# 2008 Poster

## 1. Basing quantum theory on information-processing principles

Howard Barnum, Los Alamos National Laboratory

**Abstract**. The rise of quantum information science has been paralleled by the development of a vigorous research program aimed at obtaining an informational characterization or reconstruction of the quantum formalism, in a broad framework for stochastic theories that encompasses quantum and classical theory, but also a wide variety of other theories that can serve as foils to them. Such a reconstruction, at its most ambitious, is envisioned as playing a role in quantum physics similar to Einstein's reconstruction of the dynamics and kinetics of macroscopic bodies, and later of their gravitational interactions, on the basis of simple principles with clear operational meanings and experimental consequences. Short of such an ambitious goal, it could still lead to a principled understanding of the features of quantum mechanics that account for its greater-than-classical information-processing power, an understanding which could help guide the search for new quantum algorithms and protocols.

As part of this project, I give a precis of the convex operational framework for possible physical theories, and review work by me and my collaborators, on the information-processing properties of theories in this framework. The main results reviewed are the the fact that the only information that can be obtained in the framework without disturbance is inherently classical, no-cloning and no-broadcasting theorems in the generalized framework, the existence of exponentially secure bit commitment in non-classical theories without entanglement, and the consequences for theories of the existence of a conclusive teleportation scheme. I'll also discuss sufficient conditions for "remote steering" of ensembles using entanglement, rendering insecure bit commitment protocols of the form shown to be secure in the unentangled case.

Acknowledgements: Joint work with various groups of collaborators including Jonathan Barrett, Matthew Leifer, Alexander Wilce, Oscar Dahlsten, and Ben Toner.

## 2. Quantum communications with a partially coherent beam propagating through the atmosphere

Gennady Berman, Los Alamos National Laboratory

Collaborators: Gennady P. Berman, Boris M. Chernobrod, and Aleksandr A. Chumak (Los Alamos National Laboratory, Theoretical Division, Los Alamos, NM 87545)

**Abstract**. A new concept of a free-space, high-speed (Gbps) optical communication system based on spectral encoding of radiation from a broadband pulsed laser is developed. It is shown that, in combination with the use of partially coherent laser beams and a relatively slow photosensor, scintillations can be suppressed by orders of magnitude for distances of more than 10 km. The photon density operator function is used to describe the propagation of single-photon pulses through a turbulent atmosphere. The effects of statistical properties of photon source and the effects of a random phase screen on the variance of photon counting are studied. A procedure for reducing the total noise is discussed. The physical mechanisms responsible for this reduction are explained.

## 3. Quantum information experiments in a Penning ion trap

John Bollinger, National Institute of Standards and Technology

Collaborators: N. Shiga#, J. J. Bollinger, W. M. Itano NIST, 325 Broadway, Boulder, CO 80305

**Abstract**. A Penning trap uses static magnetic and electric fields to confine charged particles. With static confinement we can form large arrays of trapped ions. In particular we have formed 2-dimensional planar arrays of a few thousand ions and large 3-dimensional arrays of up to 10^{6} ions. In this poster we summarize progress on an initial quantum information experiment involving spin squeezing of a few hundred Be9 ion planar array. We use the ground-state electron spin-flip transition, which in the 4.5 T trap magnetic field has a 124 GHz transition frequency, as the ion qubit. We have realized projection noise limited spectroscopy on this transition, which is a prerequisite for demonstrating spin squeezing. For entangling the ions we plan to use a generalization of the few-ion qubit phase gate developed at NIST to generate an exp{(i\\chi {J_{z}}^2 t)} interaction between all of the ion qubits. Improvements in the frequency stabilization of our 124 GHz source have enabled spin echo coherence times as long as 2 ms. The spin echo coherence time limits the amount of time that can be used to apply the squeezing.

Acknowledgements: #Supported by a DOD MURI program administered by ONR under Grant N00014-05-1-0420.

## 4. Coherent control of resonant cavity length

Douglas Bradshaw, Los Alamos National Laboratory, University of New Mexico

**Abstract**. The effective length of an optical resonator filled with a dispersive medium is influenced by the group velocity of the resonating light. The associated effects on cavity properties become most interesting in connection with quantum-coherent manipulations that severely alter the resonating-light\'s group velocity while maintaining its transparency within the medium. We will discuss the implications of magnified, reduced, and negative cavity lengths as made possible through these types of group-velocity modifications.

## 5. Ion Traps for Scalable Quantum Information Processing

Joe Britton, National Institute of Standards and Technology

Collaborators: J. Britton, J. M. Amini, R. B. Blakestad, C. W. Chou, D. B. Hume, T. Rosenband, S. Seidelin (*), J. H. Wesenberg (**), J. J. Bollinger, K. R. Brown, R. J. Epstein(***), J. P. Home, W. M. Itano, J. D. Jost, C. Langer (****), D. Leibfried, C. Ospelkaus, N. Shiga, A. VanDevender, and D. J. Wineland

**Abstract**. Microfabricated traps for atomic ions are a promising technology for building a scalable quantum information processor. Toward this goal we are investigating several approaches to trap fabrication, characterization and transport in multi-zone structures.

