THREE-QUBIT DEUTSCH-JOZSA IN MEASUREMENT-BASED QUANTUM COMPUTING

Three qubit Deutsch-Jozsa version three Three-Qubit Deutsch-Jozsa in Measurement-Based Quantum Computing

Measurement-based quantum computing, 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 eleven-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.

One. Introduction

Measurement-based quantum computing is an alternate paradigm for quantum computing that is conceptually different than the commonly-used circuit-based model. As opposed to the circuit model, in which entangling multi-qubit gates effectuate the computing power of quantum mechanics, measurement-based quantum computing pre-encodes the entanglement in a highly entangled multi-qubit initial state, typically a cluster state, that is prepared in advance. Single-qubit measurements on the entangled initial state are then all that is needed to unleash the power of quantum computing in full generality. The measurement-based quantum computing model can lead to alternate experimental implementations of quantum algorithms that can potentially be more flexible and efficient than circuit-based implementations. In addition, it is useful for exploring and understanding fundamental aspects of quantum computing.

With regard to experimental utility, since the quantum-specific part of entanglement is carried out at the beginning when the initial cluster state is prepared, it could be outsourced to a device that is only responsible for generating entanglement. This prepared state would then be sent to a device that must only carry out one-qubit measurements which are, in general, easy to do. This device would, in effect, function as a universal computer. On a fundamental level, measurement-based quantum computing leads