# 2013 Poster Abstracts

## 1. Ultrafast Quantum Process Tomography via Continuous Measurement and Convex Optimization

Charles Baldwin, University of New Mexico

*Abstract.* Quantum process tomography (QPT) is an essential tool to diagnose the implementation of a dynamical map. However, the standard protocol is extremely resource intensive. For a Hilbert space of dimension d, it requires d^2 different input preparations followed by state tomography via the estimation of the expectation values of d^2-1 orthogonal observables. We show that when the process is nearly unitary, we can dramatically improve the efficiency and robustness of QPT through a collective continuous measurement protocol on an ensemble of identically prepared systems. Given the measurement history we obtain the process matrix via a convex program that optimizes a desired cost function. We study two estimators: least-squares and compressive sensing. Both allow rapid QPT due to the condition of complete positivity of the map; this is a powerful constraint to force the process to be physical and consistent with the data. We apply the method to a real experimental implementation, where optimal control is used to perform a unitary map on a d=8 dimensional system of hyperfine levels in cesium atoms, and obtain the measurement record via Faraday spectroscopy of a laser probe.

## 2. Using postselection to control ground state quantum beats in Cavity QED

Pablo Barberis-Blostein, Universidad Nacional Autonoma de Mexico

*Abstract.* Pablo Barberis-Blostein (Universidad Nacional Autonoma de Mexico) Howard Carmichael (University of Auckland) Luis Orozco (University of Maryland) Andres Cimmarusti (University of Maryland) Ground state quantum beats observed in the second order intensity correlation from a continuously driven atomic ensemble inside a two mode optical cavity are subject to a frequency shift and decoherence. While driving the cavity with light of linear polarization ($\pi$ transitions) the second order autocorrelation function is measured in the undriven mode (orthogonal polarization): a first photon detection prepares a superposition of atomic ground-state Zeeman sublevels and the second measures the ground state beats. Between these two detections, the atoms can become excited and return to the ground state, emitting most of the photons into modes other than the cavity modes. Depending on the drive strength this process can happen several times. Each time there is a relative phase advance between the Zeeman sublevels. The information of this phase advance and its associated decoherence is then leaked into the modes that are not the cavity modes, which form the environment. It is possible to get information about the number of photons leaked into the environment by monitoring the driven mode. Here we propose a scheme to manipulate the loss of amplitude of the beats (decoherence) and the beat frequency shift, by postselecting on the basis of information gathered through measurement of the driven cavity mode. This proposal is a new strategy compared with controlling the decoherence and light shift through turning off the driven field. Work supported by CONACYT, NSF and the Marsden Fund of the RSNZ.

## 3. Oscillator-Field Model of Optomechanics

Ryan Behunin, Los Alamos National Laboratory

*Abstract.* We present a microphysics model for the kinematics and dynamics of optomechanics describing the coupling between an optical field, modeled here by a massless scalar field, with the internal and mechanical degrees of freedom of a moveable mirror. Instead of implementing boundary conditions on the field we introduce an internal degree of freedom and its dynamics to describe the mirror's reflectivity. Depending on parameter values, the internal degrees of freedom of the mirror in this model captures a range of its optical activities, from those exhibiting broadband reflective properties to those reflecting only in a narrow band. After establishing the model we show how appropriate parameter choices lead to other well-known optomechanical models including those of Barton & Calogeracos [1], Law [2] and Golestanian & Kardar [3]. As a simple illustrative application we derive classical radiation pressure cooling from this model. Our microphysics model can be connected to the common descriptions of a moving mirror coupled to radiation pressure (e.g., with Nx coupling, where N is the photon number and ),x is the mirror displacement) making explicit the underlying assumptions made in these phenomenological models. Our model is also applicable to the lesser explored case of small N, which existing models based on side-band approximations [4] cannot cope with. Interestingly, we also find that slow moving mirrors in our model can be described by the ubiquitous Brownian motion model of quantum open systems. The scope of applications of this model ranges from a full quantum mechanical treatment of radiation pressure cooling and quantum entanglement between macroscopic mirrors to the backreaction of Hawking radiation on black hole evaporation in a moving mirror analog. [1] G. Barton and A. Calogeracos, Ann. Phys. 238, 227 (1995). A. Calogeracos and G. Barton, Ann. Phys. 238, 268 (1995). [2] C. K. Law, Phys. Rev. A 51, 2537 (1995). [3] R. Golestanian and M. Kardar, Phys. Rev. Lett. 78, 3421 (1997); Phys. Rev. A 58, 1713 (1998) [4] H. J. Kimble, Yuri Levin, Andrey B. Matsko, Kip S. Thorne, and Sergey P. Vyatchanin, Phys. Rev. D 65, 022002 (2001)

## 4. Cavity integrated surface ion trap for enhanced light collection

Francisco Benito, Sandia National Laboratories - University of New Mexico

*Abstract.*

# Cavity integrated surface ion trap for enhanced light collection

**Francisco Benito**, Matthew Blain, Chin-wen Chou, Craig Clark, Mike Descour, Ray Haltli, Edwin Heller, Jon Sterk, Boyan Tabakov, Chris Tigges, Peter Maunz, Daniel Stick Sandia National Laboratories Center for Quantum Information and Control, University of New Mexico, MSC 07-4220, Albuquerque, NM 87131-0001

The scalable distribution of coherent information in a quantum network is a prerequisite for the creation of a quantum repeater for secure long-distance communication and a large scale quantum information processor. Ion trap systems allow the faithful storage and manipulation of qubits encoded in the energy levels of trapped ions, which can be interfaced with photonic qubits that can be easily transmitted to connect remote quantum systems. Single photons transmitted from two remote sites, each entangled with one quantum memory, can be used to generate entanglement between the two distant quantum memories [1]. In order to make this photon mediated entanglement efficient a strong interaction between atomic and photonic qubits is necessary. This can be realized by integrating an ion trap with an optical cavity and employing the Purcell effect for enhancing the light collection.

We present progress towards integrating a 1 mm optical cavity with a micro-fabricated surface ion trap. The plano-concave cavity is oriented normal to the chip surface where the planar mirror is attached underneath the trap chip. The linear ion trap allows ions to be shuttled in and out of the cavity mode. The Purcell enhancement of spontaneous emission into the cavity mode will allow us to collect up to 12% of the emitted photons, enabling remote entanglement generation much faster than the qubit coherence time.

Moehring, D. L., Maunz, P., Olmschenk, S., Younge, K. C., Matsukevich, D. N., Duan, L. M., & Monroe, C. (2007). Entanglement of single-atom quantum bits at a distance. *Nature*, *449*(7158), 68-71.