We have expanded upon our single layer gold-on-fused-silica surface electrode trap to include a patterned conducting layer under the trapping electrodes and interlayer vias. The fabrication of this architecture was demonstrated using standard microfabrication techniques and testing is underway. We are also testing a 21-zone doped-silicon surface electrode trap with closest ion-surface separation of 13 microns. In a 18-zone two-layer gold-on-alumina trap we are making tests of ion transport thru an x-junction. Techniques for measuring and minimizing ion micromotion are also discussed.

Acknowledgements: Work supported by IARPA and NIST.

Time and Frequency Division, NIST, Boulder, Colorado 80305, USA

(*) University of Grenoble, France

(**) Oxford University, UK

(***) Arete Associates, Longmont, CO

(****) Lockheed Martin, Huntsville, AL

## 6. Transversality versus universality for subsystem stabilizer codes

Xie Chen, Massachusetts Institute of Technology

**Abstract**. Certain quantum codes allow logic operations to be performed on the encoded data, such that a multitude of errors introduced by faulty gates can be corrected. An important class of such operations are transversal, acting bitwise between corresponding qubits in each code block, thus allowing error propagation to be carefully limited. If any quantum operation could be implemented using a set of such gates, the set would be universal; codes with such a universal, transversal gate set have been widely desired for efficient fault-tolerant quantum computation.

We study the structure of subsystem stabilizer codes in d-dimensional Hilbert space (for d >= 2), and show that a universal set of transversal gates cannot be found for even one encoded qudit. We prove our results in two different ways, by using different kinds of subcodes of the stabilizer. Our results strongly support the idea that additional primitive operations, based for example on quantum teleportation, are necessary to achieve universal fault-tolerant computation on additive codes and may be the determining factor for fault tolerance noise thresholds. Furthermore, the proof techniques we employ give a recipe for understanding how and when gates other than standard Clifford operations can be transversal on stabilizer codes.

## 7. Lattice Ion Traps for Quantum Simulation

Rob Clark, Massachusetts Institute of Technology

**Abstract**. Two dimensional arrays of trapped ions show great promise for simulating dynamics of interacting spin systems that are intractable on classical computers. We propose a method for constructing such a lattice of ion traps that allows one to control the structure of the lattice, enabling the inclusion of defects, and leads to relatively straightforward fabrication. As a first demonstration of this method, we report stable confinement of ions in a 1 mm-scale lattice trap. Numerical models of the trap potentials are verified by measuring the motional frequencies of trapped strontium ions, and ion-ion repulsion between charged microspheres in neighboring lattice sites is observed. Scaling this interaction to atomic ions, we estimate that ion-ion repulsion should be observable for lattice spacings of about 150 microns. Finally, we discuss progress toward a microfabricated lattice trap in which interactions between atomic ions in different potential wells can be measured.

## 8. A quantum algorithm for finding the modal value

Mark Coffey, Colorado School of Mines

Collaborators: Mark W. Coffey and Zachary Prezkuta, Department of Physics, Colorado School of Mines, Golden, CO 80401

**Abstract**. We present a quantum algorithm for finding the most often occurring (or modal) value of a data set. We thereby supplement other algorithms that can determine the mean value or similar quantities. Our algorithm [1] requires the combined use of quantum counting and extended quantum search, and gives a quadratic speed up over the classical situation. For a data list of N elements, each entry an integer in the range [1,d], our method requires O(d N^{1/2}) oracle calls, and further complexity results are described.

[1] to appear in Quantum Information Processing.

Acknowledgements: This work was partially supported by Air Force contract number FA8750-06-1-0001.

## 9. Progress Toward a Cavity-QED Realization of the Dicke Model Quantum Phase Transition

Rob Cook, University of New Mexico

**Abstract**. We present progress towards a Cavity-QED realization of the quantum phase transition seen in the Dicke Model Hamiltonian for N>1 spins coupled to a single Bosonic field mode. The implementation is based upon cesium atoms held within a high finesse optical cavity. Cavity-mediated Raman transitions between magnetically detuned Zeeman sublevels provides near critical coupling between a collective pseudo-spin and a quantized cavity mode. Progress has been made in building the necessary infrastructure to collect a million atoms in an intracavity optical lattice, while still maintaining a background pressure of ~1E-10 torr. A tandem vacuum chamber provides a pressure difference of 3 orders of magnitude. A 2D-MOT will funnel atoms from a high pressure chamber into the lower pressure science cell. Current efforts are directed towards a home built tapered amplifier diode laser, to provide at least 500 mW of light for the 2-D MOT.

