A Generalization of Deutsch's Example

TL;DR

This paper presents a probabilistic quantum algorithm that leverages quantum parallelism to efficiently determine whether a function is constant, extending Deutsch's original example to more general cases.

Contribution

It generalizes Deutsch's problem to functions with larger domains and ranges, providing a probabilistic quantum solution where deterministic solutions are impossible.

Findings

Quantum parallelism enables faster exploration of function domains.

The proposed algorithm outperforms classical sampling strategies.

It demonstrates the power of quantum computation in generalized function analysis.

Abstract

Quantum parallelism is the main feature of quantum computation. In 1985 D. Deutsch showed that a single quantum computation may be sufficient to state whether a two-valued function of a two-valued variable is constant or not. Though the generalized problem with unconstrained domain and range size admits no deterministic quantum solution, a fully probabilistic quantum algorithm is presented in which quantum parallelism is harnessed to achieve a quicker exploration of the domain with respect to the classical ``sampling'' strategy.