This work was supported by Sandia's Laboratory Directed Research and Development (LDRD) and the Intelligence Advanced Research Projects Activity (IARPA). Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the US Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

## 5. Reliable transport through a microfabricated X-junction surface-electrode ion trap*

Kenton Brown, Georgia Tech Research Institute

*Abstract.* At the heart of most ion-based quantum information processing and simulation efforts is an RF-Paul trap to confine the ion qubits. There is increasing need for complex trapping geometries that can hold larger numbers of ions beyond single linear chains. As part of GTRI's ongoing trap development effort, we have demonstrated reliable, uncooled transport of ions through a surface electrode X-junction. Through careful modeling of the junction potentials, including modeling of non-ideal effects seen during trap characterization, we reduced the transport heating sufficiently to allow for more than 60 round trip transports of an ion through the junction without cooling. These results open up the possibility of ion swapping and transport through multi-junction arrays without continual ion cooling. In addition to presenting these results, we will describe GTRI's next generation junction design that addresses confinement and control limitations observed in the first generation junction. Combined with a novel transport and storage structure, the new junction trap should be able to hold dozens of ions in separate wells and combine them as needed for gate operations. This material is based upon work supported by the Georgia Tech Research Institute and the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA) under U.S. Army Research Office (ARO) contract W911NF081-0315.

## 6. Reflective Parabolic Ion Trap for Efficient Ion Photon Collection

Chen-Kuan Chou, University of Washington

*Abstract.* Single trapped ion qubit is an excellent candidate for quantum computation and information due to its low decoherence, ease of control and detection, and ability to couple to a photon, the flying qubit. Efficiently coupling ion fluorescence into a single-mode fiber is the most challenging part in remote entangled ion qubit state generation. To address this issue, we developed an ion trap combining a reflective parabolic surface with trap electrodes. This parabolic trap design covers a solid angle close to 2 Pi, and allows precise ion placement at the focal point of the parabola. We measured approximately 39% fluorescence collection with this mirror. With the advantage of producing a collimated photon beam, we expect to couple the ion fluorescence into a single-mode fiber in a straightforward way. The improved collection efficiency will make the loophole-free Bell inequality test possible with two remotely entangled ions approximately 1 km apart.

## 7. Towards a robust cavity QED apparatus for control of quantum beats.

Andres Cimmarusti, Joint Quantum Institute

*Abstract.*

Andres D. Cimmarusti^{1}, Burkley D. Patterson^{1}, Wanderson M. Pimenta^{1,2}, Luis A. Orozco^{1}

^{1}Joint Quantum Institute, University of Maryland and National Institute of Standards and Technology, College Park, MD, USA^{2}Universidade Federal de Minas Gerais, Belo Horizonte, MG, Brazil

We present our new cavity QED apparatus for control of ground state quantum beats in Rb. We obtain our continuous cold atomic beam from a steerable, high flux Low Velocity Intense Source (LVIS) of Rb [1]. The atoms travel perpendicularly to the axis of the cavity and couple to its TEM_{00} mode. Our Fabry-Perot cavity has improved finesse for the same atom-field coupling strength. We have a dual isotope setup to handle ^{85}Rb and ^{87}Rb. Our detection system relies on the separation between the two polarization modes of the cavity. The Birefringence due to the vacuum chamber windows and the mirrors of the cavity is challenging, but we use low stress-optic coefficient windows to mitigate it. The preparation of the coherences that generate the quantum beats requires careful control of the magnetic field. For this purpose, we implement *in vacuo* three-axis magnetometry. RF/Microwave antennas allow the possibility to excite the coherences with low frequency electromagnetic fields. These hardware improvements will yield a more robust and versatile experimental apparatus to continue exploring light matter interaction in cavity QED.

Work supported by NSF from USA and FAPEMIG from Brazil

[1] Z. T. Lu, K. L. Corwin, M. J. Renn, M. H. Anderson, E. A. Cornell, and C. E. Wieman, Phys. Rev. Lett. 77, 3331 (1996).

## 8. Fast and strong feedback for control of quantum beats in a cavity QED system.

Andres Cimmarusti, Joint Quantum Institute

*Abstract.*

Andres D. Cimmarusti^{1}, Burkley D. Patterson^{1}, Christopher A. Schroeder^{1}, Wanderson M. Pimenta^{1,2}, Luis A. Orozco^{1}, Pablo Barberis-Blostein^{3} and Howard J. Carmichael^{4}

^{1}Joint Quantum Institute, University of Maryland and National Institute of Standards and Technology, College Park, MD, USA^{2}Universidade Federal de Minas Gerais, Belo Horizonte, MG, Brazil^{3}Unversidad Nacional Autonoma de Mexico, Mexico, DF, Mexico ^{4}University of Auckland, Auckland, New Zealand

Second order correlations studies reveal the generation of quantum beats from a coherent ground-state superposition created by conditional measurements on the undriven mode of a two-mode cavity QED system. Continuous drive of the system induces amplitude decoherence and frequency shifts in the beats due to the intrinsic phase diffusion process as a consequence of successive interruptions from Rayleigh scattering. Our results show we can stop this decoherence process and prevent phase shifts on the Larmor precesion, by implementing a fast and strong feedback protocol: The detection of a phtoton triggers a switch to turn down or off the drive, the systen then evolves in the dark for a pre-set time until the drive returns. The revived quantum beat shows phase accumulation only from Larmor precession and can exhibit an amplitude scaling of more than a factor of two with respect to continuous drive.

Work supported by NSF, USA; CONACYT, Mexico; The Marsden Fund of the Royal Society of New Zealand; and FAPEMIG of Brazil.

## 9. Characterization of novel surface ion trap structures for quantum information processing

Craig Clark, Sandia National Laboratory

*Abstract.* Craig Clark, Matthew Blain, Francisco Benito, Chin-wen Chou, Mike Descour, Rob Ellis, Ray Haltli, Edwin Heller, Shanalyn Kemme, Jon Sterk, Boyan Tabakov, Chris Tigges, Peter Maunz, Daniel Stick Sandia National Laboratories Center for Quantum Information and Control, University of New Mexico, MSC 07-4220, Albuquerque, NM 87131-0001 Segmented surface electrode ion traps are one of the most mature platforms among candidates for scalable quantum information processing. At Sandia National Laboratories we design, fabricate, and test such traps. Here we describe our characterization of a linear trap with integrated diffractive optic elements for collecting light into multi-mode fibers. In this trap, micro-motion is minimized, the effect of the dielectric is characterized, and the light collection efficiency is assessed by single photon counting. We also report progress towards long range compensation of stray electric fields in a trap with a ring geometry. This should allow us to trap a circular crystal of equally spaced ions tangentially confined by their mutual Coulomb repulsion. Finally, we report on initial testing of a trap structure with vastly improved in-plane optical access. In this structure in-plane beams can be focused to less than 8 microns while keeping a distance of at least 5 beam radii to the trap structure. This work was supported by Sandia's Laboratory Directed Research and Development (LDRD) and the Intelligence Advanced Research Projects Activity (IARPA). Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the US Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

## 10. Quantum trajectories for an arbitrary quantum system probed by a travelling wave non-Gaussian field

Joshua Combes, The University of New Mexico

*Abstract.* Quantum trajectories are a description of the continuous in time evolution of a quantum system undergoing a continuous in time ancilla coupled measurement. Until recently most quantum trajectory analysis was for Gaussian fields be they vacuum, coherent, squeezed, thermal or some combination thereof (see e.g. Wiseman and Milburn's Book). Using Gardiner and Collett's input-ouput theory I describe how to derive the quantum trajectories associated with an itinerant non-Gaussian probe prepared in any superposition and or mixture of: Fock states^{a} or coherent states^{b}. We focus on the trajectories associated with direct (photon counting), homodyne, and heterodyne detection. Finally I present some progress towards incorporating and then generalizing Shen, Fan and coworkers scattering matrix calculations into standard input-output theory for arbitrary fields^{c}, coupled with our results this allows for the correct description of heralded state preparation of itinerant modes.