## 10. Ground States as Resources for Universal Measurement-Based Quantum Computing

Adam G. D'Souza, University of Calgary

**Abstract**. Measurement-based quantum computation (MBQC) requires a massively entangled resource state (such as a cluster state) as input. Experimental efforts towards generating such states have typically focused on performing global entangling operations on uncorrelated qubits. As the states that result from this type of procedure are not generally ground states, they are very sensitive to decoherence effects. A more robust resource would be one that is in fact a ground state of some Hamiltonian that exhibits a reasonably large energy gap between the ground state and the various excited states. We discuss the possibility of finding simple two-body Hamiltonians whose ground states are equivalent to resource states for MBQC under stochastic protocols comprised solely of local operations and classical communication.

## 11. On the repulsive Casimir force using metamaterials

Felipe Da Rosa, Los Alamos National Laboratory

Collaborators: Diego Dalvit (T-13) and Peter Milonni (T-13), Los Alamos National Laboratory

**Abstract**. It has been known for quite some time that Casimir repulsion between a dielectric and a magnetodielectric plate is possible, and the development of metamaterials brought this phenomenon closer to experimental possibilities. The purpose of this work is to discuss as realistically as possible the role that metamaterials play in the Casimir force and bring to the surface some aspects of this issue that were previously never or very little mentioned, such as the typical anisotropy of metamaterials and the presence of a Drude background in its electric permittivity. We also study the Casimir-Polder force between an atom and a metamaterial, since this may be relevant to future experiments.

## 12. Barium Ions for Quantum Computation

Matthew Dietrich, University of Washington

**Abstract**. We report progress on investigating 137Ba+ as a trapped ion qubit candidate. The hyperfine structure and visible spectrum cooling transitions of 137Ba+ make it an excellent qubit candidate. Here we report trapping 137Ba+ in a linear Paul trap. Cooling is provided by two diode lasers, one at 650 nm and the other at 493 nm is generated by a doubled infrared laser. To create the sidebands necessary for trapping this odd isotope, an EOM is applied to the blue light, while the red is modulated directly using a bias-T on the diode’s operating current. Shelving to the D5/2 state from the ground S1/2 state has been accomplished with a 1.76 micron fiber laser and during qubit readout direct adiabatic rapid transfer will shelve the state with high fidelity. The 1.76 micron fiber laser has been locked to a pressure and temperature stabilized high finesse zerodur cavity. Rabi flops between the ground hyperfine levels will be performed using microwave pulses whose waveforms can be shaped using a homebuilt pulse sequencer. A 400 fs pulsed Ti:sapphire laser is doubled in a single pass of BBO to 455 nm, and can be used for coherent population transfer and single photon production, as well as spectroscopic measurements, using the S1/2 to P3/2 transition.

## 13. Calibration for Slightly Unbalanced Homodyne Detection

Scott Glancy, National Institute of Standards and Technology, Boulder, Colorado

**Abstract**. Homodyne detection is a very useful tool for many modern experiments in quantum optics. In this technique the light mode to be measured interferes with a strong reference beam (called the "local oscillator") at a beam splitter. One then measures the difference between the number of photons arriving from the output ports of the beam splitter. This quantity is proportional to one of the quadratures of the signal mode. By varying the local oscillator phase, one can measure many quadratures and reconstruct the quantum state of the signal mode. Here we describe methods for calibrating a homodyne detector which allow us to compensate for problems such as electronic detector noise, a beam splitter reflectivity different from 1/2, and local oscillator intensity fluctuations.

## 14. Implementation Of Spin-Based Quantum Operations

Marilyn Hawley, Los Alamos National Laboratory

**Abstract**. The long-term quantum computer goal is to achieve a large scale, fast, parallel, and easily fabricated QC. Silicon-based solid-state proposals, using nuclear or electron spins of dopants such a phosphorus as qubits, are still attractive because of the long spin relaxation times, scalability, and integratability with existing silicon technology. Our approach is to use a simplified architectural scheme involving multiple aligned duplicate pairs of interacting P spins in silicon to directly address the issue of entangling the spins using NMR and ESR methods and utilizing a optical detection method to determine the states of the spins. The QC device consists of linear arrays of P atoms 35 nm apart that act as qubits entangled through weak exchange interactions. The multiple duplicate copies are spaced far enough apart to ensure that the spins in adjacent QCs do not interact. The duplicate QCs provide enough signal strength above the spectrometer signal-to-noise ratio. The P array created on the surface of a silicon wafer is encapsulated under an isotopically pure homoepitaxial layer to activate the dopant. An external magnetic field splits the degeneracy of spins and a field gradient allows individual spins to be addressed. The 7T external field, field gradient, mm waveguide, and RF coils are housed in a custom designed He3 cryostat equipped with an optical access for the laser beam and collection of the photons emitted during the exciton recombination. The key to controlling the nuclear spin states and interactions is to use the lone P electron spins to control the nuclear spin orientation via a combination of microwave and RF pulses. Excitons, generated in the substrate by a laser beam focused on the sample diffuse to the P sites and are used to probe the state of the spins.

