Bulletin of the American Physical Society
2006 APS March Meeting
Monday–Friday, March 13–17, 2006; Baltimore, MD
Session W40: Quantum Communication, Cryptography and Computation |
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Sponsoring Units: TGQI DAMOP Chair: Steven H. Simon, Bell Labs, Lucent Technologies Room: Baltimore Convention Center 343 |
Thursday, March 16, 2006 2:30PM - 2:42PM |
W40.00001: Quantum Communication via Frequency Upconversion Aaron VanDevender , Paul Kwiat We describe a method for efficiently and coherently converting photonic qubits from one frequency to another for quantum communication. The conversion is done using quasi-phase-matched up-conversion in a Periodically Poled Lithium Niobate (PPLN) crystal. We have observed 99\%-efficient and 95\%-coherent conversion which allows faithful conversion of ``flying'' qubits to ``stationary'' qubits for use in quantum communication. We have also used up-conversion to prepare photons in arbitrary superpositions of widely separated frequency states, enlarging the accessible Hilbert space for communication of quantum states. Finally, we have seen 56\%-efficient detection of 1550-nm photons using up-conversion to the visible and silicon Avalanche Photodiodes (APD), which would enhance the performance of quantum communication protocols (e.g., BB84) based on infrared (IR) photons over what is achievable with conventional IR single-photon detectors. [Preview Abstract] |
Thursday, March 16, 2006 2:42PM - 2:54PM |
W40.00002: Relativistic Quantum Cryptography Evan Jeffrey , Paul Kwiat We present results from a relativistic quantum cryptography system which uses photon storage to avoid bit sifting, in principle doubling the useful key rate. Bob stores the photon he receives from Alice in an optical delay line until she sends him the classical basis information, allowing him to measure every photon in the correct basis. Accounting for loss in our 489-ns storage cavity, we achieve a 66\% increase in the BB84 key rate. The same system could be used for even greater gains in either the six-state protocol or cryptography using a larger Hilbert space. We show that the security of this protocol is equivalent to standard BB84: assuming the quantum and classical signals are space-like separated, no eavesdropper bound by special relativity can access both simultaneously. [Preview Abstract] |
Thursday, March 16, 2006 2:54PM - 3:06PM |
W40.00003: Quantum Cryptography in Existing Telecommunications Infrastructure Daniel Rogers , Joshua Bienfang , Alan Mink , Barry Hershman , Anastase Nakassis , Xiao Tang , Lijun Ma , David Su , Carl Williams , Charles Clark Quantum cryptography has shown the potential for ultra-secure communications. However, all systems demonstrated to date operate at speeds that make them impractical for performing continuous one-time-pad encryption of today's broadband communications. By adapting clock and data recovery techniques from modern telecommunications engineering practice, and by designing and implementing expeditious error correction and privacy amplification algorithms, we have demonstrated error-corrected and privacy-amplified key rates up to 1.0 Mbps over a free-space link with a 1.25 Gbps clock. Using new detectors with improved timing resolution, careful wavelength selection and an increased clock speed, we expect to quadruple the transmission rate over a 1.5 km free-space link. We have identified scalable solutions for delivering sustained one-time-pad encryption at 10 Mbps, thus making it possible to integrate quantum cryptography with first-generation Ethernet protocols. [Preview Abstract] |
Thursday, March 16, 2006 3:06PM - 3:18PM |
W40.00004: Alternative Design for Quantum Cryptographic Entangling Probe Howard Brandt An alternative design is given for an optimized quantum cryptographic entangling probe for attacking the BB84 protocol of quantum key distribution [1], [2]. The initial state of the probe has a simpler analytical dependence on the set error rate to be induced by the probe than in the earlier design. The new device yields the same maximum information to the probe for a full range of induced error rates. As in the earlier design, the probe contains a single CNOT gate which produces the optimum entanglement between the BB84 signal states and the correlated probe states. \newline \newline [1] H. E. Brandt, Phys. Rev. A \textbf{71}, 042312 (2005). \newline [2] H. E. Brandt, ``Design for a quantum cryptographic entangling probe,'' to appear in J. Mod. Optics (2005). [Preview Abstract] |
Thursday, March 16, 2006 3:18PM - 3:30PM |
W40.00005: $\pi/3$ Phase-Shift Quantum Searching Lov Grover Quantum searching normally consists of an alternate sequence of selective inversion and diffusion operations. The algorithm has been extensively studied and is well understood. However, there was a surprising result that was discovered last year. According to this, if we change the selective inversions to $\pi/3$ phase shifts and adjust the sign of the phase shift in a prescribed manner, we obtain an algorithm that converges monotonically towards the solution [1]. This is in contrast to the well-known search algorithm that has an oscillatory character. This leads to a number of new and interesting applications. For example, if we consider a situation where the probability of getting a target state for a random item, is $1-\epsilon$ (with $\epsilon$ unknown), then the probability of getting a target state after a single query in the new algorithm, can be increased to $1-\epsilon^3$, classically this can be increased to only $1-\epsilon^2$. The performance of the new algorithm has recently been proved to be optimal. Another important application of this technique is in correction of systematic errors [2]. \newline References - \newline (1) L.K. Grover (2005), Fixed-point quantum search, Phys. Rev. Letters, Oct. 3, 2005. \newline (2) B.W. Reichardt and L.K. Grover, Quantum error correction of systematic errors using a quantum search framework, Phys. Rev. A, Oct. 25, 2005 [Preview Abstract] |