^{a} Joint work with Ben Baragiola

^{b} Joint work with John Gough, Hendra Nurdin, and Matt James

^{c} Joint work with Chris Cesare

## 11. Single shot quantum state estimation via continuous measurement in a strong back-action regime

Robert Cook, University of New Mexico

*Abstract.* Quantum state reconstruction is a fundamental task in quantum information science. The standard approach employs many projective measurements on a series of identically prepared systems in order to collect sufficient statistics of an informationally complete set of observables. An alternative procedure is to reconstruct quantum state by performing weak continuous measurement collectively on an ensemble, while simultaneously applying time varying controls [1]. For known dynamics, the measurement history determines the initial state. In current implementations [2,3] the shot noise of the probe dominates over projection noise so that measurement-induced backaction is negligible. We generalize this to the regime where quantum backaction is significant, even for a small number of particles. Using the framework of quantum filtering theory, we model the reconstruction of the state of a qubit through collective spin measurement via the Faraday interaction and magnetic field controls, and develop a maximum-likelihood estimate. We present numerical results indicating that our estimates have an average fidelity of reconstruction that approaches an optimum bound. [1] A. Silberfarb and I. H. Deutsch, Phys. Rev. Lett. 95, 030402 (2005). [2] C. A. Riofrío et al., J. Phys. B: At. Mol. Opt. Phys. 44, 154007 (2011). [3] A. Smith et al., Arxiv:1208.5015 (2012).

## 12. Quantum information processing with trapped electrons and superconducting electronics

Nikos Daniilidis, University of California, Berkeley

*Abstract.* We describe a quantum information processing (QIP) architecture based on single trapped electrons and superconducting electronics. The electron spins function as quantum memory elements, and the electron motion is used to couple the electrons to microwave circuits. To achieve this, we propose a parametric coupling mechanism which utilizes the non-linearity of the electrostatic potential of a sharp electrode placed 10 μm from a single trapped electron. This mechanism allows parametric coupling rates higher than 350 kHz for electrons with trap frequency of 300 MHz, coupled to a 7 GHz resonant circuit. We discuss state transfer and entangling operations between distant electrons, as well as between electrons and superconducting qubits, e.g. transmon qubits. The coupling to high frequency superconducting electronics enables initialization as well as state read-out of the electron motion. In addition, the manifold of the ground and the first excited state of the electron motion can be mapped onto its spin using an oscillating magnetic field, completing all requirements for quantum computing with the electron spin. We estimate that all involved operations can be carried out with fidelities higher than 0.996, enabling fault-tolerant quantum computing.

## 13. Optimally Shaped Gates for Trapped Ion Chains

Shantanu Debnath, Joint Quantum Institute/ University of Maryland

*Abstract.* We perform entangling phase gates between selective pairs of qubits in a chain of trapped atomic ^{171}Yb^{+} ions through a coupling to multiple motional modes. We accomplish this by coherently manipulating and coupling the qubits to collective transverse modes of motion using Raman beat notes between frequency comb lines of a 355nm pulsed laser[1]. We optimally shape the phase and amplitude of Raman beat notes to implement robust gates that can operate at nearly any beat note detuning from the modes. We demonstrate a five-segment scheme[2] to entangle two Qubits with full control and high fidelity as compared to single segment gate. We extend this scheme to selectively entangle pairs of Qubits in a chain of 3 or more using shaped pulses and individual optical addressing that can be extended to much large number of Qubits. This work was supported by grants from the U.S. Army Research Office with funding from IARPA, the DARPA OLE program, and the MURI Hybrid Quantum Circuits program; and the NSF Physics Frontier Center at JQI. [1] D. Hayes et al., Phys. Rev. Lett 104, 140501 (2010). [2] S.-L. Zhu et al., Europhys. Lett., 73 (4), pp. 485-491 (2006).

## 14. The Kibble-Zurek mechanism in ion chains

Adolfo Del Campo, Los Alamos National Laboratory

*Abstract.* Structural defects in ion crystals can be formed during a linear quench of the transverse trapping frequency across the mechanical instability from a linear chain to the zigzag structure. The density of defects after the sweep can be conveniently described by the Kibble-Zurek mechanism [1,2]. In particular, the number of kinks in the zigzag ordering can be derived from a time-dependent Ginzburg-Landau equation for the order parameter, here the zigzag transverse size, under the assumption that the ions are continuously laser cooled. In a linear Paul trap the transition becomes inhomogeneous, the charge density being larger in the center and more rarefied at the edges. During the linear quench the mechanical instability is first crossed in the center of the chain, and a front, at which the mechanical instability is crossed during the quench, is identified which propagates along the chain from the center to the edges. If the velocity of this front is smaller than the sound velocity, the dynamics becomes adiabatic even in the thermodynamic limit and no defect is produced. Otherwise, the nucleation of kinks is reduced with respect to the case in which the charges are homogeneously distributed, leading to a new scaling of the density of kinks with the quenching rate. The analytical predictions are verified numerically by integrating the Langevin equations of motion of the ions, in presence of a time-dependent transverse confinement. The non-equilibrium dynamics of an ion chain in a Paul trap constitutes an ideal scenario to test the inhomogeneous extension of the Kibble-Zurek mechanism [3], and has recently led to its demonstration in the laboratory [4]. Journal-refs: [1] A. del Campo, G. De Chiara, G. Morigi, M. B. Plenio, A. Retzker, Phys. Rev. Lett. 105, 075701 (2010) [2] G. De Chiara, A. del Campo, G. Morigi, M. B. Plenio, A. Retzker, New J. Phys. 12, 115003 (2010) [3] A. del Campo, T. W. B. Kibble, W. H. Zurek, J. Phys.: Condens. Matter, 2013 (accepted). [4] K. Pyka, J. Keller, H. L. Partner, R. Nigmatullin, T. Burgermeister, D.-M. Meier, K. Kuhlmann, A. Retzker, M. B. Plenio, W. H. Zurek, A. del Campo, T. E. Mehlstäubler, arXiv:1211.7005.

## 15. Measurement-based quantum computation is contextual

Raouf Dridi. Co-author: Robert Raussendorf, University of British Columbia, Department of Physics and Astronomy, 6224 Agricultural Road, Vancouver, BC, V6T 1Z1 Canada

*Abstract.* Anders and Browne [1] have converted a specific (state dependent) proof of the Kochen-Specker Theorem [2] due to Mermin [3] into a measurement based quantum computation (MBQC). Here we show that any measurement-based quantum computation (with two settings and two outcomes per measurement) which deterministically computes a nonlinear Boolean function is contextual. The result continues to hold for slightly probabilistic computations. Furthermore, building on [4], we use the language of Grothendieck topologies and sheaves on sites to describe contextuality in quantum mechanics and its role in MBQC. In this framework, Mermin's simple proof of Kochen-Specker theorem is captured nicely and quickly as an amalgamation problem. [1] J. Anders and D.E. Browne, Phys. Rev. Lett. 102, 050502 (2009). [2] S. Kochen, and E.P. Specker, J. Math. Mech. 17, 59 (1967). [3] N. D. Mermin, Rev. Mod. Phys. 65, 803 (1993). [4] S. Abramsky and A. Brandenburger, New J. Phys 13 (2011) 113036.