## 15. Bose-Einstein Condensates in Time-Averaged Optical Dipole Potentials

Kevin Henderson, Los Alamos National Laboratory

**Abstract**. We are using Rb Bose-Einstein condensates in time-averaged optical dipole potentials to study atom interferometry and the dynamics of quantum phase transitions. The optical potential is generated by rastering a red-detuned (1064 nm, YAG) laser beam using dual acousto-optic modulators independently driven by RF arbitrary waveform generators. Axial confinement is provided by focusing the beam. We are studying the dynamics of a BEC optically trapped in these arbitrary potentials. We characterize the atom loss, heating rate, and coherence time for time-averaged optical dipole traps. We also study the robustness of manipulating multiple BECs in a variety of trapping geometries.

## 16. Progress towards distribution of entanglement in an ion trap array

Jonathan Home, National Institute of Standards and Technology

**Abstract**. Trapped atomic ions can provide a scalable architecture for large scale quantum information processing, with most of the fundamental building blocks having already been demonstrated. However, the ability to entangle, distribute, and perform subsequent entangling operations on multiple atomic ions has only been demonstrated to a limited extent. We report on progress towards distributing entangled atomic ions in an ion trap array and re-establishing a well defined motional state after distribution. Performing multiple high fidelity multi-ion quantum logic gates requires their collective modes of motion to be well initialized. Moving and separating the qubits can lead to excitation of the motion that needs to be removed before subsequent gate operations. In addition, ambient electric field noise will also contribute to the heating. Using two species ion crystals (24Mg+ and 9Be+) allows for one species to act as a sympathetic cooling ion and one to act as a logical ion qubit. We report on experiments using mixed crystals of 24Mg+ and 9Be+ ions in a multi-zone trap.

## 17. Upper Bounds on the Fault-tolerance Threshold

Mark Howard, University of California, Santa Barbara.

**Abstract**. An important question in quantum computing is how much noise can be tolerated by a universal gate set before quantum-computational power is lost. Motivated by the result of Bravyi and Kitaev (Phys. Rev. A 71, 022316), there have been a number of recent papers which provide such bounds, within the framework of a model which presumes perfect Clifford operations. The ability to perform UQC is provided by the addition of a gate from outside the Clifford group. Here we show that gates which have non-zero off-diagonal elements can tolerate dephasing noise of any strength, and provide an explicit distillation algorithm to create a "magic state" which enables universal quantum computation. We also provide threshold expressions for arbitrary unitary gates undergoing depolarizing noise, dephasing noise or both.

## 18. The Optimal Control Landscape for the Generation of Unitary Transformations

Michael Hsieh, Princeton University

**Abstract**. The generation of specific unitary transformations is central to a variety of quantum control problems. Given a target unitary transformation, the optimal control landscape is defined as the Hilbert-Schmidt distance between the target and controlled unitary transformation as a function of the control variables. The critical topology of the landscape is analyzed for controllable quantum systems evolving under unitary dynamics over a finite dimensional Hilbert space. It is found that the critical regions of the landscape corresponding to global optima are isolated points, and the local optima are Grassmannian submanifolds. The volumes of the critical submanifolds corresponding to sub-optimal critical values asymptotically vanish in the limit of large Hilbert space dimension. Furthermore, these critical submanifolds have saddlepoint topology, which cannot act as traps when searching for optimal controls. These favorable properties of the local optima suggest that the landscape topology is generally amenable to optimization. The analysis is independent of the particular structure of the system Hamiltonian, except for the assumption of full controllability, and results are universal to the control of unitary transformations of any quantum system.

## 19. Progress Towards Microwave Controlled Collisions of Cs Atoms in an Optical Lattice

Jae hoon Lee, University of Arizona

Collaborators: Worawarong Rakreungdet, Jae Hoon Lee, Enrique Montano, and Poul Jessen (College of Optical Sciences, University of Arizona, Tucson, AZ)

Brian Mischuck and Ivan Deutsch (Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM)

**Abstract**. Quantum information processing with Cesium atoms in an optical lattice requires successful implementation of both single- and two-qubit quantum gates. Accurate single-qubit control can be achieved with simple or composite microwave pulses, whereas two-qubit logic requires pairwise atom-atom interactions that can be implemented for example via controlled atomic collisions. We are currently working on a proof-of-principle experiment wherein we have developed the ability to drive well-resolved microwave transitions of atomic qubits between spatially separated lattice potential wells associated with different logical basis (spin) states. In the case of Cs, collisional interactions are sufficiently strong that the microwave excitation of one atom from a spin-down to a spin-up well can be significantly affected by the presence of a second atom in a neighboring well of the spin-down lattice. For appropriate lattice parameters a spin-up/down pair will occupy a long range molecular state whose energy can be shifted by a large amount relative to isolated, non-interacting atoms. As a first step we are attempting to observe distinct lines in the microwave spectrum corresponding to excitation of this molecular state. In principle, selective microwave excitation of the molecular transition can then be used as the basis for a controlled-phase interaction and the implementation of a two-qubit quantum gate.

