Bulletin of the American Physical Society
2005 APS March Meeting
Monday–Friday, March 21–25, 2005; Los Angeles, CA
Session V33: Quantum Computing |
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Sponsoring Units: GQI Chair: Jonathan Dowling, Louisiana State University Room: LACC 511C |
Thursday, March 24, 2005 11:15AM - 11:27AM |
V33.00001: Valence bond states in Quantum Information Theory Frank Verstraete, J.I. Cirac Many interesting states in the context of quantum information theory have a very simple parameterization in terms of valence bond states. These include the GHZ-states, cluster states, stabilizer states and error correcting codes, Kitaev's topological toric codes, ... The basic advantage of this description is that it is a local and makes the nice properties of these states very apparent. We will discuss these properties, and elucidate the relevance of valence bond states in the context of the renormalization group. [Preview Abstract] |
Thursday, March 24, 2005 11:27AM - 11:39AM |
V33.00002: Topological Quantum Compiling Layla Hormozi, Georgios Zikos, Nick Bonesteel, Steven H. Simon Certain exotic two-dimensional systems are thought to have the property that their quasiparticle excitations can be used for topological quantum computation (TQC).\footnote{A.\ Yu Kitaev, Ann. of Phys., {\bf 298}, 25 (2002); M. Freedman, M. Larsen, and Z. Wang, Comm. Math. Phys. {\bf 227} 587 (2002).} In TQC, qubits are encoded using three or more quasiparticles, and quantum gates are performed by braiding the world-lines of quasiparticles around each other in specific patterns. Because the resulting quantum gates depend only on the topology of the braid, TQC is intrinsically fault tolerant. Here, we investigate the problem of finding braiding patterns which approximate a universal set of quantum gates (single qubit rotations, and CNOT gates) to any desired accuracy. In particular, we show precisely how a CNOT gate can be performed by weaving a pair of quasiparticles from the control qubit through the quasiparticles forming the target qubit, and set the stage for numerical calculations of the required braiding patterns. We will focus on certain quantum Hall states that might be realized either in solid state two-dimensional electron systems or in rotating Bose condensates, where TQC is in principle possible.\footnote{N. Read and E. Rezayi, Phys. Rev. B {\bf 59} 8084 (1999); N.R. Cooper, N.K. Wilkin, and J.M.F. Gunn, Phys. Rev. Lett. {\bf 87} 120405 (2001).} This work is supported by US DOE. [Preview Abstract] |
Thursday, March 24, 2005 11:39AM - 11:51AM |
V33.00003: Numerical Calculations of Braiding Patterns for Topological Quantum Computation Georgios Zikos, Layla Hormozi, Nick Bonesteel, Steven H. Simon In topological quantum computation\footnote{A.\ Yu Kitaev, Ann. of Phys., {\bf 298}, 25 (2002); M. Freedman, M. Larsen, and Z. Wang, Comm. Math. Phys. {\bf 227} 587 (2002).} (TQC) quantum gates are performed by moving quasiparticle excitations of certain two-dimensional states around each other in a specific way. The world-lines of these particles then sweep out braids in 2+1 dimensions and the resulting quantum gate is determined by the topology of this braid. We present numerical results for braiding patterns which can be used for TQC with quasiparticles whose braiding properties are described by the quantum group $U_q(su(2))$ with $q = e^{i2\pi/5}$ which is believed to be relevant for certain fractional quantum Hall states.\footnote{N. Read and E. Rezayi, Phys. Rev. B {\bf 59} 8084 (1999); J.K. Slingerland and F.A. Bais, Nucl. Phys. B {\bf 612} 229 (2001).} Specifically, we show that braids obtained by a brute-force search of up to 46 crossings can be combined to produce a CNOT gate with an accuracy of $\sim 10^{-3}$. We then show how these braids can be systematically improved using the Solovay-Kitaev construction with the braid length growing polylogarithmically in the desired accuracy. This work is supported by US DOE. [Preview Abstract] |
Thursday, March 24, 2005 11:51AM - 12:03PM |
V33.00004: Convex optimizations for quantum state and process tomography Andrew Doherty, Alexei Gilchrist Verifying the performance of quantum information processing devices is one of the key challenges facing the field of quantum information science. In optical approaches it has been possible to perform both quantum state and process tomography to completely characterize state generation techniques or quantum logic gates. However, the data reduction required is lengthy and error analysis has been ad hoc beyond two-qubit state tomography. We describe convex optimizations for quantum state and process tomography; these correspond to both the standard maximum likelihood reconstruction and to minimizing the trace distance between the observed and reconstructed probability vectors. We describe error analysis procedures for these algorithms and offer physical interpretations for the Lagrange dual optimisations. These algorithms are several orders of magnitude faster than existing techniques, opening possibilities including adaptive tomography techniques based on identifying which observables are currently limiting the tomographic fit. [Preview Abstract] |
Thursday, March 24, 2005 12:03PM - 12:15PM |
V33.00005: Effect of External Control Fields on Electron Coherence in Weak Localization and Aharonov-Bohm Oscillations Doru Cuturela, Robert L. Badzey, Pritiraj Mohanty Understanding coherent electron transport through low-dimensional metals is fundamental to the field of mesoscopic physics. At low temperatures, low-dimensional conductors demonstrate electron coherence even in the presence of disordered potentials, giving rise to quantum interference effects such as weak localization and Aharonov-Bohm oscillations. Here we report our preliminary work on the effect of external control fields, both broadband and pulsed, on electron coherence in quasi-1D diffusive wires and rings at millikelvin temperatures. Engineering coherence is vital to the eventual development of practical quantum electronic devices. This work is supported by the NSF (CCF) and NSF (DMR, ECS), and the Sloan Foundation. [Preview Abstract] |
