Cluster-state quantum computation

Abstract

This article is a short introduction to and review of the cluster-state model of quantum computation, in which coherent quantum information processing is accomplished via a sequence of single-qubit measurements applied to a fixed quantum state known as a cluster state. We also discuss a few novel properties of the model, including a proof that the cluster state cannot occur as the exact ground state of any naturally occurring physical system, and a proof that measurements on any quantum state which is linearly prepared in one dimension can be efficiently simulated on a classical computer, and thus are not candidates for use as a substrate for quantum computation.

15 pages, resubmitted version accepted to Rev. Math. Phys

References in corpus (13)

• Experimental One-Way Quantum Computing
• Resource-efficient linear optical quantum computation
• Efficient high-fidelity quantum computation using matter qubits and linear optics
• Valence Bond Solids for Quantum Computation
• Fault-tolerant quantum computation with cluster states
• Computation by measurements: a unifying picture
• Simple proof of fault tolerance in the graph-state model
• Nonlinear quantum optical computing via measurement
• Measurement-Based Quantum Turing Machines and their Universality
• A relational quantum computer using only two-qubit total spin measurement and an initial supply of highly mixed single qubit states
• The Measurement Calculus
• Complexity of Graph State Preparation
• Quantum computation by measurements

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