## 16. Direct-to-Toffoli Magic-state Distillation

Bryan Eastin, Northrop Grumman Corporation

*Abstract.* In recently proposed quantum computing architectures, approximately 90% of the required resources are consumed during the distillation of single-qubit magic-states for use in performing Toffoli gates. I describe how the overhead for magic-state distillation can be reduced by merging distillation with the implementation of Toffoli gates. The resulting routines distill single-qubit magic-states directly to Toffoli ancillae, each of which can be used without further magic to perform a Toffoli gate.

## 17. Adiabatic Quantum Computation with Rydberg Atoms

Andrew Ferdinand, University of New Mexico

*Abstract.* We are developing, both theoretically and experimentally, a neutral atom qubit approach to adiabatic quantum computing (AQC). The approach uses an array of trapped Cs atoms with the qubits encoded in hyperfine ground state manifold of each atom. The entangling mechanism between qubits is mediated through the electric-dipole coupling of highly excited Rydberg states. With the laser fields off resonant from a Rydberg state, the ground state of the atoms are dressed with the Rydberg state and allow a continuous tunable interaction between qubits. Rydberg dressing of the ground states in conjunction with well developed single atom manipulation techniques allow all the necessary tools for our instance of AQC. We will develop this experimental capability to generate a two-qubit adiabatic evolution aimed specifically toward demonstrating quantum annealing in an two-spin Ising spin chain as a proof of principle experiment. Studying this two-qubit problem will test the immunity of our approach to AQC from noise processes in the control interactions as well as dissipation mechanisms associated with the trapping. We are developing our theoretical and experimental capabilities through key collaborations with the University of Wisconsin and the University of New Mexico.

## 18. Continuous measurement procedures via weak probe interactions

Jan Florjanczyk, University of Southern California

*Abstract.* It is known that given any measurement, one can construct a sequence of weak measurements that converge to it without the use of ancilla (Oreshkov, Brun, '05). This procedure relies on constructing a 1-dimensional random walk from the weak measurement operators where the ends of the walk converge to the two strong measurement operators desired. We study possible realizations of a such a procedure when the weak measurement is effectuated via weak interaction of a probe with the system in question. We give restrictions on the interaction Hamiltonians that yield such a random walk via differential conditions on the (weak measurement) step operators. We also study, in detail, the case where the probe and system are both qubits which interact via a diagonal Hamiltonian. We describe the procedure for preparing and measuring the probe qubit which yields any diagonal measurement operators on the system qubit. Our results hold in the limit of continuous monitoring via the probe.

## 19. Atom trapping in the large-angle diffraction pattern behind a pinhole for quantum computing

Travis Frazer, California Polytechnic State University, San Luis Obispo

*Abstract.* We are seeking to solve one of the few remaining problems in the field of neutral atom quantum computing, the issue of scalability. To do this, we plan to utilize the diffraction pattern of laser light shining through an array of pinholes. The diffraction pattern of each pinhole consists of localized bright and dark spots, which we have previously shown computationally to be effective dipole traps for neutral atoms. We propose to bring the atoms together and apart by changing the angles of incidence of two incoming laser beams. We are currently investigating both experimentally and computationally how the diffraction pattern changes for large angles of incidence, measuring the projection of the diffraction pattern, and building an experimental setup to physically implement these traps. We will present the computational and experimental results of our work. This work was performed in collaboration with Danielle May, Sara Monahan, David Roberts, Jason Schray, Glen D. Gillen, and Katharina Gillen-Christandl (PI). We acknowledge helpful discussions with Thomas D. Gutierrez, Ivan H. Deutsch, and Marianna Safronova. This work was supported by the National Science Foundation Grant No. PHY-0855524.

## 20. Thermodynamics and Quantum Correlations in Trapped Ion Crystals

Manuel Gessner, University of California, Berkeley

*Abstract.* Crystals of trapped ions exhibit a broad variety of physical phenomena ranging from fundamental quantum effects with applications for quantum information theory to mesoscopic physics at the border to the classical regime. In our current experiments we are investigating the melting dynamics of larger ion crystals and the distribution and transport of energy in such systems. In another experiment in the quantum regime, we are aiming at detecting the signatures of nonclassical system-environment correlations in the dynamics of an open quantum system. We present a theoretical scheme which does not require control over the environment and that can be carried out by local operations on the open system only.

## 21. Recovering quantum secrets via classical channels

Vlad Gheorghiu, Institute for Quantum Information Science at the University of Calgary

*Abstract.*

Quantum secret sharing is an important multipartite cryptographic protocol in which a quantum state (secret) is shared among a set of *n* players. The secret is distributed in such a way that it can only be recovered by certain authorized subsets of players acting collaboratively. The recovery procedure assumes that all players are interconnected through quantum channels, or, equivalently, that the players are allowed to perform non-local quantum operations. However, for practical applications, the consumption of quantum communication resources such as entanglement or quantum channels needs to minimized.

We provide a novel scheme in which quantum communication is replaced by local operations and classical communication (LOCC). Our protocol is based on embedding a classical maximum distance separable (MDS) code into a quantum error correcting code and employing the properties of the latter. Our scheme is appealing for real-world scenarios where the implementation of two-qubit gates is challenging. We illustrate the results by simple examples. Our methods constitute a first step towards attacking the important problem of decoding quantum error correcting codes by LOCC.

*Collaboration with Barry C. Sanders.

We acknowledge support from the Natural Sciences and Engineering Research Council (NSERC) of Canada and from Paciﬁc Institute for Mathematical Sciences (PIMS).## 22. Linear Density Matrix Estimation from Homodyne Measurements: Uncertainty Comparison

Scott Glancy, National Institute of Standards and Technology (Boulder)

*Abstract.* co-authors: Katelyn Weber and Emmanuel Knill In the 1990s, researchers developed linear estimators of photon number basis density matrix elements from homodyne detection data. This estimator uses a "pattern function" of the measured quadrature / phase pair, where the expectation value of the pattern function is equal to the desired density matrix element. Thus the estimate is linear and unbiased, but may result in unphysical density matrix estimates. Because the estimate is linear, we can use Hoeffding's Inequality to give uncertainty bounds. In this poster, we revisit the pattern function estimator and compare its results with the maximum likelihood estimates. We find that there exists a trade-off: the maximum likelihood estimates have lower variance but higher bias, which makes error difficult to quantify, while the pattern function estimates have higher variance but low bias, which allows for easy quantification of error. The pattern function estimates require much less computation and may be advantageous when computing power is limited but a large data set is available.

