Classical Complexity of Unitary Transformations

TL;DR

This paper explores the classical computational complexity involved in approximating finite-dimensional unitary transformations, linking it to classical descriptional complexity for quantum systems.

Contribution

It introduces a framework for analyzing the classical complexity of implementing unitary transformations on qubits, bridging quantum and classical computational theories.

Findings

Provides a formal measure of classical complexity for unitaries.

Connects classical descriptional complexity with quantum transformations.

Lays groundwork for future complexity analysis of quantum operations.

Abstract

We discuss a classical complexity of finite-dimensional unitary transformations, which can been seen as a computable approximation of classical descriptional complexity of a unitary transformation acting on a set of qubits.