2006 Poster Abstracts

The Non-Relativistic Inverted Harmonic Oscillator and Unruh/Hawking Effect

Paul M. Alsing, Air Force Research Laboratory

We demonstrate the analogy between scattering solutions of the non relativistic inverted harmonic oscillator and the thermal radiation produced from the Unruh and Hawking effect. We related this analogy to the quantum phase catastrophe in slow-light which has recently been discussed [U. Leonhardt, Phys. Rev. A 65, 043818 (2002); Nature 415, 406 (2002)] as an optical analogy for Unruh and Hawking radiation.

Solvability of Hamiltonians and Limits on Lie-Algebraic Computation

Howard Barnum, Los Alamos National Laboratory

We consider quantum computational models defined via a Lie-algebraic theory, where Lie-group-coherent initial states are acted on by unitary or non-unitary Lie algebraically generated quantum gates, and the final-state expectation value of a Lie algebra element is measured at the end. We show that these models can be efficiently simulated on a classical computer in time polynomial in the dimension of the algebra, even if the dimension of the Hilbert space where the algebra acts grows exponentially. Similar results hold for the computation of the expectation value of the gate-sequence. We also introduce a Lie-algebraic notion of generalized mean-field Hamiltonians, that is to say, ones belonging to family of faithful finite-dimensional matrix representations of polynomial-dimensional semisimple Lie algebras, and show that they are efficiently solvable by means of a Jacobi-like diagonalization method even though the representation Hilbert space may grow exponentially. Certain lattice spin systems are examples. Our results generalize earlier ones on fermionic linear optics computation, while providing close analogues to simulatability results about bosonic quantum computation with linear optics and homodyne detection (or even squeezing) and provide insight into the source of the power of the conventional model of quantum computation. If time permits, some conjectures about a possible close mathematical relationship between our results and the Gottesman-Knill theorem will be outlined.

Study of Decoherence in Photon-Substracted Entangled Non-Gaussian States

Asoka Biswas, University of Southern California

Entanglement in Gaussian states has been well discussed in literature, while that in non-Gaussian states is not much explored till date, though these states are often encountered in quantum information processing. In this work we study the dynamics of entanglement in a specific family of non-Gaussian states under different decoherence model. We consider non-Gaussian entangled states, which are photon subtracted two mode squeezed vacuum states. We study the dynamics of entanglement in these states in presence of the following environmental decays: (i) Independent amplitude decays of two modes, (ii) Correlated amplitude decays of two modes, (iii) Collective dephasing. We show existence of a whole class of decoherence-free subspace under collective dephasing.

Generalized Coherent States via Markovian Decoherence

Sergio Boixo, University of New Mexico

Coherent states were introduced in the early days of quantum physics as 'quasiclassical' quantum states of an isolated quantum system. The decoherence program defines 'quasiclassical' (or 'pointer') states as states which are most stable in the presence of a coupling with the environment. Operationally, pointer states may be identified through the extremization of an appropriate 'predictability' functional on the Hilbert space. It has been known for some time that for the harmonic oscillator algebra both concepts coincide under very generic conditions. Coherent states have been extended in the 70s to generalized coherent states. Recently, this approach has served as the basis to define generalized entanglement as well as conditions for quantum complexity. Here, we investigate the stability of generalized coherent states under Markovian open-system dynamics. In particular, we identify conditions under which generalized coherent states emerge as pointer states for systems described by algebras more general that the standard oscillator algebra. In the process, we present a streamlined method to find pointer states in the relevant weak-coupling approximation, and discuss conditions for this approximation to be valid. We find that generalized coherent states and pointer states coincide under more restrictive conditions than the canonical, harmonic-oscillator coherent states. Finally, we address the connection of generalized coherent states to decoherence free subspaces and noiseless subsystems.

Quantum Shapelets

Mark Coffey, Colorado School of Mines

Quantum shapelets arise as the solution of a d-dimensional harmonic oscillator or D-dimensional Coulomb problem and may be obtained by requiring scale-space invariance. These functions have application to image processing in conventional or quantum contexts. Novel analytic properties of these functions are presented [1]. Many of these relations also have application to the combinatorics of zero-dimensional quantum field theory.

[1] M. W. Coffey, J. Phys. A (to appear)

Implementation of Two-Qubit Deutsch-Jozsa Algorithm in Atomic Ensemble

Shubhrangshu Dasgupta, University of Southern California

We show how one can implement two-qubit Deutsch-Jozsa algorithm in an effectively decoherence-free system. In this model, two freely propagating photons dispersively interact with an atomic ensemble. The resulting Stark shifts of the atomic levels lead to a NMR-like Hamiltonian, which would be useful to implement the algorithm. Wave-plates and microwave pulses are used to provide the required single qubit operations. We provide supporting numerical results with available experimental parameters. We further discuss in detail the experimental set-up required to implement the algorithm.

Linear Optical Quantum Computing, Imaging, and Metrology

Jonathan P. Dowling, Louisiana State University

Recently it was shown that scalable quantum computing is possible with only linear optical elements and single-photon sources and detectors. I will discuss experimental and theoretical progress on these ideas and show how to adapt them to quantum communications devices as well as to sub-shotnoise quantum metrology and quantum imaging.

