# 2007 Talk Abstracts

## Quantum Simulation with Ultra-Cold Atoms (Invited)

Brian ﻿Demarco, University of Illinois

Abstract. Physical simulation as a means for resolving outstanding quantum many-body problems was first proposed by Feynmann in 1981. Since then, physicists have dreamed of using physical quantum simulation as a quantitative tool. Ultra-cold atoms trapped in an optical lattice are now emerging as an ideal tool for quantum simulation of a wide range of many-body quantum models, including the Hubbard model and quantum magnetism. I will review the developing field of quantum simulation using ultra-cold atoms and highlight our progress on simulating quantum magnetism.

## Subwavelength addressibility and spin-exchange in a double-well optical lattice

Patricia ﻿Lee, National Institute of Standards and Technology

Abstract. We report on the experimental demonstration of radio frequency addressing of atoms in every other site of a double-well optical lattice, independent of their nearest neighbors at a distance of less than an optical wavelength. By dynamically controlling the lattice and the vector light shifts, the atoms\\\' spatial and spin degrees of freedom are entangled in each double well. We have also observed a coherent spin-exchange interaction between pairs of atoms in the double-well lattice, which can be used as a mechanism for a square-root-of-swap gate.

## Progress towards Quantum Logic with Cs Atoms in an Optical Lattice

Worawarong Rakreungdet, University of Arizona

Abstract. High fidelity quantum logic is an essential part of any scheme for quantum information processing. We have for some time worked to use cold Cesium atoms trapped in an optical lattice as qubits, and to implement single- and two-qubit control through a combination of applied fields and collisional interactions. In a series of experiments we have demonstrated accurate and robust qubit rotation on the Bloch sphere with resonant microwave fields. In practice such control operations are always subject to errors, in our case spatial inhomogeneity in the microwave Rabi frequency and the light shifted qubit transition frequency. A highly useful method to observe qubit dynamics in real time has allowed us to optimize our microwave source and optical lattice and thus minimize these inhomogeneities, and this in turn has allowed us to perform Pi gates with a fidelity of 0.990(5). We have further explored the use of NMR- type composite pulses to reduce the effect of errors, and will discuss the potential for improving gate robustness in the atom/ lattice system. In more recent experiments our focus has shifted to two-qubit quantum logic based on controlled collisional interactions. Here Cesium is of unique interest because of the very large scattering lengths (of order 10^3 a0) associated with the relevant collision channels. Large scattering lengths imply faster gates, but more importantly it allows strong collisional interaction between atoms in separate but overlapping traps. Stock et al. [PRL 91, 183201 (2003)] have identified a so-called trap induced shape resonance wherein a molecular bound state of the Cs dimer is shifted into resonance with a trap vibrational state, and proposed that this phenomenon may be used as a basis for quantum logic. We will discuss two experiments to detect the large collisional energy- or phase shifts possible in an optical lattice. One is a straightforward extension of the C-Phase gate demonstrated by Mandel et al. [425, 937-940 (2003)], wherein the center-of-mass wavepackets of two qubits are split and recombined in a geometry corresponding to two partially overlapping Mach-Zender interferometers. Unfortunately this scheme has proven extremely sensitive to phase errors as the wavepackets are moved by the optical lattice. We are now working on an alternative scheme that starts with two qubits in clearly separated traps and use microwaves to drive one or both into a third trap in-between. Once the wavepackets overlap the collisional energy shift can be measured spectroscopically or used as the basis a C-Phase gate.

## Entanglement of mesoscopic optical wave-packets and collective atomic ensembles

Michael G. Raymer, University of Oregon

Abstract. I will review our progress toward creating mesoscopic-level quantum entanglement of Stokes light and atomic electronic polarization excited during single-pass, linear-regime, stimulated Raman scattering in Rb vapor. Such entanglement is decomposable into multiple bosonic mode pairs, each pair comprised of one optical wave- packet mode and one atomic-ensemble spatial mode [1]. Each mode pair undergoes independent evolution into a two-mode squeezed state. We have developed measurable criteria for entanglement verification based on the matrices of moments formalism [2,3], and find that using these in the range of 10-400 quantum excitations requires pushing the state of the art in experiments.

