# Circuit Transformations for Quantum Architectures

## TL;DR

This paper introduces efficient quantum circuit transformation methods tailored for specific architectures, utilizing advanced routing algorithms and heuristics to optimize qubit placement and movement.

## Contribution

It develops new routing procedures and extends existing algorithms to support partial permutations, improving circuit transformations for quantum architectures.

## Key findings

- Improved routing bounds for parallel qubit movement.
- Effective heuristics for qubit placement in large circuits.
- Software implementation demonstrating practical performance.

## 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.

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Source: https://tomesphere.com/paper/1902.09102