## 23. Robust quantum gates via sequential convex programming

Matthew Grace, Sandia National Laboratories

*Abstract.* Resource tradeoffs can often be established by solving an appropriate robust optimization problem for a variety of scenarios involving constraints on optimization variables and uncertainties. Using an approach based on sequential convex programming, we demonstrate that a substantial fidelity robustness is obtainable against uncertainties while simultaneously using limited resources of control amplitude and bandwidth. What is required is a specific knowledge of the range and character of the uncertainties, a process referred to in the control theory literature as "uncertainty modeling." Using a general one-qubit model for illustrative simulations of a controlled qubit, we generate robust controls for a universal gate set. Our results demonstrate that, even for this simple model, there exist a rich variety of control design possibilities. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

## 24. Improved approximation of realistic errors and its effect on quantum error-correcting circuits

Mauricio Gutierrez, Georgia Institute of Technology

*Abstract.* The Gottesman-Knill theorem allows for the efficient classical simulation of stabilizer circuits. Although not enough for universal quantum computation, these circuits can give important insights on the performance of stabilizer-based error codes and correction schemes. Errors in these circuits are commonly modeled as depolarizing channels by inserting Pauli gates randomly throughout the circuit [1]. In previous work we have proposed expanding this error model to include all operations allowed within the stabilizer formalism, namely Clifford gates and measurements in the Pauli bases followed by conditional operations. The latter addition allows us to simulate non-unital channels and to better approximate errors due to spontaneous emission [2]. Here we present our work examining if the xpanded error model still holds a considerable improvement over the depolarizing channels in the context of whole quantum error-correcting circuits. We compare the performance of several error-correcting procedures in the presence of realistic error channels with their performance in the presence of their approximate error channels. These results will show if the improvement in error approximation at the physical layer yields substantial improvements in the precision of the error at the logical level. [1] A.M. Steane, Phys. Rev. A 68, 042322 (2003) [2] M. Gutierrez, L. Svec, A. Vargo, K.R. Brown. arXiv:1207.0046

## 25. Transforming AKLT-like states to Graph-States (universal resources for measurement based quantum computation)

Poya Haghnegahdar, University of British Columbia

*Abstract.* Finding (physical) states which can serve as universal resources for measurement-based-quantum-computation (MBQC) is one of challenges of implementation for this model of quantum computing. Recently, Wei et al. have shown that the AKLT state on a 2-D Honeycomb lattice (HC) can be used as a universal resource for MBQC. This is done by observing that a typical 2-D HC lattice can be transformed (encoded) into a graph-state, which is then known to be a universal resource. The method that is used to perform this transformation however, is a specific procedure, which nonetheless need not be unique or in any way intended to be special. In a recent work, Darmawan et. al. have shown that using the same method, an entire phase of matter around the AKLT point can be transformed into useful graph-states. We expand upon these works by presenting a generalization of the previously used method that can be applied to AKLT-like states of any spin, in any spatial dimension (the present method only works for spin <=3/2). That is, we produce the map between the question of universality to a percolation problem for all such cases. In addition we investigate the robustness of this method in the presence of a particular class of noise.

## 26. Surface studies for reduction of anomalous heating in ion traps

Dustin Hite, National Institute of Standards and Technology

*Abstract.* Motional heating of trapped ions is a major obstacle to their use as quantum bits in a scalable quantum information processor. The detailed physical origin of this heating is not well understood, but experimental evidence suggests that it is caused by electric-field noise emanating from the surface of the trap electrodes. In this work, we detail our efforts to implement surface science techniques to help elucidate the origin of this problem, and to mitigate its effects. We find that an in-situ electrode-cleaning treatment of Ar-ion-beam bombardment results in a room-temperature heating rate that is reduced by more than two orders of magnitude, surpassing the performance of many cryogenic traps. We also report findings that in-situ evaporation of gold films on surface-contaminated electrodes does not reduce the heating rate, due to a growth mode that leaves the contaminants exposed at the surface. Finally, we detail progress of a novel, LIGA-fabricated, stylus ion trap that is engineered for single-ion probing of proximal surfaces, allowing for quick-turnaround heating-rate measurements from surfaces of various materials systems. This work was supported by IARPA, ARO contract No. EAO139840, ONR, and the NIST Quantum Information Program. *Collaborators (in alphabetical order): C. L. Arrington, E. Baca, K. R. Brown, J. J. Coleman, Y. Colombe, P. S. Finnegan, A. E. Hollowell, R. Jordens, J. D. Jost, D. Leibfried, K. S. McKay, D. P. Pappas, A. M. Rowen, U. Warring, A. C. Wilson, and D. J. Wineland.

## 27. A family of finite geometry codes in quantum key expansion

Kung-Chuan Hsu, University of Southern California

*Abstract.* Quantum key distribution (QKD) generates a common secret key to be securely shared between two distant parties. With the aid of an entanglement-assisted quantum error correcting code (EAQECC), QKD can be made to expand a common key rather than to generate one, in which case the process is known as quantum key expansion (QKE). Based on good EAQECCs, the performance of QKE is judged by the key rate, which is the rate of key expansion. In our work, we examined closely the families of codes constructed from finite geometry (FG), especially those with low density parity check (LDPC) matrices, and their use in QKE. We simulated QKE with one set of FG LDPC codes where the noise model is a depolarizing channel, and we observed that the performance is highly correlated with the block error rates of the codes. As a result, we proposed an improved version of the QKE protocol. Based on the simulation of QKE with this new protocol, we selected the codes, which are from the set of FG LDPC codes considered, that perform well for various channel error regions.

## 28. Scalable Quantum Networking of Trapped Ion Qubits

Ismail Inlek, Joint Quantum Institute, University of Maryland

*Abstract.* Trapped atomic ions are standard qubits for the production of entangled states for applications in QIS and metrology. Trapped ions can exhibit very long coherence times, while strong local interactions can be gated by external fields for the operation of entangling quantum logic gates. However, transferring quantum information over remote distances in a scalable fashion relies on the juxtaposition of fast ion/photonic interfaces with local gate operations. We report progress on these fronts with an experiment that combines remote and local entanglement protocols between three ions in two separate traps for the generation of both local and remote correlations. In related work, we are utilizing fast imaging optics to collect photons from trapped ions and push towards 10-100 Hz entangling rates between distant trapped ion qubits using a two-photon interference protocol. Importantly, this is several times faster than the observed coherence times of the qubits, a prerequisite for scaling to larger networks. These developments hold promise for scaling trapped ion qubits for applications in quantum communication and computation networks. This work was supported by grants from the U.S. Army Research Office with funding from IARPA, the DARPA OLE program, and the MURI Hybrid Quantum Circuits program; and the NSF Physics Frontier Center at JQI.

## 29. Quantum Information Processing with Rydberg-Dressed Atoms

Tyler Keating, University of New Mexico

*Abstract.* The Rydberg blockade effect is a powerful tool for information processing in cold neutral atoms. By dressing atomic ground states via off-resonant coupling to highly excited Rydberg levels, we can harness the blockade to produce a tunable, state-dependent interaction. When atoms are dressed in pairs, this interaction can produce CPHASE gates for circuit-model quantum computing. The same interaction can also be used for adiabatic quantum computing, by slowly ramping up the dressing on all atoms simultaneously. With the proper arrangement of atoms, this allows us to find the ground states of Ising models on a broad class of graphs that goes beyond nearest-neighbor interactions. We model proof-of-principle experiments of both varieties in realistic architectures, including details of the atomic implementation, with qubits encoded into the clock states of 133Cs, effective B-fields implemented through stimulated Raman transitions, and atom-atom coupling achieved by excitation to the 100P Rydberg level.