[1] W. Wasilewski and M.G. Raymer, "Pairwise entanglement and readout of atomic-ensemble and optical wave-packet modes in traveling-wave Raman interactions," Phys. Rev. A 73, 063816 (2006)
[2] E. Shchukin and W. Vogel, "Inseparability criteria for continuous bipartite quantum states," Phys. Rev. Lett. 95, 23002 (2005) and [3]. A. Miranowicz, M. Piani, P. Horodecki and R. Horodecki, "Inseparability criteria based on matrices of moments," arXiv: quant-ph/0605001 (2006)

## Dissipative dynamics of atomic Hubbard models coupled to a phonon bath: Dark state cooling in a Bloch band of an optical lattice

Peter Zoller, University of Innsbruck

Abstract. We propose and analyse a scheme to cool atoms in an optical lattice to ultra-low temperatures within a Bloch band, and away from commensurate filling. The protocol is inspired by ideas from dark state laser cooling, but replaces electronic states with motional levels, and spontaneous emission of photons by emission of phonons into a Bose-Einstein condensate, in which the lattice is immersed. In our model, achievable temperatures correspond to a small fraction of the Bloch band width, and are much lower than the reservoir temperature. This is also a novel realization of an open quantum optical system, where known tools are combined with new ideas involving cooling via a reservoir.

## Real-time Manipulation of Remote Atomic Ensembles for a Scalable Quantum Network

Chin-wen (James) Chou, California Institute of Technology

Abstract. In the quantum repeater scheme, entanglement is distributed by dividing a long communication channel into short segments with entangled systems at each end and then performing entanglement swapping through the chain of entangled pairs. If it is possible to store the entanglement and if there is a trigger that heralds it once it is achieved, it is possible to build up the chain by entangling different parts at different times. By conditioning the evolution of the chain to the output of its parts, an exponential enhancement is attained in the probability of success. Real-time control for synchronization of different systems is then a promising way to boost the probability of simultaneous generation of many target states, and thereby to enable the realization of elaborate procedures. As photons are the basic carriers of information over long distances, the necessity of using memory implies to control the exchange of information between matter and light. Great progress has been achieved for interfacing light fields and atomic ensembles, following the novel scheme proposed by Duan, Lukin, Cirac, and Zoller [1]. For example, generation of photon pairs, storage of single photons and efficient retrieval of stored single excitations were implemented with cold atomic ensembles. Heralded entanglement between ensembles was recently demonstrated in our group [2].
A key point that has not been experimentally addressed, however, is the extent to which these techniques enable scalable networks. We report the first implementation of real-time conditional control of two memories. The nodes consist of ensembles of cold atoms that can each store a single collective excitation in a probabilistic, but heralded way. As the excitation can be transferred efficiently to a light field in the single-photon regime, the ensembles function as heralded single-photon sources. The control allows storing an excitation in one ensemble, while waiting for a trigger indicating the presence of an excitation in the other one. Relative to operation without control, a 28-fold increase in the probability to simultaneously generate a single photon from each system is attained. As a first application of this enhancement, we carried out a two-photon interference measurement and inferred a 90% overlap for the wavepackets [3].
We will also report the application of this control capability to enhance the success probability (in this case by a factor of 19) of preparation of 4 atomic ensembles, 2 at each remote site, such that a trigger heralds the success of the preparation. The state of the ensembles, after transferred to light fields locally, can lead to joint-detection statistics of polarization-entangled photon pairs distributed to the sites. This constitutes an important step towards building a scalable quantum network for entanglement-based quantum communication, such as quantum cryptography and quantum teleportation, over long distance.

[1] L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, Nature, 414, 413 (2001)
[2] See, for example, J. Laurat, et al., Opt. Expr. 14, 6912 (2006), and references therein.
[3] D. Felinto, C. W. Chou, J. Laurat, E. W. Schomburg, H. de Riedmatten and H. J. Kimble, Nature Physics 2, 844 (2006)

## QIP with Nuclear Spins and Quantum Statistics in Group-II Neutral Atoms

Ivan Deutsch, University of New Mexico

Abstract. Implementations of quantum informaton processors require coherent quantum logical gates that induce entangling operations between qubits. In most cases, the same physical effect that gives rise to coherent couplings in the logical basis states leads to decoherence between them. We propose a a new scheme for quantum logic based on an exchange bblockade arising solely from the symmetry of identical composite particles rather than from differential coupling strengths. We consider a hybrid approach based on NMR and ultracold collisions of trapped neutral group-II atoms, whereby the nuclear spins store quantum information and act a quantum switch for mediating interactions. In addition, the decoupling of nuclear and electronic interactions allows one to re-cool motional heating via laser cooling or sympathetic cooling in a BEC without erasing or decohering the qubit. We present numerical studies of all these phenomena.