Communication-Assisted Local-Hidden-Variable Models for Stabilizer States

Matt Elliott, University of New Mexico

In this talk I present communication-assisted local-hidden-variable models for measurements of products of Pauli matrices on stabilizer states. Models are analyzed with respect to restrictions imposed and their efficacy in predicting overall measurement outcomes as well as outcomes of correlated subsets of measurements. In particular, I present a model in which the quantum mechanical results of Pauli product measurements can be predicted by a local-hidden-variable table supplemented by an efficient amount of classical communication and computation.

An Efficient Source of Single Indistinguishable Photons

Dirk Englund, Stanford University

We demonstrate an efficient source of nearly indistinguishable single photons from an InAs quantum dot coupled to a photonic crystal microcavity. This QD-cavity coupled system has applications in quantum information science.

Quantum Complexity of Partition Functions from Statistical Physics

Joseph Geraci, University of Southern California

It has been demonstrated that the exact evaluation of the partition function for the Ising Spin Glass or Potts Model is a #P problem. This means that there is very little hope of a classical algorithm that provides an exact evaluation. Further, even approximation schemes will not do well. However, just because the general problem is hard, it does not mean that all instances of the problem are intractable. Our research involves studying instances of Ising Spin Glasses and Potts Models that appear to be difficult for classical computers but that may give way to quantum algorithms. We are not interested in the algorithm per se, but in demonstrating the quantum computer's superiority at the evaluation in question, whether exact or approximate. We are using several approaches to achieve our goal including topology and certain algebraic identities. This is work in progress.

References:

D.A. Lidar, "On the Quantum Computational Complexity of the Ising Spin Glass Partition Function and of Knot Invariants", New J. Phys. 6, 167 (2004).
J. Geraci and D.A. Lidar, "A Note on the Efficient Approximation of the Potts Partition Function by Quantum Computers", to be published.

Production of Optical Coherent State Superpositions Using the Kerr Effect

Scott Glancy, NIST Boulder

One can produce superpositions of optical coherent states (also known as "cat states") by sending a single coherent state through a medium that exhibits the Kerr effect having a Hamiltonian proportional to the square of the number of photons. We examine the effect of photon absorption on this process. We calculate the fidelity with which one may hope to make cat states and find that this fidelity is a function of the ratio of the loss to the Hamiltonian's coupling strength. This ratio is much too large to allow cat production with standard optical fibers.

Quantum logic in Group-II Neutral Atoms via Nuclear-Exchange Interactions

David Hayes, University of New Mexico

The spin exchange-interaction provides a means of producing an entangling quantum-logic gate, the square-root of SWAP, at the heart protocols employing single electron quantum dots. This is typically accompanied by strong Coulomb interactions and commensurate decoherence due to strong coupling of charge degrees of freedom to the noisy environment. We propose a protocol utilizing a nuclear-exchange interaction that occurs through ultra-cold collisions of identical spin-1/2 Group-II neutral atoms. A natural advantage is gained by storing the quantum information in nuclear spin states with long coherence times. Unlike NMR protocols based on weak magnetic dipole-dipole interaction, the nuclear exchange interaction stems from strong s-wave scattering of electrons. Nuclear exchange is ensured by the Fermi symmetry of the overall wave function. We have studied this protocol in the context of 171Yb atoms trapped in far-off resonance optical dipole traps. Using numerical analysis, we show that high-fidelity operation is possible through controlled collisions in varied double-well trapping potentials.

Magnetoelectrostatic Ring Trap for Neutral Atoms

Asa S. Hopkins, California Institute of Technology

We are in the process of building a novel trap for confining cold neutral atoms in a microscopic ring using a magneto-electrostatic potential. The trapping potential is derived from a combination of a repulsive magnetic field from a hard drive atom mirror and the attractive potential produced by a charged disk patterned on the hard drive surface. We calculate a trap frequency of 42.6 kHz and a depth of 1 mK for 87Rb. A loading scheme and fabrication process have been devised. For sufficiently cold atoms, this device will provide a one-dimensional potential in a ring geometry that may be of interest to the study of trapped quantum degenerate one-dimensional gases.

Entanglement-Assisted Capacity of Quantum Multiple Access Channels

Min-Hsiu Hsieh, University of Southern California

We find a regularized formula for the entanglement-assisted (EA) capacity region for quantum multiple access channels (QMAC). We illustrate the capacity region calculation with the example of the collective phase-flip channel which admits a single letter characterization. On the way we provide a first principles proof of the EA coding theorem based on a packing argument. We observe that the Holevo-Schumacher Westmoreland theorem may be obtained from a modification of our EA protocol. We remark on the existence of a family hierarchy of protocols for multiparty scenarios with a single receiver, in analogy to the two-party case. In this way we relate several previous results regarding QMACs.