## 20. Novel two-qubit gates for trapped ions

Dietrich Leibfried, National Institute of Standards and Technology, Boulder

Collaborators: C. Ospelkaus, D. Leibfried, E. Knill, J. Amini, R. B. Blakestad, , J. Britton, K.R. Brown, J.P. Home, J.D. Jost, C. R. Langer #, A. VanDevender, J. Wesenberg+ and D.J. Wineland

**Abstract**. Atomic ions confined in an array of interconnected traps represent a potentially scalable approach to quantum information processing. The primary task is to scale the system to many qubits while minimizing and correcting errors in the system. In this context, it is desirable to minimize the overhead of laser-beam control in large scale implementations.

It will also be necessary to precisely control the transport of ions in large trap arrays. This ability can be utilized to implement one and two-qubit gates with only global control of the light fields and minimal control of the temporal pulse shape of the fields [1]. Going one step further, the small distance scales involved in microfabricated ion traps could enable the tailoring of local magnetic fields and their gradients to directly drive one- and two-qubit gates between hyperfine ground states, thereby completely avoiding laser fields and their inherent decoherence mechanisms due to spontaneous emission.

[1] D. Leibfried, E. Knill, C. Ospelkaus, and D. J. Wineland, Phys. Rev. A 76, 032324 (2007).

Acknowledgements: *Supported by IARPA and NIST.

+ Current address: Oxford University, UK;

# Current address: Lockheed Martin, Huntsville, AL, USA

## 21. High-Efficiency Tungsten Transition-Edge Sensors in the Near-Infrared

Adriana Lita, National Institute of Standards and Technology

Collaborators: A. E. Lita [1], A. J. Miller [2], S. Nam [1]

**Abstract**. Single-photon detectors operating at visible and near-infrared wavelengths with high detection efficiency and low noise are a requirement for many quantum-information applications. Detection of visible and near-infrared light at the single-photon level and discrimination between one- and two-photon absorption events place stringent requirements on TES design in terms of heat capacity, thermometry, and optical detection efficiency. We report on the demonstration of fiber-coupled, photon number resolving transition edge sensors with 95% system efficiency at 1550 nm.

Acknowledgements: [1] Optoelectronics Division, NIST, Boulder CO, USA [2] Physics Department, Albion College, MI, USA

## 22. On the accuracy of 2-RDM methods for finding ground state energies

Yi-Kai Liu, California Institute of Technology

**Abstract**. One way of computing molecular ground state energies in quantum chemistry is to find the 2-electron reduced density matrix (2-RDM), for instance by variational minimization subject to so-called N-representability conditions. N-representability is a QMA-hard problem, but in practice, simple constraints on the 2-RDM, known as p-positivity conditions, often give surprisingly accurate results. We show that, if the Hamiltonian is band-diagonal (with respect to the basis set of single-electron orbitals), then the p-positivity method gives a constant-factor approximation to the ground state energy in polynomial time.

## 23. Trapped-Ion Quantum Simulations of Spin Systems: From Two Qubits to Thousands

Warren Lybarger, Los Alamos National Laboratory

**Abstract**. Due to the exponential growth of a quantum system\'s state-space with its size, the current technological limit for simulating the evolution of many-quantum-spin systems with classical computers (CC) is 36 spin-$\\frac{1}{2}$ particles. While CC\'s cannot be scaled to meet the exponentially increased demand in computational resources, mapping the Hamiltonians of such problems onto that of a quantum simulator (QS) completely avoids this exponential scaling problem, allowing for efficient simulations of much larger systems. QS may be the first attainable application of quantum information processing, enabling exploration of parts of the phase space not accessible in the original system and possibly providing an exponential speedup of computations for even just a few tens of interacting qubits when compared to CC methods. Following the work of Porras and Cirac [Phys. Rev. Lett. 92, 207901-1 (2004)] we discuss the status of an experiment at Los Alamos for demonstrating a proof of principle QS of an Ising-like spin-spin interaction in a transverse magnetic field. We also discuss a novel architecture for microfabricated ion trap arrays geared toward enabling large scale QS and one-way quantum computing with potentially thousands of ions [arXiv:0711.0233].

