# CNOT circuit extraction for topologically-constrained quantum memories

## TL;DR

This paper introduces a novel Gaussian elimination-based method for mapping CNOT circuits onto topologically constrained quantum memories, improving efficiency over existing routines and adaptable to other circuit types.

## Contribution

It presents a new technique for quantum circuit routing using Steiner trees, specifically optimized for CNOT circuits on constrained architectures.

## Key findings

- Significantly outperforms general-purpose routines on CNOT circuits.
- Provides a reference implementation demonstrating improved efficiency.
- Extensible to CNOT+Rz circuits and circuit simplification methods.

## Abstract

Many physical implementations of quantum computers impose stringent memory constraints in which 2-qubit operations can only be performed between qubits which are nearest neighbours in a lattice or graph structure. Hence, before a computation can be run on such a device, it must be mapped onto the physical architecture. That is, logical qubits must be assigned physical locations in the quantum memory, and the circuit must be replaced by an equivalent one containing only operations between nearest neighbours. In this paper, we give a new technique for quantum circuit mapping (a.k.a. routing), based on Gaussian elimination constrained to certain optimal spanning trees called Steiner trees. We give a reference implementation of the technique for CNOT circuits and show that it significantly out-performs general-purpose routines on CNOT circuits. We then comment on how the technique can be extended straightforwardly to the synthesis of CNOT+Rz circuits and as a modification to a recently-proposed circuit simplification/extraction procedure for generic circuits based on the ZX-calculus.

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Source: https://tomesphere.com/paper/1904.00633