On Computational Power of Quantum Read-Once Branching Programs

TL;DR

This paper reviews the computational capabilities of quantum read-once branching programs, demonstrating they can efficiently compute certain Boolean functions and are closed under polynomial projections.

Contribution

It introduces a quantum fingerprinting technique and shows that Boolean functions with linear polynomial presentations are efficiently computable by quantum read-once branching programs.

Findings

Quantum read-once branching programs can compute Boolean functions with linear polynomial presentations.

The class of functions computable by these programs is closed under polynomial projections.

Efficient quantum algorithms for specific Boolean functions are demonstrated.

Abstract

In this paper we review our current results concerning the computational power of quantum read-once branching programs. First of all, based on the circuit presentation of quantum branching programs and our variant of quantum fingerprinting technique, we show that any Boolean function with linear polynomial presentation can be computed by a quantum read-once branching program using a relatively small (usually logarithmic in the size of input) number of qubits. Then we show that the described class of Boolean functions is closed under the polynomial projections.