A quantum circuit for OR

TL;DR

This paper introduces the first quantum circuit capable of reliably computing the OR of a function's outputs with a single evaluation, demonstrating quantum speedup for this logical operation.

Contribution

It presents a novel quantum circuit for OR, expanding the set of logical connectives with quantum speedup beyond XOR, and introduces a new potential quantum computational effect.

Findings

Quantum circuit for OR surpasses classical reliability with one evaluation

OR joins XOR as a logically complete set with quantum advantage

Potential new quantum computational effect identified

Abstract

We give the first quantum circuit for computing $f(0)$ OR $f(1)$ more reliably than is classically possible with a single evaluation of the function. OR therefore joins XOR (i.e. parity, $f(0) \oplus f(1)$) to give the full set of logical connectives (up to relabeling of inputs and outputs) for which there is quantum speedup. The XOR algorithm is of fundamental importance in quantum computation; our OR algorithm (found with the aid of genetic programming), may represent a new quantum computational effect, also useful as a ``subroutine''.