## Thresholds for Quantum Computation

Bryan Eastin, University of New Mexico

Abstract. Threshold bounds prove that building a universal quantum computer is possible in practice. Just how practical it is, however, depends on the exact value of the threshold, a number that is elusive at best. This tutorial is intended as an introduction to the wide world of threshold results. It covers the motivation and origin of various threshold estimates and bounds and the way in which these numbers depend on assumptions regarding error models and resources.

## Is Fault-Tolerant Adiabatic Quantum Computation Possible?

Dave Bacon, University of Washington

Abstract. Adiabatic quantum computation is an alternative method of quantum computing which has recently been shown to be equivalent to the quantum circuit model of quantum computation. This equivalence opens up the possibility for constructing new quantum computing architectures based on the adiabatic algorithms paradigm. However, this possibility is all for naught unless a theory of fault-tolerant quantum computation for adiabatic quantum computers is constructed. Here I will describe recent progress towards the development of a full theory of fault-tolerant adiabatic quantum computation, including improvements in the existing results, as well as outline the difficulties which remain.

## Noise Threshold for a Fault-tolerant Two-dimensional Lattice Architecture

Krysta Svore, Microsoft Research

Abstract. We consider a model of quantum computation in which the set of operations is limited to nearest-neighbor interactions on a 2D lattice. We model movement of qubits with noisy SWAP operations. For this architecture we design a fault-tolerant coding scheme using the concatenated [[7,1,3]] Steane code. Our scheme is potentially applicable to ion-trap and solid-state quantum technologies. We calculate a lower bound on the noise threshold for our local model using a detailed failure probability analysis. We obtain a threshold of 1.85 x 10^-5 for the local setting, where memory error rates are one-tenth of the failure rates of gates, measurement, and preparation steps. For the analogous nonlocal setting, we obtain a noise threshold of 3.61 x 10^-5. Our results thus show that the additional SWAP operations required to move qubits in the local model affect the noise threshold only moderately.

## Dynamical Error Correction without Measurement

Kaveh Khodjasteh, University of Southern California

Abstract. Alongside error correcting codes, purely dynamical (feedback-free) methods for quantum error correction exist. An important example is dynamical decoupling, which can be used to effectively cancel the interaction of the environment with a quantum information processor. We discuss three main results of dynamical decoupling: universal dynamical decoupling, concatenated pulse sequences, randomized decoupling sequences. In the case of concatenated pulse sequences we provide a rudimentary version of a fault tolerance condition, and prove that concatenated decoupling sequences outperform their periodic counterparts in the regime of physical interest. We further prove a fundamental result: application of quantum unitary operations does not increase error rates and use this as a support of fault-tolerant quantum computation in non- Markovian regimes. We conclude by hinting at two approaches for dynamically decoupled quantum computation [as opposed to quantum memory] name ly hybrid error correction codes with an embedded dynamical decoupling sequence, and self-correcting quantum operations that cancel unknown systematic errors in quantum operations automatically.

## Quantum state manipulation with photons, solid-state cavity QED systems and micromechanical structures

Dirk Bouwmeester, University of California, Santa Barbara

Abstract. The phase sensitivity of the Mach-Zehnder interferometer, when fed by a coherent state in one input port and vacuum in the other, is usually considered bounded by the standard quantum limit only when the true value of the phase shift is pi/2. For other phase values no practical scheme is known that reaches the same accuracy. For this reason the best interferometers use active phase stabilization We show that the Mach-Zehnder interferometer, when analyzed with photon number resolving detectors and using a Bayesian phase estimation strategy, can achieve the standard quantum limit independently from the true value of the phase shift. Therefore there is in principle no need to use active phase stabilization. The second topic that will be addressed is the design and control of solid-state micro cavities with embedded semiconductor quantum dots. We will report on the observation of vanishing-threshold photon crystal lasers with as active gain only 1 to 3 quantum dots, and on a most efficient polarization-controlled single photon source (20MHz detected single photons per second!). As a final topic optical cooling of micromechanical systems will be addressed. In particular we will show how active feed back by radiation pressure can cool a micromechanical cantilever from room temperature to 135 mKelvin. Furthermore we will discuss the possibility of investigating macroscopic quantum superpositions and environmental induced quantum decoherence using such methods.