Dynamical Error Correction without Measurement

Kaveh Khodjasteh, University of Southern California

Dynamical methods for protection against errors and decoherence are useful in bounded environments and require straightforward (not cheap though) resources: precise and strong control of Hamiltonians. In their simplest manifestation, dynamical decoupling (bang-bang, spin echo) removes unwanted coupling terms form a qubit Hamiltonian to preserve its arbitrary initial state. Generally speaking, Dynamical error correction is feedback (measurement) free and in its simplest setting does not require extra qubits. In this work, we review the basics of dynamical decoupling in a simple setting. We present a theoretical estimate of the efficiency of dynamical decoupling in terms of the minimum pulse switching times and pulse imperfections. As an important side note, two heuristic arguments based on operator-norm inequalities are presented on (i) why ideal dynamical decoupling does not increase error rates and (ii) why single-bit quantum operations do not introduce errors stronger than those already present. Based on our estimates, we present and compare different dynamical decoupling strategies: periodic bang-bang, concatenated, and Trotter-Suzuki decoupling. Simple simulation results on spin qubits coupled to a spin bath and some preliminary experimental data are presented. In the second part of the talk, we present a scheme for combining stabilizer quantum error correction codes with dynamical decoupling for correcting operational errors (standard dynamical decoupling only corrects quantum memory errors). As a final deliberation we ask fundamental questions on the limits of applicability of dynamical methods posed by entropy considerations.

Hitting time for quantum walks on the hypercube

Hari Krovi, University of Southern California

Hitting time for a random walk on a graph is a measure of the average time it takes the walk to reach a given ending condition. In order to give an analogous definition for quantum walks, we consider measured walks: walks with repeated measurements as well as unitary evolution. In such a walk, one first performs the unitary operation (the product of a coin flip operator and shift operator) and then a coarse-grained measurement on the vertices of the graph. This measurement is a two outcome measurement to verify if the particle is at the final vertex or not. If it reaches the final vertex, the walk stops. We derive an expression for the hitting time of a measured quantum walk on a graph in terms of superoperators acting on the initial density matrix of the particle, and evaluate it numerically for the quantum walk on the hypercube with the Grover matrix as the coin flip. Comparing the result to the classical hitting time on the hypercube, we find that the quantum hitting time is exponentially smaller. This speed-up is not necessarily true for every walk, however. We numerically demonstrate that the hitting time of the quantum walk using the DFT coin can be infinite. We then construct a projector onto all initial states which give infinite hitting times for the DFT coin. Any state that has a non-zero overlap with this projector will have an infinite hitting time. In fact, for any evolution operator, if the degeneracy is sufficiently large---more precisely, greater than the degree of the graph---there exist states which have infinite hitting times. This is caused by destructive interference at the final vertex for certain starting states, an aspect of quantum walks that has no classical analogue. These dramatic speed-ups and slow-downs for the quantum walk can be traced to the symmetry of the hypercube, though symmetry need not be the only reason. Finally, we numerically studied the effect of distortions of the hypercube on the hitting time. In this case, the quantum hitting time was longer than that of the undistorted hypercube, presumably due to loss of symmetry. Thus, symmetry seems to play a very important role in both exponential speed-ups and infinite hitting times of quantum walks.

Phase-Locked Scanning Interferometer for Frequency Stabilization of Multiple Lasers

A. Light and M.D. Di Rosa, Los Alamos National Laboratory

A simple laser stabilization scheme for use in the laser cooling of calcium monohydride (CaR) molecules is demonstrated. Because there is no convenient table-top absorption reference for CaR, we lock the four lasers needed for the cooling scheme to a single stabilized cavity. Schematically, we transfer the stability of a frequency-locked ReNe to the other lasers by way of a scanning confocal etalon (a commercial spectrum analyzer). A piezo drives one of the cavity mirrors and the cavity length is scanned sinusoidally over a portion of its free spectral range (300 MHz) at the piezo resonance near 5 kHz. The average cavity length is then phase-locked to the periodic transmission of the stabilized ReNe. This setup allows > 10x faster feedback control of the cavity length than did previous arrangements [1]. Our use of phase-sensitive detection also reduces the susceptibility of our locking technique to noise from non-synchronous sources, such as laser jitter. In principle, any other laser can be frequency-stabilized by directing its output through the analyzer and locking its periodic transmission to a particular phase of the piezo motion. By scanning the spectrum analyzer over nearly one free spectral range, we stabilize four laser sources simultaneously to a single cavity. We have found an advantage in using high multiples of the drive frequency for phase sensitive detection. We can also use the stabilized cavity to measure precise absolute frequencies with reference to the stabilized ReNe frequency if a coarse measurement is available. A simulation of the system and measurements of cavity and laser frequency stability are presented.

