# Nash embedding: a road map to realizing quantum hardware

## TL;DR

This paper proposes using Nash embedding to map quantum circuits into reversible computing models, facilitating their physical implementation in Euclidean hardware.

## Contribution

It introduces a novel mathematical approach to realize quantum circuits as reversible circuits via Nash embedding, bridging quantum and classical hardware.

## Key findings

- Quantum circuits can be mapped into reversible circuits using Nash embedding.
- This mapping enables practical realization of quantum computations in Euclidean hardware.
- The approach provides a robust mathematical framework for quantum hardware implementation.

## Abstract

The non-Euclidean nature of the mathematical model of quantum circuits leaves open the question of their practical implementation in hardware platforms which necessarily reside in the Euclidean space $\mathbb{R}^3$. On the other hand, reversible circuits are elements of Euclidean spaces, making their physical realization in hardware platforms possible and practical. Here, the quantum circuit model for quantum computing is mapped into that of reversible computing in a mathematically robust fashion using Nash embedding so that every quantum computation can be realized as an equivalent reversible one.