## Optimal Quantum Measurements

Rolando Somma, Los Alamos National Laboratory

Abstract. The standard method to obtain expectation values of observables and unitary operators of a quantum system consists of preparing many copies of the desired state, and measuring the corresponding quantity by coupling the quantum system to an apparatus. The precision of the measured value using this method is known to scale as 1/sqrt(N), where N indicates the number of copies (experiments). I will show that, with a minimal prior knowledge about the operator whose expectation value is to be measured, such a precision can be increased to 1/N. For this purpose, I will consider different variations of the phase estimation algorithm according to the quantity that is to be measured. These algorithms are particularly useful for simulating quantum systems on quantum computers, enabling efficient measurement of observables and correlation functions.

## Generalized Limits for Single-Parameter Quantum Estimation

Steven T Flammia, University of New Mexico

Abstract. We develop generalized bounds for quantum single-parameter estimation problems for which the coupling to the parameter is described by intrinsic multi-system interactions. For a Hamiltonian with $k$-system parameter-sensitive terms, the quantum limit scales as $1/N^k$ where $N$ is the number of systems. These quantum limits remain valid when the Hamiltonian is augmented by any parameter- independent interaction among the systems and when adaptive measurements via parameter-independent coupling to ancillas are allowed.

## Stark decelerated OH: magnetic trapping, precision measurement, and cooling

Benjamin Lev, JILA

Abstract. The experimental realization of large samples of ultracold, ground state polar molecules would be a major breakthrough for research in ultracold collisions and chemistry, quantum information processing, and the study of novel states of matter. To accomplish this goal, our research has focused on the use of a Stark decelerator to slow a supersonic expansion of OH. The cold molecular packets produced have enabled us to perform precision microwave spectroscopy of the OH ground state structure. This has importance for constraining fundamental constant variation and the identification of candidate molecular qubits. In addition, we have recently demonstrated the magnetic trapping of the highly polarizable OH molecule in the presence of tunable electric fields. We will present our latest results on trapping dynamics as well as discuss the feasibility of OH cavity-assisted laser cooling, which may provide access to the ultracold regime.

## Quantum information theory without independence assumptions

Renato Renner, University of Cambridge

Abstract. Results in quantum information theory are typically based on certain independence assumptions. For example, for state tomography, many identical and mutually independent copies of a given quantum system are needed. Experimentally, however, it is generally hard, if not impossible, to verify this independence. In this talk, I show how this problem can be solved theoretically, using a recently developed quantum version of de Finetti's classical representation theorem. It implies that independence can be replaced by a weaker symmetry assumption, which is usually easy to justify.

## Strengthening the quantum adversary method with negative weights

Peter Hoyer, University of Calgary

Abstract. The adversary method, originally developed by Ambainis, is one of the most successful techniques for proving lower bounds on quantum query complexity. It has been generalized and extended by several authors, giving formulations in terms of weight schemes, spectral norm of matrices, and Kolmogorov complexity. Spalek and Szegedy show that all of these formulations are in fact equivalent. We present a strengthening of the adversary method. Our new bound, which we call $\\MADV$, is always at least as large as the old adversary method $\\ADV$, and we show an example of a function for which $\\MADV(f)=\\Omega(\\ADV(f)^{1.09})$. The bound $\\MADV$ arises by allowing matrices with negative entries in the spectral norm formulation of the adversary method. We show that $\\MADV$ possesses all of the nice features of the $\\ADV$ bound: $\\MADV(f) is a lower bound on the bounded-error quantum query complexity of$f$, its square is a lower bound on the formula size of$f$, and$\\MADV$behaves well with respect to function composition. On the other hand,$\\MADV$is not bound by some of the limitations which the old adversary method faces, namely the certificate complexity barrier \'\' and the Hamming distance barrier\'\'. The certificate complexity barrier states that$\\ADV(f) < (C_0(f)C_1(f))^(1/2)$for a total function$f$, where$C_0(f),C_1(f)$are the zero and one certificate complexities of$f$, respectively. We give an example of a function$f$where$\\MADV(f)=\\Omega(C_0(f)C_1(f)^{0.545}). The Hamming distance barrier states that if every zero-instance of a partial Boolean function $f$ has relative Hamming distance at least $\ \epsilon$ from every one-instance, then $\\ADV(f)\\le 1/\\eps$. We show that this bound also does not apply in this strict sense to $\ \MADV$, although we do not know of an asymptotic separation. This opens up the possibility that the $\\MADV$ method can get better bounds where the $\\ADV$ has gotten stuck, for example triangle finding, the collision problem, or element distinctness. Although in form the $\\MADV$ bound is very similar to the $\\ADV$ bound, our proof that $\\MADV$ is a lower bound on quantum query complexity departs from previous adversary proofs. The basic adversary principle is that if an algorithm $A$ {\\em computes} a function $f$, then in particular the algorithm is able to distinguish between inputs $x$ and $y$ which take on different function values. The adversary method actually lower bounds this, potentially easier, distinguishing problem. In our proof we use a stronger property provided by the fact that the algorithm computes a function. Namely we crucially use the existence of projectors which give the right answer with high probability.