[1] W.Z. Zhao, J.E. Simsarian, L.A. Orozco, and G.D. Sprouse, Rev. Sci. lustrum. 69, 3737 (1998)

Reducing decoherence in an atomic-ion based quantum information processor

C. Langer, National Institute of Standards and Technology

Scalable quantum information processing (QIP) requires physical systems capable of reliably storing coherent superpositions for periods over which quantum error correction can be implemented. Moreover, suppressing memory error rates to very low levels allows for simpler error-correcting algorithms. In many current atomic-ion QIP experiments, a dominant source of memory error is decoherence induced by fluctuating ambient magnetic fields. We address this problem by creating long-lived qubit memories using a first-order magnetic-field-independent hyperfine transition. Our results with 9Be+ qubits show a coherence time of approximately 15 seconds, an improvement of over five orders of magnitude from previous experiments [1]. Errors during quantum gate operations must also be maintained to low levels to enable efficient error correction. In many atomic-ion based QIP architectures, off-resonant laser light is used to perform quantum gate operations. In such schemes, spontaneous photon scattering is a fundamental source of decoherence. We experimentally study the decoherence of coherent superpositions of hyperfine states of 9Be+ in the presence of off-resonant laser light. Our results indicate that the decoherence is dominated by inelastic Raman photon scattering which, for sufficient detunings from the excited states, occurs at a rate much smaller than the elastic Rayleigh scattering rate. For certain detunings, the measured decoherence rate is a factor of 19 below the calculated total scattering rate indicating that qubit coherence is maintained in the presence of photon scattering [2].

[1] C. Langer et al., Phys. Rev. Lett. 95, 060502 (2005).

[2] R. Ozeri et al., Phys. Rev. Lett. 95, 030403 (2005).

On the Consistency of Local Density Matrices

Yi-Kai Liu, University of California, San Diego

We prove the following result: Suppose we have an n-qubit system, and we are given a collection of reduced density matrices rho_l,...,rho_m, where each rho_i describes a subset C_i of the qubits. If rho_l,...,rho_m are consistent with some global state rho > 0, then they are also consistent with a state rho' of the form rho' = exp(M_l+...+M_m), where each M_i is a Hermitian matrix acting on the qubits in C_i. (This state is the quantum analogue of the Gibbs distribution.) Intuitively, our result says that a Gibbs state rho' can simulate an arbitrary state rho > 0, with respect to an observer who can only access subsets of the qubits. This is related to the study of the Local Hamiltonian problem. We also prove a more general result, for the case where the observer only knows the expectation values of an incomplete set of observables T_l,...,T_r (which need not commute). We show that any physically possible set of expectation values (assuming rho > 0) can be realized by a Gibbs state. This is related to the maximum entropy principle in statistical mechanics. While this is plausible in most physical systems, the general result is less obvious. The proof relies on the theory of quantum exponential families.

Simulating Classical Channels with Quantum Side Information

Zhicheng Luo, University of Southern California

We study and solve the problem of classical channel simulation with quantum side information. This is a generalization of both the classical reverse Shannon theorem (CRST), and the classical-quantum Slepian-Wolf (CQSW) problem. The optimal noiseless communication rate is found to be reduced from the mutual information between the sender (Alice) and receiver (Bob) by the Holevo information between Bob and the side information. Our main theorem has two important consequences: common randomness distillation and classical rate-distortion theory with quantum side information. Simple proof of the both direct coding theorems can be made based on our result. The formula for the trade-off between the one-way communication invested and the distilled common randomness also follows from our theorem.

Interferometry and Quantum Phase Transitions with a Bose-Einstein Condensate

Calum MacCormick, Los Alamos National Laboratory

We describe two experiments with a Bose-Einstein condensate confined with time-dependent optical dipole potentials. First, we are building an optical waveguide atom interferometer in which adiabatic transformation of a single optical trap into two spatially-separated traps forms the arms of the interferometer. Second, we plan to manipulate the flexible optical potential to investigate the non-equilibrium dynamics of quantum phase transitions.

Entanglement of Rotationally Symmetric States

Kiran Manne, University of New Mexico

We examine the entanglement present in states that are invariant under a global rotation. By using a technique pioneered by Terhal, Vollbrecht and Werner we are able to derive analytic expressions for the entanglement of formation for these states in a 2xd-dimensional system. We also obtain expressions for the I-concurrence, I-tangle, and the convex-roof-extended negativity. We have some partial results for the entanglement of 3xd-dimensional rotationally symmetric states.

State Preparation In an Atomic Ensemble Through the AC-Stark Shift

Seth Merkel, University of New Mexico

A quantum system is said to be controllable if the accessible Hamiltonians (as a Lie algebra) generate all unitary operators on Hilbert space. Optimal quantum state control seeks a time-dependent sequence of Hamiltonians that maximize the fidelity with an arbitrary target state given a fixed initial state. We consider optimal control of the spin of a cesium atom restricted to its F=3 ground state hyperfine manifold, with a Hilbert space of dimension 2F+1=7. Control is implemented through time varying magnetic fields in two orthogonal directions along with a quadratic AC-Stark effect created by an off-resonant laser probe. The optimization is performed under several constraints, most importantly a temporal limitation determined by decoherence due to photon scattering and parameter inhomogeneity.

Robust Single-Qubit Control and Real-Time Measurement of Neutral Atom Qubits

Brian Mischuck (University of Arizona)

We demonstrate high-precision robust control of an atomic qubit ensemble in a 3D optical lattice using a resonant microwave field. The microwave-driven spin dynamics can be continuously probed using a weak optical polarization measurement, which allows us to observe and optimize the quality of single-qubit gates in near real time. These gates are performed in the presence of unavoidable inhomogeneities in the microwave amplitudes, light shifts and magnetic fields, as a result of which the gate fidelity is degraded. By minimizing these sources of errors, we are able to achieve single qubit gate fidelities of 0.990(5) for atomic qubits trapped in a 3D optical lattice. We also investigate the use of composite pulses originally developed by the NMR community. We will present detailed results and discuss some limitations of using microwaves and composite pulses in our atom/lattice system.

