Distributed exact quantum algorithms for Deutsch-Jozsa problem

TL;DR

This paper introduces three distributed quantum algorithms for the Deutsch-Jozsa problem, leveraging problem structure to reduce qubits and circuit depth, and demonstrating significant speedup over classical distributed methods.

Contribution

The paper uncovers the inherent structure of the DJ problem in distributed settings and proposes novel exact quantum algorithms that improve efficiency and scalability.

Findings

Algorithms outperform classical distributed algorithms in speed.

Reduced qubit and circuit depth compared to standard DJ algorithm.

Extensions to multiple computing nodes are feasible.

Abstract

Deutsch-Jozsa (DJ) problem is one of the most important problems demonstrating the power of quantum algorithm. DJ problem can be described as a Boolean function $f$: $\{0,1\}^n\rightarrow \{0,1\}$ with promising it is either constant or balanced, and the purpose is to determine which type it is. DJ algorithm can solve it exactly with one query. In this paper, we first discover the inherent structure of DJ problem in distributed scenario by giving a number of equivalence characterizations between $f$ being constant (balanced) and some properties of $f$'s subfunctions, and then we propose three distributed exact quantum algorithms for solving DJ problem. Our algorithms have essential acceleration over distributed classical deterministic algorithm, and can be extended to the case of multiple computing nodes. Compared with DJ algorithm, our algorithms can reduce the number of qubits and the depth of circuit implementing a single query operator. Therefore, we find that the structure of problem should be clarified for designing distributed quantum algorithm to solve it.