## 30. Fault-Tolerant Storage of Quantum Information by Large Block Codes

Ching-Yi Lai, University of Southern California

*Abstract.* An important issue in the implementation of a quantum computer is to protect quantum information from decoherence. Concatenated quantum codes and topological quantum codes are extensively studied for fault-tolerant quantum computation. However, there is not much research on large block codes in any fault-tolerant scheme. Here we propose a method for storage of quantum information by a large block code, which has a high code rate and high distance. To access or protect the quantum information stored in a large block code requires only the fault-tolerant implementation of the gates from the Clifford group. We derive the lifetime of the quantum information stored in a large block code by CSS code construction.

## 31. Quantum enhanced interferometry with Laser light

Matthias Lang, Center for Quantum Information and Control

*Abstract.* We consider an interferometer powered by laser light (coherent state) in one input port and ask the following question: What is the optimal state to inject into the second input port to enhance the interferometer's phase sensitivity (given separate power constraints for the two ports)? This setup is of practical concern, since the easiest way to improve sensitivity in a typical phase measurement is to 'buy' more photons, with the 'cheapest' coherent source being a laser. Furthermore it has the advantage that the main power production is separated from the generation of nonclassical light. We show that the squeezed vacuum is optimal in this setup, as it minimizes the QCRLB (Quantum Cramer-Rao lower bound), and we comment on previous work by Pezze et al. that indicates which detection scheme can saturate this bound.

## 32. On-chip atom-photon interface for scalable quantum devices

Jae Hoon Lee, California Institute of Technology

*Abstract.* Conventional atomic systems, such as ion traps and neutral atoms in optical lattices, have been important platforms for studying quantum information science due to universal atomic transition energies that can be made insensitive to perturbations from the environment. Solid state systems are also advantageous as quantum information platforms for their scalability. For example, diverse sets of tools have been previously developed for photonic devices. Here we pursue an integrated system, where we utilize the merits of each system, atomic and solid state, for scalable quantum memories. We devise an on-chip device where quantum states will be stored in and retrieved from atoms (stationary qubits) through photons (flying qubits) via integrated nano-photonic solid state structures. As a first step to achieving this goal, we present experimental progress towards the realization of localized ultracold Cesium atoms near the surface of SiN nano-photonic waveguides with rectangular cross sections of sub-wavelength dimensions.

## 33. Experiments with Surface Electrode Traps at NIST

Dietrich Leibfried, National Institute of Standards and Technology

*Abstract.* We report several experiments with surface electrode traps [1] at NIST. We have implemented a universal gate set [2] and demonstrated individual addressing protocols [3] on two magnetic field independent qubits comprised of hyperfine ground states of Mg+ ions. In a setup with Be+ ions, we have studied the dependence of anomalous heating of the motional state on surface properties and trap frequency in a room temperature trap [4]. A similar trap cooled to 4K was used to study the motional quantum state exchange of two Be+ ions in separate potential wells [5] and explore avenues to entangle their spins. The long-term goal of all these experiments is scalable quantum information processing and quantum simulation in larger two-dimensional trap arrays. *This work is supported by IARPA, NSA, ONR, DARPA and the NIST Quantum Information Program. [1] J. Chiaverini et al., Quantum Inf. Comput. 5, 419 (2005). [2] C. Ospelkaus et al., Nature 476, 181 (2011). [3] U. Warring et al., arXiv:1210.6407v1 (2012). [4] D. A. Hite et al., Phys. Rev. Lett. 109, 103001 (2012). [5] K. R. Brown et al., Nature 471, 196 (2011).

## 34. Enhanced machine learning algorithms for precise adaptive single parameter estimation

Neil Lovett, Institue for Quantum Information Science, University of Calgary

*Abstract.*

Sequential adaptive measurement is a promising strategy for quantum-enhanced single-shot parameter estimation problems, but appropriate adaptive procedures are difficult to devise even for ideal cases. Machine learning techniques enable suitable procedures to be found by exploiting the learning action of these techniques to find appropriate adaptive policies able to deliver precision surpassing the standard quantum limit. Thus far, the collective-intelligence algorithm known as particle swarm optimization has been used to beat the best previous results (obtained by clever guessing) for adaptive phase measurement in quantum interferometry with an input state of an entangled multi-photon pulse. Specifically, particle swarm optimization has successfully devised procedures with a space cost that is linear in the number N of operations on the multi-photon pulse and a time that scales as *N ^{6}* [1,2]. However, the ability of machine learning has only been demonstrated in this one simple case with a binary measurement outcome. It is yet to be determined if the same techniques are able to deliver better then standard quantum limit scaling when the possible measurement outcomes increase in a non-constant fashion. As such, the applicability of machine learning techniques to quantum metrological problems is currently limited.

We devise an algorithm which allows for the precise measurement of an unknown bias in the `coin' operator of a quantum walk on the line. In this case, the possible measurement outcomes increase factorially with the number of steps the walker can take. As such, we have a non-constant increase in the possible outcomes of the decision tree at each possible measurement. We devise an efficient machine learning algorithm with a space cost linear in the number *N* operations on a fixed number of walkers and a time cost of *N ^{6}*. By developing a heuristic which restricts this non-constant measurement domain to a subset of the possible outcomes, the algorithm is able to deliver policies which give a power law scaling in precision beating the standard quantum limit. This result opens up the possibility of using machine learning techniques for a variety of quantum metrology problems.

Although using these machine learning methods is undoubtedly powerful they are severely limited by computational time and space restrictions. In fact, we note that in both the above case and that of phase estimation, the resultant procedure delivers a power-law scaling for the uncertainty versus the input resources. However, we see a sudden breakdown in this scaling (at roughly 45 input photons for phase estimation) due to a failure of the technique for specific computational resources, namely the number of particles (particle swarm optimization candidate solutions) and number of iterations. In the case of phase estimation, we are able to devise a far superior algorithm that is able to deliver much better precision for given *N* with the restriction of using the same computational resources as the competing algorithm. We show that the differential evolution approach to machine learning delivers this same power law scaling as particle swarm optimization and shows no sign of breakdown up to one hundred photons. As the true cost scales as *N ^{6}*, this doubling (at least) of the number of photons actually corresponds to a 64 fold increase in the efficiency of devising the algorithm.

[1] - A. Hentschel and B. C. Sanders, *Phys. Rev. Lett.*, **104**, 063603 (2010).

[2] - A. Hentschel and B. C. Sanders, *Phys. Rev. Lett.*, **107**, 233601 (2011).

## 35. Implementation of a five-cavity / four-qubit 3D circuit QED system

Douglas McClure, International Business Machines Thomas J. Watson Research Center

*Abstract.* Surface code error correction schemes, which have emerged as a guiding paradigm for the development of small prototype quantum processors, have a natural implementation on a skew square 2D lattice of cavities and qubits. We describe the experimental realization of a modular segment containing a unit cell of this lattice in a device consisting of five 3D waveguide cavities and four superconducting transmon qubits. In this system, we demonstrate high-fidelity one- and two-qubit gates with low crosstalk. Moreover, this device provides an extensible framework for tests of protocols needed for error correction in much larger systems.