Progress towards trapped-ion quantum information processing at McMaster

Jason Nguyen, McMaster University

Progress towards trapped-ion quantum information processing at McMaster

University Jason Nguyen, Jiajia Zhou, Laura Toppozini, Brian King Department of Physics and Astronomy, McMaster Univeristy Hamilton, ON We present our recent progress in constructing a trapped-ion quantum information processor to explore quantum computing technology and applications and general quantum state engineering. Our approach uses /\{24}Mg/\{+} and /\{25}Mg/\{+} ions in a linear RF (Paul) trap geometry, using the ground-state hyperfine levels of the /\{25}MgA{+} ions as internal-state qubits and the ions' shared motional degree of freedom as a "quantum data bus." In particular, we discuss a fibre-laser-based solid-state source of280-nm UV laser light.

Photon Blockade in an Optical Cavity with One Trapped Atom

Tracy Northup, California Institute of Technology

The phenomenon of photon blockade occurs when the absorption of a first input photon by an optical device blocks the transmission of a second one, thereby leading to nonclassical output photon statistics. In the context of cavity quantum electrodynamics (cQED), the blockade is due to the anharmonicity of the Jaynes Cummings ladder of eigenstates. If an incoming photon: resonantly excites the atom cavity system from its ground state to jl,+(-)> (where jn,+(-)> denotes then-excitation dressed state with higher (lower) energy), then a second photon at the same frequency will be detuned from either of the next steps up the ladder, i.e. from states 12,+(-)>. In the strong coupling regime, for which the coherent rate of evolution exceeds the atomic and cavity decay rates, this detuning is much larger than the excited-state linewidths, so that the two-excitation manifold will rarely be populated. This in tum leads to the ordered flow of photons in the transmitted field, which emerge from the cavity one at a time. We have recently observed photon blockade in the light transmitted by a high-finesse optical cavity containing one trapped Cesium atom strongly coupled to the cavity field [1]. The coherent excitation at the cavity input is near-resonant with one of the two sidebands in the previously-determined vacuum-Rabi spectrum for our system [2]. Measurements of the second-order intensity correlation function at the cavity output show that the emerging photon stream displays antibunching and sub-Poissonian statistics. The atom is localized within the cavity mode by the anharmonic potential of a red-detuned far-off resonant trap. The axial and radial motion-induced modulation on the atom-cavity coupling can be observed on the cavity transmission and hence on its correlation function. A Fourier transform of the second order intensity correlation function reveals a narrow peak just below the calculated maximum oscillation frequency in the axial direction, corresponding to the lowest-lying vibrational level. We use the shape of this peak to estimate that the atoms are distributed among only the lowest ten levels, with maximum energy for axial motion E/kB 250 microKelvin. In addition, we discuss schemes for generation of polarized single photons from a cQED system. Our previous work generated single photons "on demand" which were randomly polarized [3]; here, we propose to generate photons in a single polarization mode. A variation on this method produces photons whose polarization is entangled with the Zeeman state of the atom in the cavity.

[1] K. M. Birnbaum et al., Nature 436, 87 (2005).

[2] A. Boca et al., Phys. Rev. Lett. 93, 233603 (2004). [3] J. McKeever et al., Science 303, 1992 (2004).

Novel Micron-Scale Ion Traps

Steven Olmschenk, University of Michigan

Two of the major hurdles in realization of an ion trap quantum computer are scalability of ion trap structures and anomalous heating of the trapped atoms. Novel ion trap designs have allowed us to investigate these obstacles. First, we report the successful operation of an integrated radiofrequency trap etched from a doped gallium-arsenide heterostructure. The use of semiconductor micro-electromechanical systems (MEMS) technology in the fabrication process eliminates the need for manual assembly and alignment, making such structures suitable for miniaturization and scaling. Second, the employment of a double needle quadrapole trap has allowed for a precise study of the anomalous heating that plagues ion traps. Here, the variable spacing of the needle electrodes and the ability to cool the electrodes via a liquid nitrogen reservoir has lead to characterization and suppression of this heating.

Steps towards scalable trapped-ion QIP at NIST*

Roee Ozeri, NIST Boulder

Recent progress towards realizing a scalable trapped-ion quantum information processor at NIST will be reviewed. Quantum algorithms have been performed on registers of up to six ion-qubits in a multi-zone linear RF Paul trap. For example, many particle entanglement was studied by generating Schroedinger cat states of up to six ions. Steps towards achieving fault-tolerant quantum computation were implemented: memory coherence times were extended using a qubit transition which, to first order, is independent of the magnetic field. The fundamental limits to stimulated-Raman induced quantum gates were investigated by studying the effect of spontaneous scattering of photons on hyperfine coherence. More complex trap architectures and fabrication methods that will enable the scaling of ion-traps to a large multiplexed trap array are also being developed.

