Input independence

TL;DR

This paper proves a principle in quantum computing stating that the probability of a quantum circuit following a specific computation path is independent of its input, highlighting a fundamental property of quantum circuit behavior.

Contribution

It introduces and formalizes the input independence principle for quantum circuits, providing a new theoretical insight into quantum computation paths.

Findings

Probability of path $$ is input-independent in quantum circuits.

Formal proof of the input independence principle.

Implications for quantum circuit analysis and design.

Abstract

We establish the following input independence principle. If a quantum circuit $\mathcal C$ computes a unitary transformation $U_\mu$ along a computation path $\mu$, then the probability that computation of $\mathcal C$ follows path $\mu$ is independent of the input.