## 36. Motional heating of ions in a stylus trap

Kyle McKay, NIST

*Abstract.* The anomalous heating of the motion of trapped ions is a major barrier to the scalability and performance of ion traps used for quantum information processing. Efforts to reduce the anomalous heating rates have focused on reducing electric field noise from the trap surface by cooling and cleaning the surface or by exploring different materials. We present results on a micro-fabricated stylus ion trap. The stylus trap can be used as a probe to measure the electric field noise of a foreign surface.The design and operation of the trap is presented along with heating rates of the bare trap attained using Raman sideband spectroscopy. This work was supported by IARPA and the NIST Quantum Information program.

## 37. Magic-state distillation with the four-qubit code

Adam Meier, National Institute of Standards and Technology, Boulder

*Abstract.* The distillation of magic states is an often-cited technique for enabling universal quantum computing once the error probability for a special subset of gates has been made negligible by other means. I will present a routine for magic-state distillation that reduces the required overhead for a range of parameters of practical interest. Each iteration of the routine uses a four-qubit error-detecting code to distill the +1 eigenstate of the Hadamard gate at a cost of ten input states per two improved output states. Use of this routine in combination with the 15-to-1 distillation routine described by Bravyi and Kitaev allows for further improvements in overhead. I will also discuss how multiple levels of multiple-output distillation routines may be chained together to yield higher quality magic states. This work was performed in collaboration with B. Eastin and E. Knill.

## 38. Trapped Atoms and Polarimetry in a Nanofiber-based Quantum Interface

Pascal Mickelson, University of Arizona

*Abstract.* We describe an experiment that will use atoms trapped in the evanescent-wave field of a tapered optical fiber (nanofiber) as an optical quantum bus to control the atoms' collective spin. When probe laser light interacts with a trapped atomic sample with high optical depth, the probe light undergoes Faraday rotation proportional to the atomic magnetization. If the atom-light coupling is strong enough, polarimetry of the probe light will provide a measurement of the magnetization with resolution better than the spin projection noise, at which point measurement back-action can be used for quantum control of the spin. When atoms are trapped in the evanescent mode of a nanofiber, probe light traveling through the nanofiber is particularly well mode-matched to the atom sample, and high optical depth on the order of 100 is expected. Here, we report experimental progress towards loading cold atoms samples into these nanofiber traps in addition to shot-noise-limited polarimetry in the nanofiber without trapped atoms.

## 39. Many Particle Quantum Random Walk With Interactions

Daniel Minsky, Univeristy California San Diego

*Abstract.* The theory of random walks has proven to be a valuable resource for studying classical physical phenomena, specifically Brownian motion and the heat equation. With this as inspiration we have studied the case of a many particle quantum random walk on the complete graph. The set up is based on Farhi and Gutmann's version of continuous Grover search. For a fixed number of particles, we are able to describe the time evolution of the system as the size of the complete graph grows. In particular, we found that tuning the strength of the interaction amplifies the probability of formation for specific particle configurations. The over-arching goal of this research is to determine if the limiting behavior of such a system is governed by the non-linear Schrodinger equation.

## 40. Superconducting qubit readout using capture-disperse-release of microwave field

Eric Mlinar, University of California, Riverside

*Abstract.* Eric Mlinar(1), Eyob A. Sete(1), Andrei Galiautdinov(2), John M. Martinis(3), Alexander N. Korotkov(1) (1) University of California, Riverside (2) University of Georgia, Athens (3) University of California, Santa Barbara We analyze a measurement scheme for superconducting qubits via controlled capture, dispersion, and release of a microwave field. The Purcell effect is circumvented by using a tunable coupler to decouple the microwave resonator from the transmission line during dispersive interaction with the qubit. We show that fast and high-fidelity qubit readout can be achieved for nonlinear dispersive qubit-resonator interaction and for sufficiently adiabatic tuning of the qubit frequency. Interestingly, the Jaynes-Cummings nonlinearity results in quadrature squeezing of the microwave field which leads to a significant decrease in measurement error. The effects of qubit anharmonicity and imperfect quantum efficiency of the microwave amplification on the measurement error are also discussed.

## 41. Progress towards a polarization spectroscopy experiment for quantum control of collective spin

Enrique Montano, University of Arizona

*Abstract.* We report preliminary results from an experiment that will implement quantum control of the collective spin of an atomic ensemble. In our setup, a weak probe laser interacts with a cold, trapped atomic sample of cesium atoms with high optical depth, leading to Faraday rotation of the probe light proportional to the atomic magnetization. If the atom-light coupling is strong enough, polarimetry of the probe light will provide a measurement of the magnetization with resolution better than the spin projection noise, at which point measurement back-action will become significant enough to be used for quantum control of the spin. Thus far, we have prepared an ensemble of atoms with high optical depth by loading into a crossed optical dipole trap and we have generated squeezing of the collective spin of the ensemble. Work is ongoing to increase atom-light coupling thus increasing the generated squeezing. We also plan to use individual atom control, which has been developed in our lab, to prepare initial spin states that will lead to more squeezing.

## 42. Optimizing Passive Quantum Clocks

Mike Mullan, National Institute of Standards and Technology

*Abstract.* We describe quantum interrogation schemes for passive atomic clocks. During any given interrogation period, the optimal strategy depends on the state of the clock - specifically on the frequency deviation of the flywheel (classical oscillator) from the atomic standard. As a clock runs, it is possible to estimate this deviation. Nonetheless, traditional schemes use the same, fixed strategy for each interrogation period, which is necessarily independent of this prior knowledge. Here we present a dynamic scheme, tailoring our strategies to the clock's state before each interrogation. These strategies are derived by constructing a complete model of a passive clock. Specifically, a probability distribution describing the estimated average offset frequency of the flywheel during both the upcoming interrogation period and interrogation periods in the past is updated via appropriate noise models and by measurements of the atomic standard. To reduce the deviation from an ideal clock we optimize the next interrogation strategy by means of a semidefinite program for atomic state preparation and measurement whose objective function depends on the updated state. We implement a full simulation of the clock with power-law noise models and find significant improvements by applying our techniques. This work is in collaboration with Manny Knill and Till Rosenband.

## 43. Improvements to microwave parametric amplifiers

Josh Mutus, University of Californa, Santa Barbara

*Abstract.* Parametric amplifiers have long been of interest for readout of superconducting qubits due to their high gain and near quantum limited performance. In collaboration with UC Berkeley, we are improving upon their proven parametric amplifier design, which consists of a lumped element LC resonator, with a SQUID providing a tunable nonlinear inductance. We report on the design of a single-ended amplifier using our 7-layer fabrication process, combining photo and electron beam lithography. These changes enable us to use a smaller and simpler chip mount with separate signal and flux ports. The high bandwidth of the flux port allows us to flux pump the amplifier and should allow dynamic frequency tuning on ns timescales. In order to improve the dynamic range of these amplifiers, multiple SQUIDs are used in series in order to distribute the non-linearity across many junctions. We explore the experimental optimization of the device by characterizing the gain bandwidth product, saturation power, and noise temperature.

