrew M. Childs, Eddie Schoute+1 more|arXiv (Cornell University)|Jan 1, 2019

Quantum Computing Algorithms and Architecture42 references53 citations

TL;DR

This paper proposes efficient circuit transformations for quantum architectures by modeling qubit movement as partial permutations using two frameworks: Partial Routing via Matchings (for minimizing circuit depth) and Partial Token Swapping (for minimizing circuit size). The authors introduce new algorithms for common architectures like grids and modular designs, demonstrate superior performance over Qiskit’s transformation in weighted depth and size, and release open-source tools for benchmarking quantum circuit mappings under hardware constraints.

ABSTRACT

Quantum computer architectures impose restrictions on qubit interactions. We propose efficient circuit transformations that modify a given quantum circuit to fit an architecture, allowing for any initial and final mapping of circuit qubits to architecture qubits. To achieve this, we first consider the qubit movement subproblem and use the ROUTING VIA MATCHINGS framework to prove tighter bounds on parallel routing. In practice, we only need to perform partial permutations, so we generalize ROUTING VIA MATCHINGS to that setting. We give new routing procedures for common architecture graphs and for the generalized hierarchical product of graphs, which produces subgraphs of the Cartesian product. Secondly, for serial routing, we consider the TOKEN SWAPPING framework and extend a 4-approximation algorithm for general graphs to support partial permutations. We apply these routing procedures to give several circuit transformations, using various heuristic qubit placement subroutines. We implement these transformations in software and compare their performance for large quantum circuits on grid and modular architectures, identifying strategies that work well in practice.

Motivation & Objective

• To address the challenge of mapping arbitrary quantum circuits onto constrained quantum architectures with minimal overhead.
• To develop scalable, polynomial-time algorithms for qubit movement and placement that minimize circuit depth or size.
• To provide theoretical bounds and practical implementations for routing qubits efficiently under architectural constraints.
• To compare heuristic strategies for qubit placement and movement in real-world architectures like 2D grids and modular systems.
• To enable better resource estimation and architecture design by providing tools that model realistic hardware constraints.

Proposed method

• Model the architecture as a simple graph where vertices are qubits and edges represent allowed two-qubit gates.
• Introduce Partial Routing via Matchings to optimize parallel qubit movement with tighter theoretical bounds for partial permutations.
• Develop a 4-approximation algorithm for Partial Token Swapping to minimize circuit size in general graphs.
• Implement multiple heuristic qubit placement strategies (mappers) to optimize for depth or size, combining them with permuter subroutines.
• Construct circuit transformations by composing mappers and permuters, enabling flexible, architecture-aware circuit mapping.
• Evaluate performance on large random and QSP circuits using weighted depth and size metrics across grid and modular architectures.

Experimental results

Research questions

• RQ1 Can partial permutations be efficiently routed in quantum architectures using a generalized version of Routing via Matchings?
• RQ2 How do different heuristic qubit placement strategies affect the overhead in circuit transformations for grid and modular architectures?
• RQ3 What is the performance trade-off between minimizing circuit depth versus circuit size in architecture-respecting transformations?
• RQ4 Can Partial Token Swapping provide better circuit size optimization than traditional swap-based routing in practice?
• RQ5 How do the proposed transformations compare to Qiskit’s circuit transformation in terms of weighted depth and size for large-scale quantum circuits?

Key findings

• The greedy swap circuit transformation outperformed other methods in minimizing both weighted depth and weighted size for large QSP circuits, demonstrating strong practical scalability.
• Partial Routing via Matchings provided superior depth performance on random circuits, especially when optimized for depth, while Qiskit and the greedy method were competitive in certain cases.
• The tf(s, qiskit) transformation performed surprisingly well in minimizing depth despite being designed for size, indicating potential cross-objective benefits.
• The proposed framework with Partial Token Swapping and heuristic mappers achieved near-optimal size performance, with some configurations slightly outperforming standard approaches.
• The open-source implementation of the transformations, along with benchmark circuits and results in TSV format, enables reproducible evaluation and future tool development.