Thursday, March 16, 2006 3:30PM - 3:42PM |
W40.00006: Relativistic Connection of Continuous and Discrete Quantum Walks Frederick Strauch Quantum algorithms, based on a quantum-mechanical generalization of random walks, have been shown to be very effective at solving local search problems. These quantum walks come in two very different forms (discrete and continuous-time) with surprisingly similar properties. An open problem has been to identify just what makes these two walks so similar. In this talk I present the analytical connection of these two walks, by way of an analogy with properties of the Dirac equation, including entanglement, zitterbewegung, and most importantly, relativistic wave-packet spreading. [Preview Abstract] |
Thursday, March 16, 2006 3:42PM - 3:54PM |
W40.00007: Mixing and Decoherence in Continuous-Time Quantum Walks Leonid Fedichkin , Dmitry Solenov , Christino Tamon , Vladimir Privman We present analytical results showing that decoherence can be useful for speed-up of mixing in a continuous-time quantum walks on finite cycles. Our treatment of continuous-time quantum walks includes a continuous monitoring of all vertices that induces the decoherence process. We identify the dynamics of the probability distribution and observe how mixing times undergo the transition from quantum to classical behavior as our decoherence parameter grows from zero to infinity. Our results show that, for small rates of decoherence, the mixing time improves linearly with decoherence, whereas for large rates of decoherence, the mixing time deteriorates linearly towards the classical limit. In the intermediate region of decoherence rates, our numerical calculations confirm the existence of a unique optimal rate for which the mixing time is minimized. [Preview Abstract] |
Thursday, March 16, 2006 3:54PM - 4:06PM |
W40.00008: Decoherence by Correlated Noise and Quantum Error Correction Eduardo Novais , Harold U. Baranger We study the decoherence of a quantum computer in an environment which is inherently non-Markovian and spatially correlated. We first derive the non-unitary time evolution of the computer and environment in the presence of a stabilizer error correction code. Our results demonstrate that effects of long-range correlation can be systematically reduced by suitable changes in the error correction codes. The new element that we discuss is that the periodic measurements in the QEC method separate the environmental modes into high and low frequencies. This natural ``new'' scale can then be used to better engineer quantum codes. As an example of this general discussion, we study decoherence in a quantum memory protected by Steane's three qubit code. The memory interacts with a bosonic enviroment through the spin-boson Hamiltonian. We calculate explicitly the long-range correlations in this case and demonstrate that a simple change in Steane's code reduces their effect. [Preview Abstract] |
Thursday, March 16, 2006 4:06PM - 4:18PM |
W40.00009: Topological Quantum Computing with Only One Mobile Quasiparticle Steven H. Simon , Nick Bonesteel , Michael Freedman , Layla Hormozi , Nada Petrovic In a topological quantum computer, universal quantum computation is performed by dragging quasiparticle excitations of certain two dimensional systems around each other to form braids of their world lines in 2+1 dimensional space-time. We show that any such quantum computation that can be done by braiding $n$ identical quasiparticles can also be done by moving a single quasiparticle around $n-1$ other identical quasiparticles whose positions remain fixed. This result may greatly reduce the technological challenge of realizing topological quantum computation. [Preview Abstract] |
Thursday, March 16, 2006 4:18PM - 4:30PM |
W40.00010: CNOT for Fibonacci anyons with only one mobile quasiparticle Layla Hormozi , Georgios Zikos , Nick Bonesteel , Steven H. Simon Certain two-dimensional systems with non-abelian quasiparticle excitations can be used for topological quantum computation (TQC). In TQC qubits are encoded using 3 or 4 quasiparticles and quantum gates are carried out by braiding quasiparticle world lines. We focus on the problem of finding explicit braiding patterns that yield a universal set of quantum gates, using Fibonacci anyons --- quasiparticles which are thought to exist in an experimentally observed fractional quantum Hall state at filling fraction $\nu = 12/5$. In previous work\footnote{N.E. Bonesteel, L. Hormozi, G. Zikos, and S. H. Simon, Phys. Rev. Lett. {\bf 95}, 140503 (2005).} we have shown how to construct arbitrary controlled rotation gates (which together with single qubit gates provide a universal set of quantum gates) by moving a pair of quasiparticles from the control qubit around the quasiparticles in the target qubit while keeping the latter at fixed positions. In this talk we show how to take advantage of one of the structural properties of Fibonacci anyons (namely the fusion matrix) to construct a certain class of two-qubit gates (including CNOT) with only {\it one} mobile quasiparticle --- therefore reducing the number of braiding operations by a factor of two. [Preview Abstract] |