## Quantum algorithms for hidden quadratic structures

Andrew Childs, California Institute of Technology

Abstract. One of the major open problems in quantum information is to develop new quantum algorithms. Much of the work on this question has focused on the nonabelian hidden subgroup problem (HSP), attempting to extend Shor\'s solution of the abelian HSP. Unfortunately, these efforts have met with only limited success. In this talk, I will describe an alternative way of generalizing the success of Shor\'s algorithm. One application of Shor\'s algorithm is to find hidden linear structures. Suppose we are given a black box function that is constant on some unknown subspace of a vector space over a finite field, constant on any parallel flat, and distinct on different parallel flats. Then Shor\'s algorithm allows us to efficiently determine the hidden subspace. A natural generalization of this problem is to find hidden structures of higher degree. Specifically, I will describe several black box problems involving hidden quadratic structures. These problems can be sol ved efficiently by a quantum computer, whereas a classical computer provably requires exponentially many queries to the black box to solve them. This is joint work with Leonard Schulman and Umesh Vazirani.

## The operational meaning of quantum conditional information

Jon Yard, California Institute of Technology

Abstract. Classical information theory is centered around four fundamental quantities: entropy, mutual information, and their conditional counterparts. These quantities are constructed from certain linear combinations of the entropies of marginal probabilities. Analogous quantities arise in the quantum generalization. Until recently, all but the final quantity - quantum conditional mutual information (QCMI) - had been shown to have an operational interpretation. In this talk, I will show how QCMI answers a fundamental question: "how much quantum communication is needed to transfer a quantum system between two parties holding side information?" The optimal protocol achieving this task - 'quantum state redistribution' - satisfies some elegant and intuitive properties which I will also recall. This talk is based on joint work (quant-ph/0612050) with Igor Devetak.

## Quantum Control Theory

Navin Khaneja, Harvard University

Abstract. The subject of automatic control grew out of world war needs with development of concepts of feedback, stability and frequency domain methods. Space age provided further incentive for the development of theory of optimal control, estimation and filtering. In this talk, we will argue that problems in measurement and control of quantum systems provide new vistas and opportunities for development and applications of control theory. I will discuss several case studies demonstrating applications of methods of control theory to problems in measurement and manipulation of quantum systems. These problems include optimal steering of quantum systems in presence of decoherence, robust broadband control of quantum dynamics, and real time monitoring and feedback of quantum systems. Applications to areas of coherent spectroscopy, quantum information science and quantum metrology will be discussed. Finally we will emphasize the need for new methodology development arising from new problems and applications involving control of quantum systems.

## Optical Coherent State Discrimination via a Closed-Loop Measurement

JM Geremia, University of New Mexico

Abstract. In quantum state discrimination, one must determine the state of quantum system based on the outcome of a measurement and a list of candidate states from which to choose. When the candidate states are not orthogonal, basic quantum mechanics dictates that no measurement can distinguish perfectly between them. The objective is therefore to optimize some information theoretic metric (such as the mutual information, entropy, or probability of error) characterizing the quality of the state discrimination over the space of allowed quantum measurements. When minimizing the probability of error, the optimal state-discriminating measurement for pure states involves projecting onto a superposition (or cat-state) basis. Unfortunately, implementing cat-state measurements in the laboratory is extremely challenging, if not generally impractical. In this talk I will describe an experiment in which we utilize real-time quantum feedback control in place of a cat-state to achieve quantum-limited discrimination between optical coherent states.

