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A 2-year postdoctoral position in Quantum Information Science is opening in the Department of Physics and Astronomy at the University of British Columbia in Spring 2012, in the group of Dr. Robert Raussendorf. Possible areas of research include - but are not restricted to - models of quantum computation, quantum error-correction and quantum algorithms. The application deadline is December 15, 2011. For details, click here.
Our work is in quantum information, ranging from `Models of quantum computation' and quantum fault-tolerance to entanglement theory and many-body physics. For more information click here
.Featured publication: AKLT states as computational resources. [Posted February 24, 2011] We show that the ground state of an isotropic quantum antiferromagnet in two spatial dimensions, a so-called Affleck-Kennedy-Lieb-Tasaki (AKLT) state, is a universal resource for measurement-based quantum computation. This may become useful in two ways: (1) It may bring closer to experimental reality the possibility of creating computational resource states by cooling, and (2) More generally, it strengthens the overlap between the field of measurement-based quantum compuation and condensed matter physics. Could this overlap generate novel ideas and approaches for the classification of all computationally universal resource states?
An initial highly entangled resource state is the key ingredient in measurement-based quantum computation, where the process of computation itself is driven by single-spin measurements. Universal resource states are known to be rare. Recent quests for them have turned to ground states of short-ranged, preferably two-body interacting Hamiltonians, as they may be created by cooling. In particular, success has been obtained in the family of the AKLT models, in which single-qubit operations are shown to be possible. However, it remained open whether any state in the AKLT family can provide the full capability for universal quantum computation. Our results show that this is indeed the case for the two-dimensional spin-3/2 AKLT state supported on the honeycomb lattice.
The AKLT state was originally constructed in 1987 to understand the low-energy phenomenology of rotationally invariant spin Hamiltonians, a question at the center of condensed matter physics but outside the realm of quantum information. Amazingly, however, this happened not long after the notion of quantum computation started to develop, through the works of Feynman (1982) and Deutsch (1985).
[Journal Reference: Tzu-Chieh Wei, Ian Affleck, Robert Raussendorf, Physical Review Letters 106, 070501 (2011). An analogous result has been obtained independently by A. Miyake; See arXiv:1009.3491.]
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AKLT states as universal computational resources. At the techical level, our constructions proceeds by reducing the 2D AKLT state to a 2D cluster state through local operations (POVMs and projective measurements). The 2D cluster is the standard universal resource. The mapping requires three steps. (1) We devise a suitable generalized local measurement (local POVM) which breaks the rotational symmetry of the AKLT state. (2) We show that the resulting state is an encoded graph state on a random planar graph. Therein, the planar graph depends on the random but short-range correlated POVM outcomes. The encoding can be undone by local measurements. (3) A planar graph state can be further reduced to a 2D cluster state if it is large and has traversing paths, i.e., is in the supercritical phase of percolation (a). We show that this is indeed the case for typical graph states resulting from the POVM in Step 1, by Monte-Carlo simulation (b). |
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Robert Raussendorf |
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Poya Haghnegahdar |
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Cihan Okay |
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Matthew Scholte
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Vijay Singh |
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Arman Zaribafiyan |
Tzu-Chieh Wei, faculty at Stony Brook Pradeep Sarvepalli, Georgia Tech
Angela Ruthven (UBC Enginerring Physics) Len Goff (UBC Economics) Cedric Lin (MIT), Matthew Low, Philip Ketterer (University of Mainz, Germany, and MIT), Philip Allen Mar
P. Sarvepalli and P. Wocjan, Quantum Algorithms for One-Dimensional Infrastructures, arXiv:1106.6347 (2011).
P. Sarvepalli, Quantum Codes and Symplectic Matroids, arXiv:1104.1171 (2011).
Jingfu Zhang, Tzu-Chieh Wei, and Raymond Laflamme, Experimental Quantum Simulation of Entanglement in Many-body Systems, arXiv:1104.0275 (2011).
Roman Orus and Tzu-Chieh Wei, Global quantum correlations in the spin-1 bilinear-biquadratic chain, arXiv:1010.5029 (2010).
Roman Orus and Tzu-Chieh Wei, Geometric entanglement of one-dimensional systems: bounds and scalings in the thermodynamic limit, arXiv:1006.5584 (2010).
Robert Raussendorf, Quantum computation, discreteness, and contextuality, arXiv:0907.5449 (2009).
Wei-Bo Gao, Austin G. Fowler, Robert Raussendorf, Xing-Can Yao, He Lu, Ping Xu, Chao-Yang Lu, Cheng-Zhi Peng, Youjin Deng, Zeng-Bing Chen, and Jian-Wei Pan, Experimental demonstration of topological error correction, arXiv:0905.1542 (2009).