Thursday, March 16, 2006 4:30PM - 4:42PM |
W40.00011: Quantum Phase Transitions and Typical Case, Polynomial Time Solution of Randomly Generated NP-Complete Problems via Adiabatic Quantum Computation William Kaminsky , Seth Lloyd We argue theoretically that adiabatic quantum computation using only polynomial resources can solve almost all members of a nontrivial randomly generated set of NP-complete problem instances, namely the problem of finding the ground states of spin glasses on 3D cubic lattices having independent, identically Gaussian-distributed couplings. The argument uses the droplet model of quantum spin glasses, particularly its prediction that the paramagnet-spin glass transition is unstable to even infinitesimal longitudinal fields. We then review the ongoing debate as to how well the droplet model describes 3D spin glasses and note that those inclined to view the intractability of NP-complete problems as a guiding physical intuition could take the results presented here as justifying greater suspicion toward the droplet model. Finally, due to this uncertainty as well as uncertainty in regard to the typical case classical complexity of this random NP-complete problem, we outline work using rigorous mean-field methods on a NP-complete problem whose typical-case classical complexity on random instances is better established, namely MAX CLIQUE on random graphs. [Preview Abstract] |
Thursday, March 16, 2006 4:42PM - 4:54PM |
W40.00012: Adiabatic Quantum Computing in systems with constant inter-qubit couplings Vadim Smelyanskiy , Sergei Knysh We propose an approach suitable for solving NP-complete problems via adiabatic quantum computation with an architecture based on a lattice of interacting spins (qubits) driven by locally adjustable magnetic fields. Interactions between qubits are assumed constant and instance-independent, programming is done only by changing local magnetic fields. Implementations using qubits coupled by magnetic-dipole, electric-dipole and exchange interactions are discussed. [Preview Abstract] |
Thursday, March 16, 2006 4:54PM - 5:06PM |
W40.00013: Quantum Phase Transition and complexity of adiabatic quantum algorithm for Constraint Satisfaction problem Sergei Knysh , Vadim Smelyanskiy We study the dynamics of adiabatic quantum computation (AQC) for solving the problem of satisfiability of randomly chosen clauses, each with 3 Boolean variables (3sat). We map this problem to that of a diluted long-range spin glass in traverse magnetic field and derive a self-consistent equation for the order parameter. We show the existence of the first-order quantum phase transition and investigate analytically and numerically the phase diagram on the plane: strength of the transverse field $\Gamma$ vs the ratio $\gamma$=M/N of a number of clauses M to a number of variables N. We show that the phase transition line approaches $\Gamma$=0 at the point of a classical replica symmetry breaking transition $\gamma_{RSB}$. We discuss the implications of the quantum phase transition for the complexity of the AQC for the 3sat. [Preview Abstract] |
Thursday, March 16, 2006 5:06PM - 5:18PM |
W40.00014: Computation in Finitary Quantum Processes Karoline Wiesner , James P. Crutchfield We introduce quantum finite-state generators as a first step toward a computational description of quantum dynamical processes. We developed their mathematical foundations, establishing probability conservation, reversibility, and consistency with quantum mechanical laws, and connect the class to the existing theory of finite-state recognizers and generators. These computational models allow for a quantitative description of quantum languages generated by quantum dynamical systems. Their descriptive power is explored via several example quantum dynamical systems. [Preview Abstract] |
Thursday, March 16, 2006 5:18PM - 5:30PM |
W40.00015: Some Thoughts Regarding Practical Quantum Computing Debabrata Ghoshal , Richard Gomez , Marco Lanzagorta , Jeffrey Uhlmann Quantum computing has become an important area of research in computer science because of its potential to provide more efficient algorithmic solutions to certain problems than are possible with classical computing. The ability of performing parallel operations over an exponentially large computational space has proved to be the main advantage of the quantum computing model. In this regard, we are particularly interested in the potential applications of quantum computers to enhance real software systems of interest to the defense, industrial, scientific and financial communities. However, while much has been written in popular and scientific literature about the benefits of the quantum computational model, several of the problems associated to the practical implementation of real-life complex software systems in quantum computers are often ignored. In this presentation we will argue that practical quantum computation is not as straightforward as commonly advertised, even if the technological problems associated to the manufacturing and engineering of large-scale quantum registers were solved overnight. We will discuss some of the frequently overlooked difficulties that plague quantum computing in the areas of memories, I/O, addressing schemes, compilers, oracles, approximate information copying, logical debugging, error correction and fault-tolerant computing protocols. [Preview Abstract] |
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