## Quantum State Control in a Large Spin System

Souma Chaudhury, University of Arizona

Abstract. Quantum systems with Hilbert space dimension higher than two (qudits) are often considered as carriers of quantum information, usually by isolating a convenient pair of states and working exclusively with this qubit embedded in the larger space. This situation naturally raises the issue of quantum control of the entire qudit system and whether this might be useful for information processing tasks. Quantum control of large systems, especially collective spins, also has near-term applications in quantum metrology. We will describe how to achieve universal quantum control of the F=3 spin manifold in the ground hyperfine state of atomic Cesium, by driving the atom with a combination of magnetic fields and a rank-2 tensor light shift. A relatively simple optimization routine can be used to design time dependent controls that transform an initial fiducial state |F=3,mf=3> into a desired target state. In a series of experiments we have used this procedure to generate a broad range of target states, including squeezed and other non-classical states. In general we achieve yields (fidelity of the actual state relative to the target state) in the range ~ 85% - 90%, limited mostly by errors in the control fields and by light scattering. Our current protocol does not optimize for robustness against errors, and finding a systematic way to do so will likely be essential for improvements in control fidelity. We have compared our optimal control approach to an adiabatic spin-squeezing scheme proposed by Molmer and Sorensen, and find that while the latter is more robust to errors, the optimal control method can be quicker. In the future we hope to extend a version of our optimal control scheme to the entire ground manifold of Cesium.

## Towards a scalable ion trap for quantum information processing

S. Seidelin, J. M. Amini, R. B. Blakestad, J. J. Bollinger, J. Britton, K. R. Brown, J. Chiaverini [a], R. J. Epstein, J. P. Home, D. B. Hume, W. M. Itano, J. D. Jost, C. Langer [b], D. Leibfried, R. Ozeri [c], R. Reichle [d], N. Shiga, J. H. Wesenberg and D. J. Wineland.

NIST, Time and Frequency Division, Boulder, CO.

Abstract. To build a useful trapped-ion quantum information processor, the number of individually controlled ions must be increased significantly from what is possible in current state-of-the-art ion traps. We have proposed and developed RF Paul traps with a novel and simplified geometry where the electrodes are located in a single plane and the ions are confined above this plane [1,2,3]. This design has the potential for being scaled up to hold a large number of individually accessible ions. We have performed sideband cooling to the ground state in this trap, and preliminary measurements indicate a heating rate that is relatively low considering the small distance (40 micrometers) between ions and electrodes. An extension of this trap design therefore constitutes a potential means of controlling many ion-qubits for quantum processing applications.

Work supported by the DTO and NIST.

[a] Current address: Los Alamos National Laboratories, NM.
[b] Current address: Lockheed Martin, Palmdale, CA
[c] Current address: Weizmann Institute, Rehovot, Israel
[d] Current address: University of Ulm, Germany.

[1] J. Chiaverini et al., Quantum Inf. Comput. 5, 419 (2005).
[2] S. Seidelin et al., Phys. Rev. Lett. 96, 253003 (2006).
[3] J. Britton et al., quant-ph/0605170.
[4] R. Reichle et al. Nature 443, 838, 2006

## QIP implementation and small algorithms with trapped ions at NIST

D. Leibfried, J. Amini, B. Blakestad, J.J. Bollinger, J. Britton, K.R. Brown, R. Epstein, J.P. Home, J.D. Jost, E. Knill, C. Langer, R. Ozeri, R. Reichle, S. Seidelin, N. Shiga, J. Wesenberg, and D.J. Wineland, National Institute of Standards and Technology

Abstract. Atomic ions confined in an array of interconnected traps represent a potentially scalable approach to quantum information processing. All basic requirements have been experimentally demonstrated in one and two qubit experiments. The remaining task is to scale the system to many qubits while minimizing and correcting errors in the system. While this requires extremely challenging technological improvements, no fundamental roadblocks are currently foreseen. This talk will complement Signe Seidelin's talk on trap development in the same session and give a survey of recent progress at NIST in practically implementing quantum algorithms with up to 6 qubits. It will also discuss some new approaches to minimizing the overhead of laser beam control in large scale implementatons. *Supported by DTO and NIST.

## Progress toward Simulations of Quantum Systems with Trapped Ions at LANL

John Chiaverini, Los Alamos National Lab

Abstract. Trapped ions have proved to be a very good system for carrying out quantum information processing (QIP). One of the first applications of QIP will likely be the simulation of the Hamiltonian evolution of collections of interacting quantum particles, a task that is, in general, exponentially difficult using classical computing techniques. At Los Alamos National Lab (LANL), we are developing the required interactions to simulate Ising- and Heisenberg-type Hamiltonians of spin-1/2 particles by mapping the problem onto a system of trapped ions. We will discuss our experimental progress toward a useful quantum simulator.