## 24. Ion Trap for efficient single Photon-Atom Coupling

Robert Maiwald, National Institute of Standards and Technology

**Abstract**. Excitation of a single atom by a single photon is a fundamental process of physics, yet fairly inefficient in today\'s realizations. We present the design of a compact ion trap with superior optical access compared to conventional designs that allows for the localization of an ion in the focal point of a deep parabolic mirror. The electrode geometry results in a trapping potential that follows the axial symmetry of the mirror and provides optical access to the ion from almost the entire solid angle. The latter property is essential for efficient coupling of single ions to single photons in free space. The trap design can be adapted for other applications by replacing the mirror by a planar electrode. Using this more general design the ion can still be optically accessed from at least half to over 90% of the solid angle. The generation of a suitable mode-matched, dipole-like excitation pattern is discussed as well. Applications of an efficient light-matter coupling scheme include decoherence studies, quantum repeaters and quantum memories.

## 25. Efficient Generation of Large Number-Path Entanglement Using Spontaneous Parametric Down-Conversion

Kevin McCusker, University of Illinois at Urbana-Champaign

**Abstract**. We show how a large number-path entangled state (commonly called a N00N state) can be efficiently created using heralded spontaneous parametric down-conversion. The basic procedure is to use a pulsed source incident on a nonlinear crystal to create pairs of linearly polarized photons. One of these photons is detected, and the other is emitted into a polarization insensitive cavity. When the trigger photon is detected, all of the photons in the cavity are rotated by N/180 degrees. After N pairs are created, what remains in the cavity is a N00N state in the left/right polarization basis. This scheme can offer an exponential speed up over methods of creating N00N states using linear optics. We calculate the theoretical performance as a function of the transmission of the cavity, and discuss several other factors limiting overall efficiency.

## 26. A Clifford simulator for modeling fault-tolerance

Adam Meier, National Institute of Standards and Technology

Collaborators: K. Costello, B. Eastin, S. Glancy and E. Knill.

**Abstract**. A classical computer is capable of efficiently simulating certain subsets of quantum processes. One such subset, according to the Gottesman-Knill theorem, consists of logical qudit preparation, application of Clifford gates, and measurement in the logical basis which together comprise so-called Clifford circuits. We are writing a Clifford (circuit) simulator with the dual aims of providing a test bed for quantum fault-tolerance techniques and overseeing experimental quantum error-correction. In addition to being asymptotically faster than previous Clifford simulators in many cases of interest, our simulator is being designed to work with qudits of arbitrary size and, eventually, with non-stochastic error models. We present aspects of the design as well as some speed profiles and possible uses for the simulator.

## 27. Quantum Nondemolition Detection of Photons through an Enhanced Cross-Kerr Interaction

Kevin Mertes, Los Alamos National Laboratory

**Abstract**. We describe an experiment currently underway at Los Alamos National Laboratory that aims to demonstrate the quantum nondemolition (QND) measurement of single to several photons through the cross-phase modulation inherent in the giant Kerr nonlinearity theoretically predicted by Schmidt and Imamoglu. Our experiment will overlap three laser beams -- a signal, a probe, and a drive -- within an atomic vapor. The signal beam contains the one to several photons to be nondestructively counted. In the cross-Kerrr interaction, photons within the signal beam impress a phase shift on the probe beam that is proportional to the photon number. The drive beam mediates the interaction in a way that both augments the interaction cross section and minimizes the probe- and signal-beam absorption. To our knowledge, our experimental work will represent the first QND measurement of one to several photons by without recourse to a cavity.

## 28. Probing Atomic Interactions of Cs in an Optical Lattice for Quantum Information

Brian Mischuck, University of New Mexico

Collaborators: Brian Mischuck, Ivan Deutsch, Worawarong ("O") Rakreungdet,Jae Hoon Lee,Enrique Montano and Poul Jessen

**Abstract**. We study a method to probe the spectrum of interacting Cs atoms in an optical lattice. Transport of the atoms to overlapping wells is achieved through a microwave drive between hyperfine levels in a lin-perp-lin polarization-gradient lattice. The spectral response of pairs of atoms to microwaves can be used to measure the effect of the interactions, even in the presence of a large background of unpaired atoms. Control of such interactions may have applications in quantum information processing such as quantum walks on a lattice and quantum simulations of many-body Hamiltonians.