Ying Li, Daniel E. Browne, Leong Chuan Kwek, Robert Raussendorf, and Tzu-Chieh Wei, Thermal States as Universal Resources for Quantum Computation with Always-on Interactions, Phys. Rev. Lett. 107, 060501 (2011).
P. Sarvepalli, Topological Color Codes over Higher Alphabet. In Proc. of IEEE Information Theory Workshop, Dublin, Ireland Aug 30-Sep 3, 2010.
P. Sarvepalli, R. Raussendorf. Local equivalence of surface code states. TQC'10 Proceedings of the 5th conference on Theory of quantum computation, communication, and cryptography. Lecture Notes in Computer Science, 2011, Volume 6519/2011, 47-62.
Pradeep Sarvepalli, Entropic Inequalities for a Class of Quantum Secret Sharing States, Phys. Rev. A 83, 042303 (2011).
Pradeep Sarvepalli, Bounds on the Information Rate of Quantum Secret Sharing Schemes, Phys. Rev. A 83, 042324 (2011).
Tzu-Chieh Wei, Johnathan Lavoie, and Rainer Kaltenbaek, Creating multi-photon polarization bound-entangled states, Phys. Rev. A 83, 033839 (2011).
Lin Chen, Huangjun Zhu, and Tzu-Chieh Wei, Connections of geometric measure of entanglement of pure symmetric states to quantum state estimation Phys. Rev. A 83, 012305 (2011).
Tzu-Chieh Wei, Smitha Vishveshwara and Paul M. Goldbart, Global geometric entanglement in transverse-field XY spin chains: finite and infinite systems, Quantum Inf. Comput. 11, 0326-0354 (2011)
Tzu-Chieh Wei, Ian Affleck, Robert Raussendorf, The 2D AKLT state is a universal quantum computational resource, Physical Review Letters 106, 070501 (2011).
P. Sarvepalli, Topological Color Codes over Higher Alphabet. In Proc. of IEEE Information Theory Workshop, Dublin, Ireland Aug 30-Sep 3, 2010.
R. Raussendorf, Shaking up ground states Nature Physics 6, 840 (2010); News and Views on J. Lavoie et al., Optical one-way quantum computing with a simulated valence-bond solid , Nature Physics 6, 850 (2010).
Roman Orus and Tzu-Chieh Wei, Visualizing elusive phase transitions with geometric entanglement, Phys. Rev. B 82, 155120 (2010).
Wade DeGottardi, Tzu-Chieh Wei, Victoria Fernandez, and Smitha Vishveshwara, Accessing nanotube bands via crossed electric and magnetic fields, Phys. Rev. B 82, 155411 (2010).
Pradeep Sarvepalli and Robert Raussendorf, On Local Equivalence, Surface Code States and Matroids, Phys. Rev. A 82, 022304 (2010).
Matthew Killi, Tzu-Chieh Wei, Ian Affleck, Arun Paramekanti, Tomonaga-Luttinger liquid physics in gated bilayer graphene , Phys. Rev. Lett. 104, 216406 (2010).
Tzu-Chieh Wei, Entanglement under the renormalization-group transformations on quantum states and in quantum phase transitions , Phys. Rev. A 81, 062313 (2010).
Tzu-Chieh Wei, Exchange symmetry and global entanglement and full separability , Phys. Rev. A 81, 054102 (2010).
Pradeep Sarvepalli and Robert Raussendorf, Matroids and Quantum Secret Sharing Schemes, Phys. Rev. A 81, 052333 (2010).
Pradeep Sarvepalli and Andreas Klappenecker, Degenerate quantum codes and the quantum Hamming bound, Phys. Rev. A 81, 032318 (2010).
Tzu-Chieh Wei, Michele Mosca, and Ashwin Nayak, Interacting boson problems can be QMA-hard, Phys. Rev. Lett. 104, 040501 (2010).
M. Van den Nest, W. Duer, R. Raussendorf, H. J. Briegel, Quantum algorithms for spin models and simulable gate sets for quantum computation, Phys. Rev. A 80, 052334 (2009).
Robert Raussendorf, Measurement-based quantum computation with cluster states ( PhD thesis, Ludwig-Maximilians-Universitaet Munich, 2003), Int. J. of Quantum Information 7, 1053 - 1203 (2009).
Sayatnova Tamaryan, Tzu-Chieh Wei, and DaeKil Park, Maximally entangled three-qubit states via geometric measure of entanglement, Phys. Rev. A 80, 052315 (2009).
Pradeep Kiran Sarvepalli and Andreas Klappenecker, Sharing classical secrets with Calderbank-Shor-Steane codes, Phys. Rev. A 80, 022321 (2009).
H. J. Briegel, D. E. Browne, W. Duer, R. Raussendorf and M. Van den Nest, Measurement-based quantum computation, Nature Physics 5, 19 (2009).