## Long distance decoy state quantum key distribution

Jim Harrington, Los Alamos National Laboratory

Abstract. Quantum key distribution (QKD) can in principle offer unconditional security of establishing secret keys between physically separated parties. Practical QKD systems often suffer from imperfections in their sources and detectors, but decoy state protocols have offered a way to achieve high performance out of weak laser pulse implementations without sacrificing security. I will present an experiment done in collaboration between LANL and NIST in 2006 where secure keys were produced over a record-setting 107 km of dark fiber. I will also highlight what modifications are expected to extend this to much longer distances.

## Coherent Communication with Continuous Variables

Mark M. Wilde, University of Southern California

Abstract. The coherent bit (cobit) channel is a resource intermediate between classical communication and quantum communication. The cobit channel produces coherent versions of the teleportation and superdense coding protocols. We extend the cobit channel to the continuous variables of quantum optics. We provide a general definition of the "coherent nat" (conat) channel when only finite- squeezing resources are available. Coherent teleportation provides sufficient conditions and coherent superdense coding provides necessary conditions for a channel to be a finite-squeezing approximation to an ideal conat channel. We illustrate several protocols that use both a position quadrature and a momentum quadrature conat channel. Finally, we address the reversibility of coherent teleportation and coherent superdense coding with only finite-squeezing resources.

## A General Linear-Optical Quantum State Generator

Nickolas Vanmeter, Louisiana State University

Abstract. We introduce a notion of a linear-optical quantum state generator (LOQSG). This is a device that prepares a desired quantum state using product inputs from photon sources, linear-optical networks, and post-selection using photon counters. We show that the LOQSG can be concisely described in terms of polynomial equations and unitary constraints. We illustrate the power of this language by applying the Groebner-basis technique along with the notion of vacuum extensions to solve the problem of how to construct a LOQSG analytically for any desired state. Moreover, we show how the optimal LOQSG can be found using the methods of convex optimization. In particular, we disprove a conjecture concerning the preparation of the maximally path-entangled \"NOON\" state by providing a counterexample using these methods, and we derive a new upper bound on the resources required for NOON-state generation.

## Atomtronics: Creating ultracold atom analogs of electronic circuits and devices

Abstract. The fundamental component of classical computation using logic devices is the bipolar junction transistor. The transistor itself is a byproduct of a p-n junction. "Atomtronics" focuses on creating an analogy between electronic devices and circuits with ultracold atoms. Such an analogy comes from the Mott insulator characteristic of ultracold gases trapped in optical lattices. The highly tunable parameters of optical lattices allow one to construct, and precisely manipulate them. This allows one to create conditions that cause atoms in lattices to exhibit the same behavior of electrons moving through solid state media. We present our early results of the atomtronic diode and bipolar junction transistor. Atomtronic systems could be integrated into quantum computing devices since they deal with the coherent transport of atoms and amplification of atomic signals. These atomtronic components also seem to build off of one another and it could be possible to get to the point where flip-flops and logic gates can be constructed. The reversible nature within atomtronic systems could lead to quantum logic gates as well.

## Rapid control and measurement of clock-state qubits in Yb and Sr

Nathan S. Babcock, University of Calgary

Abstract. Rapid control and measurement of clock-state qubits in Yb and Sr N. S. Babcock, R. Stock, B. C. Sanders Institute for Quantum Information Science, University of Calgary, Alberta The optical clock transitions in Yb and Sr are prime candidates for encoding qubits for quantum information processing. Electric dipole one- and two- photon transitions between 1S0 and 3P0 states are dipole and parity forbidden, respectively, resulting in extremely low decoherence rates for qubits stored using these states. To perform single-qubit operations, we propose a coherent, recoil-free, three-photon transition [1]. Single Yb or Sr atoms are stored in spatially-separated optical microtraps created by strongly focused laser beams. An entangling operation can be achieved via the collisional interaction between atoms as a pair of traps are brought together and separated adiabatically. Precise operation timing and symmetrization requirements ensure high gate fidelity. Qubit measurements are performed using fast readout of the 3P0 state via photo-ionization. The rapid control and measurement we describe are crucial for high-speed synchronization of atom-based quantum information mation processors. Furthermore, we explore the possibility of "loophole free" tests of Bell inequalities using spatially-separated entangled qubits.

[1] T. Hong, C. Cramer, W. Nagourney, E. N. Fortson, Phys. Rev. Lett. 94, 050801 (2005).

