Bulletin of the American Physical Society
2008 APS March Meeting
Volume 53, Number 2
Monday–Friday, March 10–14, 2008; New Orleans, Louisiana
Session J15: Quantum Computation 
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Sponsoring Units: GQI Chair: Gerardo Ortiz, Indiana University Room: Morial Convention Center 207 
Tuesday, March 11, 2008 11:15AM  11:27AM 
J15.00001: Quantum simulated annealing Sergio Boixo, Rolando Somma, Howard Barnum We develop a quantum algorithm to solve combinatorial optimization problems through quantum simulation of a classical annealing process. Our algorithm combines techniques from quantum walks and quantum phase estimation, and can be viewed as the quantum analogue of the discretetime Markov Chain Monte Carlo implementation of classical simulated annealing. [Preview Abstract] 
Tuesday, March 11, 2008 11:27AM  11:39AM 
J15.00002: Domain Nucleation as a Failure Mode of Adiabatic Quantum Computation William Kaminsky, Seth Lloyd The bottleneck limiting the runtime of an adiabatic quantum algorithm is generically a quantum phase transition point for the computer's qubits. We show that if the qubits undergo this phase transition simultaneously as in a continuous quantum phase transition in a homogeneous system, then the runtime is only polynomial in the number of qubits. However, we next show that if the qubits have finite range interactions in 3 or fewer dimensions, then it is much more likely that they undergo this phase transition in piecemeal fashion by nucleating domains. The runtime then grows faster than any polynomial, though it often remains subexponential. We show this via a scaling argument based on the SuzukiTrotter mapping. Our argument extends previous similar ones in that it explicitly shows how domain excitations typically must lead to computational errors as interdomain couplings typically are insufficient to allow the excitations to reconcile with one another and lead back to a valid solution. We close by remarking on ways to minimize domain nucleation, identifying algorithms with continuous symmetries and/or nearly fullyconnected topologies as promising. [Preview Abstract] 
Tuesday, March 11, 2008 11:39AM  11:51AM 
J15.00003: A quantum algorithm for finding the modal value Mark Coffey, Zachary Prezkuta We present a quantum algorithm for finding the most often occurring (or modal) value of a data set. We thereby supplement other algorithms that can determine the mean value or similar quantities. Our algorithm [1] requires the combined use of quantum counting and extended quantum search, and gives a quadratic speed up over the classical situation. For a data list of N elements, each entry an integer in the range [1,d], our method requires O(d N$^{1/2})$ oracle calls, and further complexity results are described. [1] to appear in Quantum Information Processing. [Preview Abstract] 
Tuesday, March 11, 2008 11:51AM  12:03PM 
J15.00004: A Many Body Eigenvalue Problem for Quantum Computation Selman Hershfield A one dimensional many body Hamiltonian is presented whose eigenvalues are related to the order of $G_N$. This is the same order of $G_N$ used to decode the RSA algorithm. For some values of $N$ the Hamiltonian is a noninteracting fermion problem. For other values of $N$ the Hamiltonian is a quantum impurity problem with fermions interacting with a spinlike object. However, the generic case has fermions or spins interacting with higher order interactions beyond two body interactions. Because this is a mapping between two different classes of problems, one of interest in quantum computing and the other a more traditional condensed matter physics Hamiltonian, we will show (i) how knowledge of the order of $G_N$ can be used to solve some novel one dimensional strongly correlated problems and (ii) how numerical techniques, particularly for quantum impurity limit, can be used to find the order of $G_N$. [Preview Abstract] 
Tuesday, March 11, 2008 12:03PM  12:15PM 
J15.00005: Generating PseudoRandom Quantum States with Cluster Computation Winton G. Brown, Yaakov S. Weinstein, Lorenza Viola We revisit existing algorithms for generating pseudorandom pure quantum states in the light of clusterstate quantum computation. Reformulation of previous networkbased algorithms in terms of appropriate measurement patterns suggests a (nearly) optimal distribution of local singlequbit gates, which results in a significant improvement in the asymptotic rate of purity decay. Surprisingly, this distribution is not the one corresponding to arbitrary random single qubit rotations. We find that the rate at which the expected purity approaches the prediction based on the Haar measure is asymptotically constant with respect to the number of logical qubits. Connectivity of the underlying qubit coupling topology as well as the occurrence of saturation and cutoff effects are analyzed. [Preview Abstract] 
