Three-qubit Deutsch-Jozsa in measurement-based quantum computing

TL;DR

This paper reformulates the three-qubit Deutsch-Jozsa algorithm within measurement-based quantum computing using ZX-calculus, providing a new graphical implementation and demonstrating its flexibility with different oracle realizations.

Contribution

It introduces a novel ZX-calculus-based method to encode the three-qubit Deutsch-Jozsa algorithm as a measurement-based quantum computation, including a detailed graph-diagram and lattice cluster state.

Findings

Graphical ZX representation of the three-qubit Deutsch-Jozsa algorithm

Implementation of the algorithm on an 11-qubit cluster state

Flexible oracle implementation through measurement choices

Abstract

Measurement-based quantum computing (MBQC), an alternate paradigm for formulating quantum algorithms, can lead to potentially more flexible and efficient implementations as well as to theoretical insights on the role of entanglement in a quantum algorithm. Using the graph-theoretical ZX-calculus, we describe and apply a general scheme for reformulating quantum circuits as MBQC implementations. After illustrating the method using the two-qubit Deutsch-Jozsa algorithm, we derive a ZX graph-diagram that encodes a general MBQC implementation for the three-qubit Deutsch-Jozsa algorithm. This graph describes an 11-qubit cluster state on which single-qubit measurements are used to execute the algorithm. Particular sets of choices of the axes for the measurements can be used to implement any realization of the oracle. In addition, we derive an equivalent lattice cluster state for the algorithm.