Publikationen – Institut für Theoretische Physik

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The one way quantum computer (QCc)

The one way quantum computer (QCc), aka. measurement based quantum computation. I have invented the QCc jointly with Hans Briegel (US patent 7,277,872). It is a scheme of universal quantum computation by local measurements on a multi-particle entangled quantum state, the so-called cluster state. Quantum information is written into the cluster state, processed and read out by one-qubit measurements only. As the computation proceeds, the entanglement in the resource cluster state is progressively destroyed. Measurements replace unitary evolution as the elementary process driving a quantum computation.

A universal resource for the QCc is the cluster state, a highly entangled mult-qubit quantum state that can be easily generated unitarily by the Ising interaction on a square lattice. In the figure to the left, the qubits forming the cluster state are represented by dots and arrows. The symbol used indicates the basis of local measurement. Dots represent cluster qubits measured in the eigenbasis of the Pauli operator Z, arrows denote measurement in a basis in the equator of the Bloch sphere. The pattern of measurement bases can be regarded as representing a quantum circuit, i.e., the "vertical" direction on the cluster specifies the location of a logical qubit in a quantum register, and the "horizontal" direction on the cluster represents circuit time. However, this simple picture should be taken with a grain of salt: The optimal temporal order of measurements has very little to do with the temporal sequence of gates in the corresponding circuit.

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2010

Sarvepalli P, Raussendorf R. Local equivalence, surface-code states, and matroids. Physical Review A - Atomic, Molecular, and Optical Physics. 2010 Aug 5;82(2):022304. doi: 10.48550/arXiv.0911.1571, 10.1103/PhysRevA.82.022304

Sarvepalli P, Raussendorf R. Matroids and quantum-secret-sharing schemes. Physical Review A - Atomic, Molecular, and Optical Physics. 2010 Mai 24;81(5):052333. doi: 10.48550/arXiv.0909.0549, 10.1103/PhysRevA.81.052333

2009

Briegel HJ, Browne DE, Dür W, Raussendorf R, Van Den Nest M. Measurement-based quantum computation. Nature physics. 2009 Jan 2;5(1):19-36. doi: 10.48550/arXiv.0910.1116, 10.1038/nphys1157

Raußendorf R. Measurement-based quantum computation with cluster states. International Journal of Quantum Information. 2009 Sep;7(6):1053-1203. doi: 10.48550/arXiv.quant-ph/0301052, 10.1142/S0219749909005699

Van Den Nest M, Dür W, Raussendorf R, Briegel HJ. Quantum algorithms for spin models and simulable gate sets for quantum computation. Physical Review A - Atomic, Molecular, and Optical Physics. 2009 Nov 30;80(5):052334. doi: 10.48550/arXiv.0805.1214, 10.1103/PhysRevA.80.052334

2007

Bravyi S, Raussendorf R. Measurement-based quantum computation with the toric code states. Physical Review A - Atomic, Molecular, and Optical Physics. 2007 Aug 6;76(2):022304. doi: 10.48550/arXiv.quant-ph/0610162, 10.1103/PhysRevA.76.022304

Han YJ, Raussendorf R, Duan LM. Scheme for Demonstration of Fractional Statistics of Anyons in an Exactly Solvable Model. Physical Review Letters. 2007 Apr 12;98(15):150404. doi: 10.48550/arXiv.quant-ph/0702031, 10.1103/PhysRevLett.98.150404

Raussendorf R, Harrington J. Fault-Tolerant Quantum Computation with High Threshold in Two Dimensions. Physical review letters. 2007 Mai 11;98(19):190504. doi: 10.48550/arXiv.quant-ph/0610082, 10.1103/PhysRevLett.98.190504

Raussendorf R, Harrington J, Goyal K. Topological fault-tolerance in cluster state quantum computation. New journal of physics. 2007 Jun 29;9:199. doi: 10.1088/1367-2630/9/6/199

2006

Goyal K, McCauley A, Raussendorf R. Purification of large bicolorable graph states. Physical Review A - Atomic, Molecular, and Optical Physics. 2006 Sep 15;74(3):032318. doi: https://doi.org/10.48550/arXiv.quant-ph/0605228, 10.1103/PhysRevA.74.032318

Hein M, Dür W, Eisert J, Raussendorf R, Van Den Nest M, Briegel HJ. Entanglement in graph states and its applications. in Casati G, Shepelyansky DL, Zoller P, Benenti G, Hrsg., Proceedings of the International School of Physics "Enrico Fermi": Quantum Computers, Algorithms and Chaos. IOS Press. 2006. S. 115-218. (Proceedings of the International School of Physics "Enrico Fermi"). doi: 10.3254/978-1-61499-018-5-115

Raussendorf R, Harrington J, Goyal K. A fault-tolerant one-way quantum computer. Annals of physics. 2006 Sep;321(9):2242-2270. Epub 2006 Apr 18. doi: 10.48550/arXiv.quant-ph/0510135, 10.1016/j.aop.2006.01.012

2005

Duan LM, Raussendorf R. Efficient Quantum Computation with Probabilistic Quantum Gates. Physical review letters. 2005 Aug 19;95(8):080503. doi: 10.48550/arXiv.quant-ph/0502120, 10.1103/PhysRevLett.95.080503

Raussendorf R, Briegel HJ. Computational Model for the One-Way Quantum Computer: Concepts and Summary. in Beth T, Leuchs G, Hrsg., Quantum Information Processing. Wiley-Blackwell. 2005. S. 28-43 doi: 10.48550/arXiv.quant-ph/0207183, 10.1002/3527606009.ch3

Raussendorf R, Bravyi S, Harrington J. Long-range quantum entanglement in noisy cluster states. Physical Review A - Atomic, Molecular, and Optical Physics. 2005 Jun 14;71(6):062313. doi: 10.48550/arXiv.quant-ph/0407255, 10.1103/PhysRevA.71.062313

Raussendorf R. Quantum cellular automaton for universal quantum computation. Physical Review A - Atomic, Molecular, and Optical Physics. 2005 Aug;72(2):022301. doi: 10.48550/arXiv.quant-ph/0412048, 10.1103/PhysRevA.72.022301

Raussendorf R. Quantum computation via translation-invariant operations on a chain of qubits. Physical Review A - Atomic, Molecular, and Optical Physics. 2005 Nov;72(5):052301. doi: 10.48550/arXiv.quant-ph/0505122, 10.1103/PhysRevA.72.052301

2003

Raussendorf R, Browne DE, Briegel HJ. Measurement-based quantum computation on cluster states. Physical Review A - Atomic, Molecular, and Optical Physics. 2003 Aug 25;68(2):32. doi: 10.48550/arXiv.quant-ph/0301052, 10.1103/PhysRevA.68.022312

Raußendorf R. Measurement-based quantum computation with cluster states. München: Ludwig–Maximilians–Universität München, 2003.

Raußendorf R, Briegel HJ. Method for Quantum Computing. WO0227653A3. 2003 Nov 20.