Tuesday, March 11, 2008 12:15PM  12:27PM 
J15.00006: Ground States as Resources for Universal MeasurementBased Quantum Computing Adam G. D'Souza, David L. Feder Measurementbased quantum computation (MBQC) requires a massively entangled resource state (such as a cluster state) as input. Experimental efforts towards generating such states have typically focused on performing global entangling operations on uncorrelated qubits. As the states that result from this type of procedure are not generally ground states, they are very sensitive to decoherence effects. A more robust resource would be one that is in fact a ground state of some Hamiltonian that exhibits a reasonably large energy gap between the ground state and the various excited states. We will discuss the possibility of finding simple twobody spin Hamiltonians whose ground states are equivalent to resource states for MBQC under stochastic protocols comprised solely of local operations and classical communication. [Preview Abstract] 
Tuesday, March 11, 2008 12:27PM  12:39PM 
J15.00007: Quantum Nondemolition measurements of single spins in semiconductors Mohan Sarovar, Kevin Young, Thomas Schenkel, K. Birgitta Whaley For the development of largescale quantum computers, electron spinencoded qubits in solidstate are appealing because of their favorable decoherence time scales, high potential for scalability, and many handles for precision control. However, an additional requirement that is traditionally challenging in the solidstate is a capacity for highfidelity qubit readout. We propose a scheme for measuring the state of a single donor electron spin using a fieldeffect transistor induced twodimensional electron gas and electrically detected magnetic resonance techniques. The scheme is facilitated by hyperfine coupling to the donor nucleus. We analyze the potential sensitivity and outline experimental requirements. Our measurement provides a singleshot, projective, and effectively quantum nondemolition measurement of an electron spinencoded qubit state. [Preview Abstract] 
Tuesday, March 11, 2008 12:39PM  12:51PM 
J15.00008: Adiabatic optical twoqubit operation with electron spins in separate quantum dots Semion Saikin, Clive Emary, Duncan Steel, Lu Sham We develop an adiabatic scheme to control the entanglement of two electron spins localized in separate InAs/GaAs quantum dots via the Coulomb interaction between two negative trions optically excited in the different dots. The scheme gives a unitary operation in the spin subspace and can be used as a two qubit gate for quantum information processing. The slowly varying adiabatic pulses drive the system in a such way that effects of pulse imperfections and relaxation of the trion states are minimized. For spin dynamics we provide an exact numerical solution that accounts for dissipation and analyze the essential processes within a ``dressed state'' model. Our calculations for verticallystacked quantum dots show that for a broad range of dot parameters a twospin state with the concurrence $C>0.85$ can be prepared coherently from an initially polarized state by four optical fields with the pulse duration $\Delta t\sim 1$~ns. [Preview Abstract] 
Tuesday, March 11, 2008 12:51PM  1:03PM 
J15.00009: Universal sets of quantum gates based on geometric phases Yu Shi, Qian Niu We rigorously study adiabatic and nonadiabatic geometric phases of two Heisenbergcoupled identical spins in a rotating magnetic field. The geometric phase of the total system is still some solid angle, and is independent of Heisenberg coupling constant. The adiabatic geometric phase is also independent of the magnetic field rotating speed. Using this result, for both adiabatic and nonadiabatic cases, we explicitly and exactly construct novel robust dynamicgeometrichybrid twoqubit square root of swap and controlledNOT gates, as well as purely geometric single qubit gates, including $\pi/8$ and Hadamard gates, thus presenting a complete scheme of robust universal quantum computing. This scheme can be implemented in NMR, quantum dots and cold atoms. [Preview Abstract] 
Tuesday, March 11, 2008 1:03PM  1:15PM 
J15.00010: Quantum Logic with Composite Pulse Sequences on $Sr^+$ Ruth Shewmon, Jaroslaw Labaziewicz, Yufei Ge, Shannon Wang, Isaac L. Chuang The optical $5S_{1/2} \rightarrow 4D_{1/2}$ transition in $Sr^+$ is an attractive qubit because it can be addressed by diode lasers, which are relatively inexpensive and easy to operate. We characterize singlequbit rotations as well as a CNOT gate on a $Sr^+$ ion in a surface electrode Paul trap. To improve these operations, the frequency of the clock laser is stabilized to a highfinesse optical cavity. The resulting linewidth of the laser is approximately 300Hz. Composite pulse sequences, a technique adapted from NMR, have been shown to reduce the effects of systematic errors in a variety of quantum systems. We demonstrate several composite sequences that improve the fidelity of quantum logic operations on $Sr^+$. [Preview Abstract] 
