Research
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Our work is in quantum information, specifically `Models of quantum computation' and quantum fault-tolerance. For more information click here.
Featured publication: Wigner Function Negativity and Contextuality in Quantum Computation on Rebits. [Posted May 4, 2015] We describe a universal scheme of quantum computation by state injection on rebits (states with real density matrices). For this scheme, we establish contextuality and Wigner function negativity as computational resources, extending results of M. Howard et al. [Nature (London) 510, 351 (2014)] to two-level systems. For this purpose, we define a Wigner function suited to systems of multiple rebits and prove a corresponding discrete Hudson's theorem. We introduce contextuality witnesses for rebit states and discuss the compatibility of our result with state-independent contextuality.
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Negativity and contextuality for rebits. Left: Rebit Wigner function of a three-qubit graph state. This state is local unitary equivalent to a Greenberger-Horne-Zeilinger (GHZ) state. Negativity of the Wigner function for the three-qubit graph state indicates non-classicality. Contrary to qudits in odd prime dimension, for rebits negativity is not synonymous wit contextuality. Nevertheless, the negativity in the Wigner function for the three-qubit graph state is strong enough to witness contextuality. Right: From the perspective of contextuality in quantum computation with magic states, Mermin's square and star, and all their cousins, are ``little monsters''. For explanation, see below. |
State-independent contextuality, as exhibited by Mermin's square and star, provides beautifully simple proofs for the Kochen-Specker theorem in dimension 4 and higher. However, for establishing contextuality as a resource only posessed by magic states, state-independent contextuality poses a problem: If ``cheap'' Pauli measurements already have contextuality, then how can one say that contextuality is a key resource provided by the magic states? For qudits, the problem doesn't exist because there is no state-independent contextuality w.r.t. Pauli measurements. For rebits, the problem is overcome by the operational restriction to CSS-ness preserving gates and measurements.
Click here for previous posts.
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Robert Raussendorf |
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Dr. Dmytro Bondarenko |
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Dr. Polina Feldmann |
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Dr. Daniel Huerga (QMI) |
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Dr. Wang Yang |
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Arnab Adhikary |
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Luis Mantilla Calderon |
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Paul Herringer |
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Ryohei Weil |
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Michael Zurel |
Tzu-Chieh Wei, Associate Prof at Stony Brook University, NY, USA Pradeep Sarvepalli, Associate Prof at IIT Madras, Chennai, India Leon Loveridge, Associate Professor, University of South-East Norway, Norway Raouf Dridi, 1Qbit, Vancouver Vijay Singh, SFU Burnaby Dongsheng Wang, Associate Professor at Chinese Academy of Sciences, Beijing, China Cihan Okay, Assistant Prof (Math), Bilkent University, Ankara, Turkey
Angela Ruthven (UBC Enginerring Physics) Len Goff (UBC Economics) Matthew Scholte Cedric Lin (MIT), Matthew Low (University of Chicago), Philip Ketterer (Ludwig Maximilians University Munich, Germany), Philip Allen Mar (University of Toronto), Cihan Okay (University of Western Ontario), Philippe Allard Guerin (2015: University of Vienna, PhD; 2020: postdoc at PI) Jake Bian (Silicon Valley, Toronto, Imperial College London) Navid Siami (UBC Economics) David Stephen (2017: PhD student at the Max-Planck Institute for Quantum Optics, Garching, Germany) Emily Tyhurst (2018: PhD student at the University of Toronto) Andrew Elias Hirsh Kamakari (2019: Caltech, PhD) Joe Jackson (2019: Masters at Lancaster University, UK) Julian Ding [2022: Undergraduate Research Thesis] Amritabha Guha [2022: Undergraduate Research Thesis] Aslan Zhang [2022: Undergraduate Research Thesis]
Wang Yang, Alberto Nocera, Paul Herringer, Robert Raussendorf, Ian Affleck, Symmetry analysis of bond-alternating Kitaev spin chains and ladders, Phys. Rev. B 105, 094432 (2022).
Karol Horodecki, Jingfang Zhou, Maciej Stankiewicz, Roberto Salazar, Pawel Horodecki, Robert Raussendorf, Ryszard Horodecki, Ravishankar Ramanathan, Emily Tyhurst, The rank of contextuality, arXiv:2205.10307.