* Supported by DOT, ONR & NIST .

Robust Single-Qubit Control and Real-Time Measurement of Neutral Atom

Qubits, Worawarong Rakreungdet, University of Arizona

A Quasi-Hermitian Pseudopotential for Higher Partial Waves

Iris Reichenbach, University of New Mexico

The interaction between atoms in separated traps leads to interesting effects, e.g. to trap induced shape resonances. Their very complicated interaction potential can be modeled by a pseudo potential, which is proportional to a delta shell at a small radius s and the scattering length. For higher partial waves this pseudo potential is not hermitian, but quasi hermitian, leading to a biorthonormal set of eigenfunctions. However, these eigenfunctions can still be used as a basis to expand and diagonalize the additional part of the Hamiltonian, which is due to the separation. This procedure will be explained.

Networking surface-electrode ion traps for large-scale QIP*

Rainer Reichle, NIST Boulder

We discuss how surface-electrode ion traps, i.e., planar miniaturized Paul traps where all electrodes reside in a single plane and ions reside above the plane, have many advantages over their multilayer variants for large scale trapped-ion quantum computing. In addition to their relatively simple manufacturing by standard microfabrication techniques, we consider some issues that make them preferable for their use in large scale structures. In the proposed multiplexing versions for large scale ion trap architectures, nodal points are required. These nodes serve as junctions for the ion qubits, to reliably and arbitrarily transfer quantum information from one location to another in the two planar dimensions. We propose optimized geometric layouts for these nodal points that allow for simple concatenation to a multiplexed architecture. High-fidelity simulations show that the proposed layouts are capable of reliably shuttling ion qubits between these elementary units. More explicitly, we identify problems that might arise in the realization of the nodal points and show how they can be eliminated. We provide accurate analytical models for surface-electrode ion traps for characterizing their global behavior, discuss design issues to avoid sites of anti-binding, introduce electrode shapes to smooth the transport characteristics near nodal points, and present ideas to compensate for micromotion in surface-electrode traps. Comparisons between simulations and preliminary experimental data are consistent to within a few percent. * supported by DTO and NIST. # present address: LANL.

Microfabricated surface-electrode ion traps*

Signe Seidelin, NIST Boulder

We report trapping of laser-cooled 24Mg+ ions in a microfabricated linear Paul trap where all the electrodes reside in a single plane [1]. Such surface-electrode traps are amenable to complex, multi-zone ion trap structures of the sort needed by next generation quantum information processing experiments. Of note is the relative ease of fabrication of this design which arises from the use of standard techniques, including photolithography, electroplating and deep reactive ion etching (DRIB). We find evidence for heating rates comparable to typical two-layer miniature linear Paul trap, even though the trapping region lies about only 50 $\mu$m above the surface of the planar electrodes. The ion lifetime is not noticeably lower than conventional two-layer traps, despite a trap depth more than ten times smaller (approximately 0.17 eV).

*supported by DTO and NIST.

[1] J. Chiaverini, J. Britton, J. D. Jost, C. Langer, D. Leibfried, R. Ozeri, and D. J. Wineland, Quant. Inform. Comp. 5, 419-439 (2005).

Quantum Codes Welcome Spatially Correlated Errors

Alireza Shabani, University of Southern California

A formulation for evaluating the performance of quantum error correcting codes under a general error model is presented. In this formulation the concept of correlated errors is quantified based on a Hamiltonian description of the noise. In particular, we studied CSS codes and surprisingly we observed a better performance for some types of non-local bath models versus a local one. This finding weakens the belief that correlated errors are necessarily fatal for threshold results in fault-tolerant quantum computation. We also found that, to achieve maximum efficiency, the time at which the correction step is applied is an important parameter in the design of a coding system.

Measuring With Qubits

Anil Shaji, University of New Mexico

Using quantum properties of the probes in measurement schemes can lead to measurement accuracies that beat the standard quantum limit. When qubits are used to probe a quantum system, it is known that initializing N probes in a Schrodinger cat state, rather than in a separable state, can reduce the measurement uncertainty by a factor of $1/\sqrt{N}$. We study measurement schemes using quantum probes made of several qubits when the individual qubits are subject to decoherence. The total duration of the measurement is limited by decoherence if we want to preserve the enhancement in precision obtained by using an entangled state of the probe qubits. We estimate this limit for different models of decoherence. We also present the general theory of how entanglement and decoherence in the probe qubits affect the precision of the measurement.

Quantum state tomography via continuous measurement

Andrew Silberfarb, University of New Mexico

We present a protocol for quantum state reconstruction based on weak continuous measurement of an ensemble average. This procedure applies the techniques of quantum control theory and quantum measurement theory to achieve a more efficient reconstruction than those performed using standard projective measurement techniques. This efficiency allows reconstruction of a quantum state using an single ensemble with minimal quantum backaction, setting the stage for state-based feedback control. An experimental demonstration of the technique will be presented in the context of reconstruction of the spin state of the F=3 hyperfine ground-state manifold of Cs-133 using continuous polarization spectroscopy.