## Tunneling resonances and entanglement dynamics of cold bosons in a double well

Dimitri Dounas-Frazer, Colorado School of Mines

Abstract. We study the quantum sloshing of ultracold bosons in a tilted double-well potential via exact diagonalization of the two- mode Bose-Hubbard Hamiltonian. Tunneling is extremely sensitive to a small potential difference between wells, or tilt. However, when the barrier is high, atom-atom interactions can compensate the tilt and produce a unneling resonance [1, 2]. At resonance, tunneling times on the order of 10-100 ms are possible. Furthermore, tunneling resonances constitute a dynamic scheme for creating robust few-atom entangled states in the presence of many bosons.

[1] D. R. Dounas-Frazer and L. D. Carr, e-print: quant-ph/0610166 (2006).
[2] D. R. Dounas-Frazer, A. M. Hermundstad, and L. D. Carr, e-print: quant-ph/ 0609119 (2006).

## Quantum separability of correlated qutrits in noisy channels

Krzysztof Wodkiewicz, University of New Mexico

Abstract. We consider a generalized Werner state of two qutrits and investigate the separability condition in the presence of spontaneous emission noise. We choose three-level atoms in the V-configuration to be qutrit states. The separability condition is investigated using quantum quasi distribution functions on generalized 8-dimensional Bloch sphere. Noisy channels are described by Kraus operators constructed from Gell-Mann matrices. The influence of spontaneous emission on the separability of Werner states for qutrit and qubit states is compared.

## Geometric phases and Bloch sphere for two qubits

A.R.P.Rau, Louisiana State University

Abstract. A two-sphere ("Bloch" or "Poincare") is familiar for describing the dynamics of a spin-1/2 particle or light polarization. The relevant group of transformations for such a qubit is SU(2). This paper will present an analogous construction for higher groups SU(N) and, in particular, for SU(4) which describes a pair of qubits and thereby all possible logic gates of quantum computation. For many Hamiltonians of such two spin systems, a pair of Bloch two-spheres and a four-sphere provide the relevant generalization. The nature of the manifold for the completely general SU(4) case will also be discussed. This work has been done with D. Uskov and has been supported by the National Science Foundation.

## Multiply constrained bounds on measures of entanglement

Anil Shaji, The University of New Mexico

Abstract. We place bounds on non-operational measures of entanglement using multiple operational measures as constraints. Non-operational measures like the entanglement of formation, tangle and concurrence are physically significant, but they do not admit efficient procedures for computing because computing them involves finding optimal pure state decompositions for mixed states. On the other hand, there are operational measures of entanglement that can be computed relatively easily for arbitrary states. Bounding non- operational measures using a single operational measure as constraint has previously been done. We generalize this method to more than one constraint. We work out examples in which bounds are obtained for the entanglement of formation, tangle and concurrence of a family of states using the operational entanglement measures constructed from two positive, but not completely positive maps as constraints. The two maps are the partial transpose map and the $\\Ph i$-map introduced by Breuer [H-P. Breuer, e-print, quant-ph/0605036].

## A Bootstrapping Approach for Generating Maximally Path-Entangled Photon States

Kishor Kapale, Jet Propulsion Laboratory

Abstract. We propose a bootstrapping approach to generation of maximally path-entangled states of photons, so called NOON states, achievable within the current experimental technology. Strong atom-light interaction of cavity QED can be employed to generate NOON states with about 100 photons; which can then be used to boost the existing experimental Kerr nonlinearities based on quantum coherence effects to facilitate NOON generation with arbitrarily large number of photons. We also offer an alternative scheme that uses an atom-cavity dispersive interaction to obtain sufficiently high Kerr-nonlinearity necessary for arbitrary NOON generation.

## Quantum cellular automata and quantum simulation

Peter Love, Haverford College

Abstract. Quantum information theory can address ground state properties through DMRG-like classical methods, and through proposals for the use of phase estimation-based quantum algorithms. However, the dynamics of quantum systems present greater challenges to both classical and quantum computational methods. Quantum cellular automata provide a simple arena in which to address questions about quantum dynamics. Prior work has yielded decision procedures to determine when the local rule leads to globally unitary dynamics. I will describe a particular class of automata, unitary by construction, and discuss their relevance to the quantum computational complexity of quantum dynamics.

## Printed quantum circuits

Andrew Landahl, University of New Mexico

Abstract. I will describe a model of quantum computation in which gates are fabricated directly in a planar architecture without the need for classically controlled external pulses to initiate the gates. In this architecture, the data moves to the gates rather than the other way around as is true, e.g., with Cirac-Zoller type quantum computing architectures. This architectural construction proves that quantum walks on two-dimensional planar graphs are universal for quantum computation.