Wang Yang, Alberto Nocera, Chao Xu, Arnab Adhikary, Ian Affleck, Emergent SU(2)_1 conformal symmetry in the spin-1/2 Kitaev-Gamma chain with a Dzyaloshinskii-Moriya interaction, arXiv:2204.13810.
Daniel Huerga, Variational Quantum Simulation of Valence-Bond Solids, arXiv:2201.02545.
Cihan Okay, Michael Zurel, and Robert Raussendorf, On the extremal points of the Lambda polytopes and classical simulation of quantum computation with magic states, Quant. Inf. Comp 21, 1091-1110 (2021); arXiv:2104.05822.
Robert Raussendorf, Cihan Okay, Michael Zurel, Polina Feldmann, The role of cohomology in quantum computation with magic states, arXiv:2110.11631.
Michael Zurel, Cihan Okay, Robert Raussendorf, Arne Heimendahl, Hidden Variable Model for Quantum Computation with Magic States on Any Number of Qudits of Any Dimension, arXiv:2110.12318.
Woo-Ram Lee, Zhangjie Qin, Robert Raussendorf, Eran Sela, V.W. Scarola, Measurement-Based Time Evolution for Quantum Simulation of Fermionic Systems, arXiv:2110.14642.
Dmytro Bondarenko, Constructing k-local parent Lindbladians for matrix product density operators, arXiv:2110.13134.
C. Okay and R. Raussendorf, Homotopical approach to quantum contextuality, Quantum 4, 217 (2020).
R. Raussendorf, E. Tyhurst, C. Okay, J. Bermejo-Vega, M. Zurel, Phase space method for simulating quantum computation with magic states on qubits, Phys. Rev. A 110, 012350 (2020).
Xiruo Yan, Warit Asavanant, Hirsh Kamakari, Jingda Wu, Jeff Young, Robert Raussendorf, A quantum computer architecture based on silicon donor qubits coupled by photons, Adv. Quantum Technol., doi:10.1002/qute.202000011 (2020).
Daniel Azses, Rafael Haenel, Yehuda Naveh, Robert Raussendorf, Eran Sela, Emanuele G. Dalla Torre, Identification of symmetry-protected topological states on noisy quantum computers, Phys. Rev. Lett. 125, 120502 (2020).
Michael Zurel, Cihan Okay, Robert Raussendorf, A hidden variable model for universal quantum computation with magic states on qubits, [Phys. Rev. Lett. 125, 260404 (2020)].
R. Raussendorf, Cohomological framework for contextual quantum computations, Quant. Inf. Comp. 19, 1141 - 1170 (2019).
D.T. Stephen, H.P. Nautrup, J. Bermejo-Vega, J. Eisert, R. Raussendorf, Subsystem symmetries, quantum cellular automata, and computational phases of quantum matter, Quantum 3, 142 (2019).
R. Raussendorf, C. Okay, D.S. Wang, D.T. Stephen, H. Poulsen Nautrup, A computationally universal quantum phase of matter, Phys. Rev. Lett. 122, 090501 (2019).
Juan Bermejo-Vega, Dominik Hangleiter, Martin Schwarz, Robert Raussendorf and Jens Eisert, Architectures for quantum simulation showing a quantum speedup, Phys. Rev. X 8, 021010 (2018).
Dongsheng Wang, Ian Affleck, and Robert Raussendorf, Topological qubits from valence bond solids, Phys. Rev. Lett. 120, 200503 (2018).
C.Okay, E. Tyhurst, R. Raussendorf, The cohomological and the resource-theoretic perspective on quantum contextuality: common ground through the contextual fraction, Quant. Inf. Comp. 18, 1272-1294 (2018), arXiv:1806.04657.
David T. Stephen, Dong-Sheng Wang, Abhishodh Prakash, Tzu-Chieh Wei, Robert Raussendorf, Determining the computational power of symmetry protected topological phases, Phys. Rev. Lett 119, 010504 (2017).
Juan Bermejo-Vega, Nicolas Delfosse, Dan E. Browne, Cihan Okay, Robert Raussendorf, Contextuality as a resource for qubit quantum computation, Phys. Rev. Lett. 119, 120505 (2017).
Nicolas Delfosse, Cihan Okay, Juan Bermejo-Vega, Dan E. Browne, Robert Raussendorf , Equivalence between contextuality and negativity of the Wigner function for qudits, New J. Phys. 19, 123024 (2017).
