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Measurement-based quantum computation on cluster states

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TLDR
This work gives a detailed account of the one-way quantum computer, a scheme of quantum computation that consists entirely of one-qubit measurements on a particular class of entangled states, the cluster states, and proves its universality.
Abstract
We give a detailed account of the one-way quantum computer, a scheme of quantum computation that consists entirely of one-qubit measurements on a particular class of entangled states, the cluster states. We prove its universality, describe why its underlying computational model is different from the network model of quantum computation, and relate quantum algorithms to mathematical graphs. Further we investigate the scaling of required resources and give a number of examples for circuits of practical interest such as the circuit for quantum Fourier transformation and for the quantum adder. Finally, we describe computation with clusters of finite size.

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Citations
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Quantum entanglement

TL;DR: In this article, the basic aspects of entanglement including its characterization, detection, distillation, and quantification are discussed, and a basic role of entonglement in quantum communication within distant labs paradigm is discussed.
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Entanglement in many-body systems

TL;DR: In this article, the properties of entanglement in many-body systems are reviewed and both bipartite and multipartite entanglements are considered, and the zero and finite temperature properties of entangled states in interacting spin, fermion and boson model systems are discussed.
Journal ArticleDOI

Linear optical quantum computing with photonic qubits

TL;DR: In this article, the authors reviewed the original theory and its improvements, and a few examples of experimental two-qubit gates are given, and the use of realistic components, the errors they induce in the computation, and how these errors can be corrected is discussed.
Journal ArticleDOI

Surface codes: Towards practical large-scale quantum computation

TL;DR: The concept of the stabilizer, using two qubits, is introduced, and the single-qubit Hadamard, S and T operators are described, completing the set of required gates for a universal quantum computer.
Journal ArticleDOI

Quantum information with Rydberg atoms

TL;DR: Rydberg atoms with principal quantum number $n⪢1$ have exaggerated atomic properties including dipole-dipole interactions that scale as ${n}^{4}$ and radiative lifetimes that scale at least{n}−3}$ as mentioned in this paper, and it was proposed a decade ago to implement quantum gates between neutral atom qubits.
References
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Book

Quantum Computation and Quantum Information

TL;DR: In this article, the quantum Fourier transform and its application in quantum information theory is discussed, and distance measures for quantum information are defined. And quantum error-correction and entropy and information are discussed.
Journal ArticleDOI

Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer

TL;DR: In this paper, the authors considered factoring integers and finding discrete logarithms on a quantum computer and gave an efficient randomized algorithm for these two problems, which takes a number of steps polynomial in the input size of the integer to be factored.
Journal ArticleDOI

Simulating physics with computers

TL;DR: In this paper, the authors describe the possibility of simulating physics in the classical approximation, a thing which is usually described by local differential equations, and the possibility that there is to be an exact simulation, that the computer will do exactly the same as nature.
Proceedings ArticleDOI

A fast quantum mechanical algorithm for database search

TL;DR: In this paper, it was shown that a quantum mechanical computer can solve integer factorization problem in a finite power of O(log n) time, where n is the number of elements in a given integer.
Journal ArticleDOI

A scheme for efficient quantum computation with linear optics.

TL;DR: It is shown that efficient quantum computation is possible using only beam splitters, phase shifters, single photon sources and photo-detectors and are robust against errors from photon loss and detector inefficiency.
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