Non-destructive Quantum State Reconstruction of Cold Atomic Spins

Greg Smith, University of Arizona

We present results from an experiment to estimate the density matrix for individual spins in an ensemble of cold, neutral atoms. The estimation procedure utilizes a probe-induced quadratic light shift in conjunction with a carefully crafted magnetic field to drive the ensemble on a trajectory that fully explores state space. A real-time measurement record obtained by analysis of an optical probe polarization measurement during this evolution can then be used to estimate the most likely single-atom density matrix. Our experiments use laser-cooled Cs atoms with a large spin angular momentum of F=3, and show that high fidelity can be achieved for a wide variety of initial spin states. Because the measurement is minimally perturbing and can be achieved in a single realization of the experiment, this technique provides a new tool for the study of quantum dynamics. Furthermore, the quantum control tools upon which the measurement is founded hold promise for arbitrary! state generation, which may be achieved by designing a trajectory that targets a specific state instead of exploring all of state space.

Quantum Simulations of Spin Systems Using Trapped Ions

Rolando D. Somma, Los Alamos National Laboratory

Quantum spin systems can be efficiently studied and simulated using trapped ions interacting with laser beams of different intensities, frequencies, and polarizations. In general, this is a hard task for a conventional computer due to the exponential growth of the dimension of the associated Hilbert space with the volume of the system. Following the work of D. Porras and J. I. Cirac [1] we show that, in certain limits, an external magnetic field together with a state-dependent dipole force acting on the ions produces an effective Ising-type evolution of the system. In particular, a two-spin model is numerically simulated and the error of the simulation as a function of temperature (i.e., decoherence) is studied. This will be the basis for future experiments. Many-body simulations beyond the Ising model are also discussed. ·

[1] D. Porras and J. I. Cirac, Phys. Rev. Lett. 92, 207901-1 (2004).

Quantum Logic in Optical Lattices via Controlled Collisions of Cesium Atoms

Rene Stock, University of Calgary

Controlled collisions of ultracold atoms in optical traps and optical lattices provide new avenues for quantum control and quantum information processing as well as for the controlled production of cold molecules. The ability to precisely vary optical lattice parameters and the rich internal structure of the trapped atoms allow for novel quantum state manipulation. Of particular interest is the investigation of controlled collisions of atoms in separated but close wells. In previous research, we showed that for certain well separations, resonances between molecular bound states and trap eigenstates appear when a weakly bound molecular state is shifted by the potential energy (ac-Stark shift) of the separated wells into resonance with a vibrational eigenstate of the trap. These trap-induced resonances provide a new handle for coherently controlling two-atom ground-state interactions and open up new possibilities for designing robust quantum logic gates. Here, we consider this new type of trap-induced resonance for the case of Cs-133 atoms, trapped in separated wells of a polarization-gradient optical lattice. The anomalously large scattering lengths and the presence of a very weakly bound molecular state in Cesium, lead to the possibility of creating trap-induced resonances under realistic experimental conditions. The short-range molecular interaction is accurately treated through a newly derived multichannel pseudopotential, parameterized by the K-matrix, which captures both the bound molecular spectrum as well as the energy-dependent scattering for all partial waves. Our theoretical studies establish realistic operating conditions under which the trap-induced resonance could be observed and show that this strong and coherent interaction could be used as a basis for high-fidelity two-qubit quantum logic operations in standard and addressable optical lattice systems.

A 2D Double-Well Optical Lattice for Manipulating Individual Atom Pairs

Jennifer Strabley, NIST Gaithersburg

We describe the design of a 2D double well optical lattice suitable for isolating and manipulating an array of individual pairs of atoms in an optical lattice. The topology of the lattice is phase stable against phase noise imparted by vibrational noise on mirrors. The properties of the double well: the barrier height and the "tilt" (energy offset between sites within the double well), can be easily and dynamically controlled. Atoms in the lattice can be placed in a double well with any of their four nearest neighbors. This lattice can be used to test neutral atom motion control and perform two-qubit gates.

A Universal Model of a Quantum Robot

Soraya Taghavi, University of Southern California

Quantum Robot is described as a quantum system that moves in, and interacts with, an external environment of quantum systems. Such environments consist of arbitrary numbers and types of particles in two or three dimensional space lattices. The focus in this study is mainly on the universality of the quantum robot, which is shown in two steps. In the first step, using some concepts of Lie Algebra, the Robot can perform all single-body Hamiltonians on each particle. In the second step, the Single-body Hamiltonians together with a specific entangling Hamiltonian enable the robot to perform a general unitary operation on all particles. The argument in this step is based on a corollary to a theorem in majorization theory.

Quantum Chaos and Entanglement for Two Coupled Spins

Collin M. Trail, University of New Mexico

Quantum chaos is the study of the quantum mechanical features of systems for Hamilitonians whose classical description exhibits chaos. Recent work suggests that there is a connection between the rate of entanglement generation of a bipartite quantum mechanical system and the existence of chaos in the classical limit of that system. This work further explores this connection for the case of two spins in an atom, electron and nuclear, coupled by the hyperfine interaction and driven by an external magnetic field. We have studied numerical simulations of the classical limit of this system, and have results which show the appearance or lack of chaos for a variety of different fields and initial conditions.