Robert Raussendorf, Dongsheng Wang, Abhishodh Prakash, Tzu-Chieh Wei, David Stephen, Symmetry-protected topological phases with uniform computational power in one dimension , Phys. Rev. A 96, 012302 (2017).
Dong-Sheng Wang, David T. Stephen, Robert Raussendorf, Qudit quantum computation on matrix product states with global symmetry, Phys. Rev. A 95, 032312 (2017).
C Okay, S Roberts, SD Bartlett, R Raussendorf, Topological proofs of contextuality in quantum mechanics, Quantum Information and Computation 17, 1135-1166 (2017), arXiv:1701.01888.
Raussendorf, R.; Sarvepalli, P.; Wei, T. -C., Haghnegahdar, P., Symmetry constraints on temporal order in measurement-based quantum computation , Information and Computation 250, 115-138 (2016).
Tzu-Chieh Wei and Robert Raussendorf, Universal measurement-based quantum com- putation with spin-2 Affleck-Kennedy-Lieb-Tasaki states, Phys. Rev. A 92, 012310 (2015).
Nicolas Delfosse, J. Bian, P. Allard Guerin, R. Raussendorf, Contextuality and Wigner negativity in quantum computation on rebits, Phys Rev X 5, 021003 (2015).
Loveridge L, Dridi R, Raussendorf R., Topos logic in measurement-based quantum computation, Proc. R. Soc. A 471: 20140716 (2015).
T.-C. Wei, P. Haghnegahdar and R. Raussendorf, Hybrid valence-bond states for universal quantum computation, Phys. Rev. A 90, 042333 (2014).
M.J. Hoban, J.J. Wallman, H. Anwar, N. Usher, R. Raussendorf, D.E. Browne, Measurement-based classical computation, Phys. Rev. Lett 112, 140505 (2014). [Editors pick].
C. Monroe, R. Raussendorf, A. Ruthven, K. Brown, P. Maunz, L.M. Duan and J. Kim, Large Scale Modular Quantum Computer Architecture with Atomic Memory and Photonic Interconnects, Phys Rev A 89, 22317 (2014) [selected for Physics spotlight].
R. Raussendorf, Contextuality in measurement-based quantum computation, Phys. Rev. A 88, 022322 (2013).
Leonard Goff and Robert Raussendorf, Classical simulation of measurement-based quantum computation with higher-genus surface code states, Phys. Rev. A 86, 042301 (2012).
R. Raussendorf, P. Sarvepalli, T.-C. Wei, P. Haghnegahdar, Symmetry constraints on tem- poral order in measurement-based quantum computation, Electronic Proceedings in Theoretical Computer Science (EPTCS) 95, pp. 219-250 (2012).
Tzu-Chieh Wei, Ian Affleck, Robert Raussendorf, The 2D AKLT state on the honeycomb lattice is a universal resource for quantum computation, Phys. Rev. A 86, 032328 (2012).
R. Raussendorf, Key concepts in fault-tolerant quantum computation, Philosophical transactions. Series A, Mathematical, physical, and engineering sciences 370, 454 (2012).
Robert Raussendorf and Tzu-Chieh Wei, Quantum Computation by Local Measurement, Annu. Rev. Condens. Matter Phys 3, 239 (2012).
Xing-Can Yao, Tian-Xiong Wang, Hao-Ze Chen, Wei-Bo Gao, Austin G. Fowler, Robert Raussendorf, Zeng-Bing Chen, Nai-Le Liu, Chao-Yang Lu, You-Jin Deng, Yu-Ao Chen, and Jian-Wei Pan, Experimental demonstration of topological error correction, Nature 482, 489 (2012).
P. Sarvepalli and R. Raussendorf, Efficient decoding of topological color codes, Phys. Rev. A 85, 022317 (2012).
Roman Orus and Tzu-Chieh Wei, Geometric entanglement of one-dimensional systems: bounds and scalings in the thermodynamic limit, Quantum Information and Computation Vol. 11, No. 7, 563 (2011).
Jingfu Zhang, Tzu-Chieh Wei, and Raymond Laflamme, Experimental Quantum Simulation of Entanglement in Many-body Systems, Phys. Rev. Lett. 107, 010501 (2011).
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).