## 29. Progress Toward Atomic Magnetometry Beyond the Conventional Heisenberg Scaling

Heather Partner, University of New Mexico

Collaborators: Heather L. Partner, Brigette D. Black and JM Geremia (Department of Physics and Astronomy, The University of New Mexico, Albuquerque, New Mexico 87131 USA)

**Abstract**. We describe an atomic magnetometer whose field estimation uncertainty is expected to decrease faster than the conventional Heisenberg (1/N) scaling with the number of atoms in the atomic sample. Our procedure makes use of the effective two-body atomic interactions obtained by double-passing an off-resonant probe laser through the atomic sample during atomic Larmor precession. Performing balanced polarimetry on the transmitted probe field provides a continuous measurement signal that can be used to estimate the value of the magnetic field. We report on numerical simulations of our proposed quantum parameter estimation procedure and describe our ongoing efforts to implement our proposal using room-temperature Cs atoms.

## 30. Enhancing performance of a single-photon source with continuous monitoring

Shesha Raghunathan, University of Southern California

**Abstract**. In this work we numerically show that the performance of a single-photon source can be enhanced with continuous monitoring. We analyse a two-level atom ($2LA$) and a three-level atom ($3LA$) whose first excited state is resonantly coupled to the cavity mode of the atom $+$ cavity system. We continuously monitor the excited state/s of the atom and use stochastic master equation (SME) to evolve the system. Integrating the output "current" obtained due to continuous monitoring of the atom, we generate an estimate of $when$ the atom relaxed to its ground state. Since the output ``current\'\' due to monitoring is inherently noisy, we use a well known signal processing technique called affine mean-squared error estimation (AMSEE) to better estimate $when$ the atom relaxed to its ground state. In the parameter regime that we consider in this work, the information regarding $when$ the atom relaxed to its ground state closely follows $when$ a photon leaks out of the cavity. This estimate is thus used to control variable delay at the output of a single-photon source to reduce time-uncertainity of photons leaking out of the cavity, enhancing performance of a single-photon source.

## 31. Photoassociation of alkaline earths

Iris Reichenbach, University of New Mexico

**Abstract**. Photoassociation on the very narrow clock transitions of alkaline-earth like elements, 1S->3P, allows both the accurate examination of molecular state at large separation, and the manipulation of scattering properties via optical Feshbach resonances. The latter could be used to tailor the scattering properties between different atoms to vastly simplify the construction of quantum gates. We calculate the long-range molecular potentials of alkaline-earth-like elements for photoassociation on the narrow intercombination line, for the first time including hyperfine interactions and the effects of magnetic fields. We investigate the existence of purely long-range bound states, caused by anticrossings induced by the hyperfine interaction.

## 32. Continuous Measurement Quantum State Reconstruction in an Almost Decoherence-Free Protocol

Carlos Riofrio, University of New Mexico

**Abstract**. Quantum state reconstruction techniques based on weak continuous measurement have the advantage of being fast, accurate, and almost non-perturbative. Moreover, they have been successfully implemented in experiments on large spin systems (PRL 97, 180403 (2006)). The performance of these techniques is generally limited by decoherence, however, as controlling optical fields lead to spontaneous emission. In this poster, an application of the reconstruction algorithm developed by Silberfarb et al. (PRL 95, 030402 (2005)) is presented for the reconstruction of quantum states stored in the ground-electronic hyperfine manifolds (F=3, F=4) of an ensemble of 133Cs atoms controlled by microwaves and radio-frequency magnetic fields. This system is advantageous in the sense that its evolution only depends on the dynamics of the ground state, giving as a result an almost decoherence-free protocol.

## 33. Open-Access Micro Optical Cavities on Atom Chips

Peter Schwindt, Sandia National Laboratories

**Abstract**. We are developing high-finesse, open-access optical cavities to achieve strong atom-photon coupling in small mode volume cavities. Such devices are essential for quantum computers and networks based on neutral atoms as the qubits. One mirror of the optical cavity is formed by a hemispherical void etched into a Si wafer and the other mirror is the coated tip of an optical fiber. In this way, the optical axis is normal to the plane of the atom chip. In parallel, we are fabricating high quality atom chips using Al conductors in multilayer structures to form magnetic traps and guides for neutral atoms. We are working to integrate the optical cavity and Al conductor processes to form an integrated atom chip. We will present details on the design, fabrication, and characterization of the conductors and optical cavities and on our efforts to develop an experiment to test our atom chips with cold atoms.

## 34. PT-Symmetric Quantum Evolution and Logic

Torey Semi, Colorado School of Mines

Collaborators: Mark W. Coffey, Torey Semi (Department of Physics, Colorado School of Mines, Golden, Colorado)

**Abstract**. There has been much recent interest in PT-symmetric quantum mechanics (QM) as an alternative formulation of quantum theory. We investigate the potential of this formulation for quantum computation and simulation.

PT-symmetric QM replaces the usual postulate that a system’s Hamiltonian must be Hermitian. It argues instead that the Hamiltonian can be symmetric with respect to combined parity and time-reversal and, for certain parametric regions, still produce real eigenvalues and maintain unitary time evolution. Besides being of fundamental interest, this approach allows for a fresh perspective on many QM applications.