Tuesday, March 11, 2008 1:15PM  1:27PM 
J15.00011: Static and Dynamic Properties of Flying Spin Qubits Vanita Srinivasa, Jeremy Levy Domain walls in dimerized spin1/2 chains may be used to transport spin qubits rapidly and with high fidelity (PRB \textbf{76}, 094411 (2007)). Threespin rings constitute the simplest system in which these ``flying spin qubits'' may be realized. We explore some general properties of threespin rings with modulated Heisenberg exchange coupling by calculating the corresponding static and dynamic spin states. We also discuss how the motion of domain walls in individual and coupled pairs of rings may be used to carry out single and twoqubit unitary operations within these systems. [Preview Abstract] 
Tuesday, March 11, 2008 1:27PM  1:39PM 
J15.00012: Topological Quantum Computing with ReadRezayi States Layla Hormozi, Nick Bonesteel, Steven H. Simon In topological quantum computation quantum operations are carried out by moving quasiparticle excitations of certain quantum systems around each other in two space dimensions or equivalently by braiding their worldlines in threedimensional spacetime. Fractional quantum Hall states are among the prime candidates for realizing such quasiparticles. In particular, it has been shown that quasiparticles associated with the socalled ReadRezayi (RR) states at $k>2, k\neq 4$ can be used for universal quantum computation. In previous work we have shown how to construct twoqubit gates by braiding the socalled Fibonacci anyons  a class of nonAbelian anyons that are closely related to the quasiparticles of the $k = 3$ RR state. These twoqubit gates then together with singlequbit gates form a universal set of quantum gates. In this talk we point to certain properties of the quasiparticles of the $k = 3$ RR state which are unique to this state and which allow us to construct twoqubit gates in a simple and efficient way. We then present a method that can be used to efficiently construct twoqubit gates for any quasiparticle in the RR sequence at $k>2, k\neq 4$. This work is supported by US DOE. [Preview Abstract] 
Tuesday, March 11, 2008 1:39PM  1:51PM 
J15.00013: Polyoxometalates as spin qubits A. GaitaAri\~no, M. AlDamen, J.M. ClementeJuan, E. Coronado, J. Lehmann, D. Loss, P. Stamp Polyoxometalates (POMs) are discrete fragments of metal oxides, clusters of regular MO$_n$ polyhedra. POMs show a remarkable flexibility in composition, structure and charge state, and thus can be designed according to specific electric and magnetic needs. The two localized spins with S = 1/2 on the V atoms in [PMo$_{12}$O$_{40}$(VO)$_2$]$^{q}$ can be coupled through the delocalized electrons of the central core. This system was recently used for a theoretical scheme involving twoqubit gates and readout: the electrical manipulation of the molecular redox potential changes the charge of the core and thus the effective magnetic exchange between the qubits. Polyoxometalates can encapsulate magnetic ions, protecting them by a diamagnetic shell of controlled geometry. A great potential of POMs as spin qubits is that they can be constructed using only even elements, such as O, W, Mo and/or Si. Thus, there is a high abundance of polyoxometalate molecules without any nuclear spin, which could result in unusually low decoherence rates. There is currently an effort involving highly anisotropic, high magnetic moment, lanthanide@polyoxometalate molecules acting as spin qubits. [Preview Abstract] 

J15.00014: ABSTRACT WITHDRAWN 
Tuesday, March 11, 2008 2:03PM  2:15PM 
J15.00015: Hitting time for the continuous quantum walk Martin Varbanov A new definition of hitting (absorbing) time is formulated for the case of continuous quantum walks. The walk is measured randomly according to a Poisson process with measurement rate $\lambda$. We derive an explicit formula for the hitting time and explore its dependence on the measurement rate. We show that in the two limits of the measurement rate going to 0 or infinity the hitting time diverges, where the second limit is representative of the quantum Zeno effect. Several different conditions for existence of infinite hitting time are proven by analyzing the analytical structure of the formula for the infinite hitting time. A different condition for existence of infinite hitting times based on the disconnectedness of the complementary graph is proven as well. [Preview Abstract] 
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