Hidden Geometric Phases and Holonomies of the SU(4) Group of Two-Qubit Unitary Transformations

Dmitry Uskov, Louisiana State University

Any unitary transformation of an arbitrary n-qubit system can be decomposed into a product of local operations and two-qubit binary operations. Therefore two-qubit operations are viewed as elementary building blocks of multiqubit quantum gates. From the mathematical point of view such operations are elements of the IS-dimensional SU(4) Lie group, and its (sub-)Riemannian geometry determines computational cost of various quantum operations. Intriguingly, geometric and algebraic properties of the SU(4) group are much richer than corresponding properties of an arbitrary SU(N) group because there exists an accidental isomorphism between the su(4) Lie algebra and the so(6) Lie algebra of orthogonal rotations of Euclidean 6-dimentional space. We exploit this properties to identify a set of new fiber bundles embedded in the SU(4) manifold and construct holonomies on these fiber bundles complementary to the well-known Berry and Wilczek Zee geometric phases. We demonstrate some advantages of using these holonomies for constructing error-robust quantum gates.

Simulating Quantum Systems with Trapped Ions

Kendra Vant, Los Alamos National Laboratory

Many quantum systems cannot be simulated efficiently on a deterministic classical computer due to the large Hilbert space they inhabit. They may instead be investigated using a quantum simulator - a device which uses a number of more-easily controllable quantum bits to mimic the quantum spins in the system to be studied. The states of the simulator follow the same equations of motion as the real system, yet are directly accessible to the experimenter. Trapped ions may make this kind of simulation possible. Long-lived internal states of individual ions (qubits) can be coupled through both the Coulomb interaction and applied radiation fields. We will describe the experimental status of the proposed LANL trapped-ion quantum simulator. In particular, we will discuss our ideas for the generation of spin-dependent optical forces to produce ion-ion interactions that mimic interactions in Ising-like model Hamiltonians. Prospects for using this interaction as the basis of a few-ion simulator for this model and others will also be described. In addition, recent collaboration between Los Alamos and Sandia National Labs has led to the construction of microfabricated trapping structures; development of their use for quantum simulations will also be a major focus in the near future. These multizoned traps should be more suitable for quantum simulation than single well traps. We will discuss the trap development and testing.

Reducing the sensitivity of the M-S gate to unbalanced laser intensities

Janus H. Wesenberg, NIST Boulder

High-fidelity quantum gates have been experimentally demonstrated for ions confined in strongly binding RF-traps. One notable example is the geometric gate implemented at NIST in Boulder. This gate is closely related to a gate suggested by Moelmer and Soerensen, but implementation is simpler because only one pair of Raman beams is used, in contrast to the two pairs employed by the Moelmer-Soerensen (M-S) gate. Unfortunately, the simpler NIST gate does not work if the qubit is encoded in field insensitive states, that is, states with vanishing differential Zeeman shift. Since such encodings have many advantages over field-sensitive encodings, there is a renewed interest in implementing the original M-S gate. In the originally proposed form, the M-S gate is highly sensitive to differences in effective strength between the two pairs of Raman beams. Since avoiding such strength differences would present significant experimental difficulties, it is preferable to modify the gate to make it intrinsically insensitive to strength differences. We show that such intrinsic insensitivity can be achieved by means of a simple modification of the gate operation, combined with traditional re-focusing techniques.

Towards Experimental Realization of Cavity QED with

Future possibilities for this experiment include trapping an atom to the cavity mode and coupling multiple resonators on a single chip.

[1] S.M. Spillane et al, Phys. Rev. A, 71, 013817 (2005)

Shuttling Ions in Two Dimensions: The T-Junction

Mark Yeo, University of Michigan

We demonstrate a two-dimensional 11-zone ion trap array, where individual laser-cooled atomic ions are stored, separated, shuttled, and swapped. The trap geometry consists of two linear rf ion trap sections that are joined at a 90 degree angle to form aT shaped structure. We shuttle a single ion around the corners of the T-junction and swap the positions of two crystallized ions using voltage sequences designed to accommodate the nontrivial electrical potential near the junction. Full two-dimensional control of multiple ions demonstrated in this system may be crucial for the realization of scalable ion trap quantum computation and the implementation of quantum networks.

Simulated Quantum Computation ofPorphyrin Excited States

Alexander Slepoy, Sandia National Laboratories

Configuration Interaction (CI) is a technique for computing the energy of a molecular state in which the problem size grows exponentially with the size of the molecule considered. Aspuru-Guzik and coworkers reported a classical simulation of a quantum computer using n qubits to represent 2**n configurations, thereby mapping the exponential-time classical algorithm into a polynomial-time quantum algorithm. We demonstrate that Aspuru-Guzik et al.'s method can be used to compute the excited states of porphyrin molecules using the Gouterman model, a class of molecules important in biology and chemical applications. Scaling such an application to larger molecules could provide a meaningful calculation that could be performed on a primitive quantum computer using dozens of qubits that would nonetheless be prohibitive on a classical computer.