It is known that for one-qubit PT-symmetric systems the evolution time from an initial state to a final state can be made arbitrarily small. We report on applying PT-symmetric Hamiltonians for two-qubit systems to quantum logic.

## 35. Optimal Measurements for Quantum Control in the Regime of Strong Feedback

Alireza Shabani, University of Southern California

**Abstract**. We consider the feedback control of an arbitrary (N-dimensional) quantum system, in the regimes of good control and strong feedback. Under the minimal constraints that the strength of the measurement is limited, we obtain the measurement strategy that achieves locally optimal control. That is we obtain the measurement that optimizes the control objective for each infinitesimal time-step. This measurement is partially, but not fully, unbiased with respect to the system state. We compare the performance of the resulting feedback algorithm to more pedestrian algorithms in which the measurement is fixed during feedback.

## 36. Kinetics of Quasiparticle Tunneling in a Pair of Superconducting Charge Qubits

Matthew Shaw, University of Southern California / NASA Jet Propulsion Lab

**Abstract**. We directly observe the statistics of non-equilibrium quasiparticle tunneling in a pair of charge qubits based on the single Cooper-pair box. Incoherent tunneling processes are a significant problem in single-charge devices, which must be engineered away for applications in quantum computing. We measure the odd-to-even and even-to-odd transition rates as a function of temperature, and interpret these results using a kinetic theory. At short times and low temperatures, the odd-to-even transitions are found to deviate from a simple Poisson process, in accordance with the theory. Furthermore, at low temperatures the odd-to-even transition rate is found to decrease with temperature, implying that the low-temperature quasiparticles are out of thermal as well as chemical equilibrium.

## 37. Using Quantum Control to Measure and Null Background Magnetic Fields in Cold Atom Experiments

Aaron Smith, University of Arizona

**Abstract**. Quantum control of atomic spins requires precise control of the total magnetic field acting on the spins. This makes accurate nulling of the (generally time dependent) background magnetic field one of the most important limiting factors of a real-world control experiment. We have devised a convenient method to use the atoms themselves as an in situ probe, combining spin-echo techniques and polarization spectroscopy to generate a highly sensitive signature of a desired component of the field. This allows us to quickly measure three orthogonal components of the total field with a resolution of a few tens of µG in a bandwidth of ~1kHz, and to apply the inverse of the measured field with three sets of Helmholz coils driven by arbitrary waveform generators. The resulting background field is typically less than ~50µG, an overall reduction of about one order of magnitude compared to the uncompensated AC field in our laboratory.

## 38. Hitting time for the continuous quantum walk

Martin Varbanov, University of Southern California

**Abstract**. The hitting (stopping) time for the case of continuous quantum walks is defined. The walk is measured randomly according to a Poisson process with a fixed measurement rate. This allows us to derive an explicit formula for the hitting time and explore its depends on the measurement rate. In the two limits of the measurement rate going to 0 or infinity the hitting time diverges, where the second limit is representative of the quantum Zeno effect. Several conditions for existence of infinite hitting times are explored

## 39. Quantum Computer Simulations of Time Dependent Hamiltonians

Nathan Wiebe, University Of Calgary

**Abstract**. In 1982, Feynman suggested a quantum computer would efficiently simulate quantum systems and illustrated this concept with Heisenberg chains (Int. J. Theor. Phys, 21, 467), which are difficult to solve on a classical computer. Since then a number of sophisticated quantum simulation schemes have been created to simulate time independent Hamiltonians, but to date only simplistic simulation schemes have been proposed for simulating time dependent Hamiltonians.

In this talk I will present a sophisticated quantum algorithm that can simulate the evolution of a sufficiently smooth and sparse time dependent Hamiltonian, which uses a number of gate operations that is comparable to the best known simulation schemes for time independent Hamiltonians. Applications of this algorithm to simulating Hamiltonian based quantum computing schemes in the circuit model (such as adiabatic quantum computing) will also be discussed.

## 40. Quantifying nonlocality in states and experiments

Yanbao Zhang, University of Colorado-Boulder

Collaborators: E. Knill, K. Coakley and S. Glancy.

**Abstract**. We consider the use of statistics to quantify experimental evidence against local realism. We base the quantification on measures related to the Kullback-Leibler (KL) divergence, as suggested by W. van Dam, P. Grunwald and R. Gill [arXiv:quant-ph/0307125]. Optimal measurement settings and states can be obtained by maximizing the KL divergence of the experimental statistics predicted by quantum mechanics from the best local realistic model. We performed the maximization for the CHSH and GHZ tests and found results consistent with the results of W. van Dam, P. Grunwald and R.Gill. The advantage of statistical quantifications of non-locality is that they can be applied to the case of any number of parties, measurement settings and measurement outcomes, in which case useful Bell-type inequalities are hard to find.