Thursday, March 24, 2005 12:15PM - 12:27PM |
V33.00006: Efficient quantum circuits for qudits Gavin Brennen, Stephen Bullock, Dianne O'Leary We describe quantum circuits for exactly universal quantum computation on multiple d-level quantum systems (qudits). In a single qudit we identify a coupling graph associated with the logical basis states as nodes and couplings as links and show that any unitary can be constructed efficiently provided the graph is connected. We prove a lower bound on the number of two qudit gates necessary to built an arbitrary (structureless) n-qudit unitary and provide a constructive algorithm that asymptotically matches this bound. The algorithm is a variant of the QR matrix decomposition and scales well in the presence of architectural constraints to qudit interactions [Preview Abstract] |
Thursday, March 24, 2005 12:27PM - 12:39PM |
V33.00007: Evidence for the robustness of geometric quantum computation Shi-Liang Zhu, Paolo Zanardi The fact that geometric phases can be used to realize universal quantum computation (QC) is in itself a significant contribution to the field of quantum information that attracted a lot of attention. However, regarding to its realistic application, the key prediction that geometric quantum gates may have built-in fault-tolerant features has still the status of a conjecture. One of the main difficulties in proving, or rejecting, the above robustness conjecture is that one does not have a suitable model which allows a direct and ``fair" comparison between geometrical and dynamical operations. Here we describe a model which can be used to attack this problem. The model analyzed is, in a sense, a hybrid between purely geometric gate and standard dynamic one. We find that the maximum of fidelity in the model corresponds to those cases in which the dynamic phase is zero. The results might be the first convincing evidence of the robustness of geometric QC. Our predictions can be, in principle, experimentally tested in already existing QC prototypes. [Preview Abstract] |
Thursday, March 24, 2005 12:39PM - 12:51PM |
V33.00008: Energetic Suppression of Decoherence in Exchange-Only Quantum Computation C. Stephen Hellberg, Yaakov S. Weinstein We present a scheme for universal quantum computation requiring only the Heisenberg exchange interaction. The combination of an always-on exchange interaction between the three physical qubits comprising the encoded qubit and a global magnetic field generates an energy gap between the subspace of interest and all other states. This energy gap suppresses decoherence. Always-on exchange couplings greatly simplify the implementation of the logical gates. A controlled phase gate can be implemented using only three Heisenberg exchange operations all of which can be performed simultaneously. \\ \\ http://arxiv.org/abs/quant-ph/0408037 [Preview Abstract] |
Thursday, March 24, 2005 12:51PM - 1:03PM |
V33.00009: Quantum cellular automata for quantum information processing Robert Raussendorf, Yiyang Gong In this talk I discuss applications of simple quantum cellular automata in quantum information processing. A two-dimensional lattice of qubits is considered that has engineered defects (qubits missing) or a boundary of a suitable shape. The state of the system is updated by an alternation of simultaneous conditional phase gates between all pairs of next-neighboring qubits and simultaneous Hadamard transformations on all qubits. The system is ``programmed'' by the choice of the boundary shape. The following examples for applications are given: (1) transmission, (2) an encoding circuit, (3) encoded transmission through an error-detecting channel i.e., encoding, encoded transmission and decoding. [Preview Abstract] |
Thursday, March 24, 2005 1:03PM - 1:15PM |
V33.00010: Taming of decoherence-optimal control approach Ilya Grigorenko, Dmitri Khveshchenko We carry out an analysis of the system of two coupled qubits, each of which is subject to its own dissipative environment. We find a combination of the inter-qubit couplings that provides for the lowest possible decoherence rates of the two-qubit register. Using this result, we construct optimized implementations of the CNOT and other universal two-qubit gates that, unlike in the most of previously proposed protocols, are carried out in a single step. The new protocols require tunable inter-qubit couplings but, in return, show a significant improvements in the quality of gate operations. [Preview Abstract] |
Thursday, March 24, 2005 1:15PM - 1:27PM |
V33.00011: A dynamic learning paradigm for quantum computers Elizabeth Behrman, James Steck, Preethika Kumar, Steven Skinner We present a dynamic learning paradigm for ``programming'' a general quantum computer. We first apply the method to a system of two coupled superconducting quantum interference devices (SQUIDs), and demonstrate learning of both XOR and XNOR for a pure quantum state. Theoretical exact solutions confirm our results. The method can be also be used for mixed states. We next apply the method to a system of three SQUIDs and demonstrate learning of the Toffoli and Fredkin gates. Experimental work is in progress. [Preview Abstract] |
Thursday, March 24, 2005 1:27PM - 1:39PM |
V33.00012: Quantum Interference from Independent Photons Rainer Kaltenbaek, Bibiane Blauensteiner, Markus Aspelmeyer, Anton Zeilinger Quantum interference of photons generated from independent sources is a topic of wide interest both for fundamental quantum optics and for quantum communication. Regarding the latter, such effects are crucial to distribute entanglement over long distances and thus allow quantum networking. We will discuss recent experiments towards quantum interference of truly independent single and entangled photons. [Preview Abstract] |
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