## 44. Minimum energy-surface required by quantum memory devices

Hieu Nguyen, ucsb

*Abstract.* We address the question what physical resources are required and sufficient to store classical information. While there is no lower bound on the required energy or space to store information, we find that there is a nonzero lower bound for the product (*P = <E><r ^{2}>*) of these two resources. Specifically, we prove that any physical system of mass

*m*and

*d*degrees of freedom that stores

*S*bits of information will have lower bound on the product

*P*that is proportional to (

*d*)(exp(

^{2}/m*S/d*)-1)

^{2}. This result is obtained in a non-relativistic quantum mechanical setting, and it is independent from earlier thermodynamical results such as the Bekenstein bound on the entropy of black holes.

## 45. Ion-Photon Entanglement with Barium Ions

Thomas Noel, University of Washington

*Abstract.* We present preliminary evidence of entanglement between the ground state of a trapped ^{138}Ba^{+} ion and the polarization state of the photons it spontaneously emits. The spontaneously emitted photons result from weak excitation by short (~40 ns) pulses of resonant CW laser light of the ions initially prepared in a single Zeeman ground state. This protocol is facilitated by the presence near the trap of an integrated electrode that allows ground state spin flips to be driven in under a microsecond. We also present our work toward improved entanglement fidelity by employing ultrafast pulses from a mode-locked Ti:Sapphire laser for ion excitation, with the ultimate goal of doing remote entanglement of barium ions in distant traps. Barium is a particularly good candidate for such research due to the relatively long wavelength of the transitions involved, which makes it suitable for fiber optic transmission over long distances.

## 46. Squeezing of Spin Waves in a Three-Dimensional Atomic Ensemble

Leigh Norris, University of New Mexico

*Abstract.* Leigh Norris (CQuIC-University of New Mexico), Ben Baragiola (CQuIC-University of New Mexico), Enrique Montano (CQuIC-University of Arizona), Pascal Mickelson (CQuIC-University of Arizona), Poul Jessen (CQuIC-University of Arizona) and Ivan Deutsch (CQuIC-University of New Mexico) Spin squeezed states (SSS) have generated considerable interest for their potential applications in quantum metrology and quantum information processing. Many protocols for generating SSS in atomic gases rely on the Faraday interaction that creates entanglement between atoms through the coupling of the ensemble's collective spin to the polarization modes of an optical field. Most descriptions of this process rely on an idealized one-dimensional plane wave model of light-matter interactions that is not appropriate for describing a real system consisting of a cigar-shaped cold atomic cloud in a dipole trap interacting with a probe laser beam. We provide a first principles three-dimensional model of squeezing via a quantum nondemolition measurement of the collective magnetization, for an ensemble of atoms with hyperfine spin f. The model includes spin waves, diffraction, paraxial modes, and optical pumping, derived by a full master equation description. Our model easily generalizes to atoms with f>1/2, for which it was recently demonstrated that state preparation of the ensemble using internal hyperfine control of the atoms substantially enhances the entangling power of the Faraday interaction [Norris et al., PRL 109, 173603 (2012)]. Including dissipative dynamics, we find the optimal ensemble geometry and input Gaussian beam parameters to maximize spin squeezing for a variety of state preparations and spin sizes f.

## 47. Quantum Operation for Nondeterministic Approximately Noiseless Amplification

Shashank Pandey, Center for Quantum Information and Control, Department Physics and Astronomy, University of New Mexico

*Abstract.* It is known that quantum mechanics does not allow phase preserving noiseless linear amplification [1]. In [2], Ralph and Lund, describe a process for heralded nondeterministic noiseless but approximate amplification,the amplified output state is truncated in number basis for small amplitude coherent state inputs. There have been various experimental implementations of this idea using quantum scissors, photon number addtion and subtraction etc.. We prove the impossibility of nondeterministic noiseless phase preserving amplification, using Unambiguous State Discrimination bounds for symmetric distribution of coherent states on a circle. Thus even probabilistically only approximate noiseless amplification is possible. We pose the problem of finding the process for nondeterministic approximate noiseless amplification as an optimization one. We maximize the fidelity of the output state truncated to N-photons in number basis with the amplified coherent state, for a given probability of working. This is sufficient to determine the optimal Kraus operators for nondeterministic approximate noiseless amplification for coherent state inputs lying within a disk of radius N in phase space. We also point out that noiseless amplification corresponds to a quantum operation with a non physical state in the auxiliary mode of a two mode squeeze operator. This points to the possibility of processes with noise intermediate to noiseless amplification and ideal linear amplification that could occur probabilistically but approximately, if heralded. [1]C.M. Caves,``Quantum limits on noise in linear amplifiers,'' Phys.Rev.D 26, 1817--1839 (1982). [2]T. C. Ralph and A. P. Lund, ``Nondeterministic noiseless linear amplification of quantum systems,'' in Quantum Communication, Measurement and Computing, ed. A. Lvovsky, Vol.1110 of AIP Conference Proceedings

## 48. An Adiabatic Approach to Quantum Computing Using Rydberg-Dressed Neutral Atoms

L. Paul Parazzoli, Sandia National Laboratories

*Abstract.* We are implementing an adiabatic quantum computation (AQC) algorithm using neutral atoms trapped in optical tweezers with interactions mediated via the Rydberg blockade mechanism~\cite{blockade}. Adiabatic evolution offers potential to solve computationally difficult problems by mapping the problem of interest onto the Hamiltonian such that the ground state encodes the solution. To find the solution, one begins by initializing in the ground state of a 'simple' Hamiltonian and then evolving adiabatically to the 'problem' Hamiltonian. Neutral atoms offer advantages because of their demonstrated robust quantum coherence (e.g. atomic clocks), long lived hyperfine states (the qubit basis), and also because they are highly isolated from the external environment. We control the adiabatic evolution of the system by imposing various light shifts on the hyperfine levels. The interaction between the atoms is generated by creating a Rydberg-dressed state that, via Rydberg blockade, creates the necessary conditional shift.

## 49. Optical pumping induced spectral modifications to a QED-cavity system

Xiaodong Qi, University of New Mexico

013/program.php?day=1">Thursday from )*Abstract.* This piece of work presents a theoretical study of the optical pumping effects to an optical cavity with excitons. Under the weak excitation condition, this study based on Green function method shows that increasing the power of optical pump leads to the increase of the population of excitons coupled to the cavity, and hence leads to comprehensive spectral modifications in terms of the cavity's spectral shape, bandwidth and resonance. The increased excitation population of the exciton ensemble can also equivalently enhance the optical coupling strength between the cavity field and the target exciton, which has a relatively large coupling strength and is close to the cavity spectral peak. The target exciton, in return, affects the luminescent properties of the background dipoles and their coupling to the cavity. It shows that all these modification effects can be explained by considering the inhomogeneous broadening and frequency repulsion effects of collective emissions, which are sensitive to the number, the resonance distribution and the linewidth of the background and target excitons in the frequency domain. This study investigates the optical pumping modification effects and spectral stability of an optical cavity system, and provides a perspective on the control of the optical properties of cavities and individual excitons through collective excitation.

## 50. Quantum memory with telecom quantum frequency conversion

Qudsia Quraishi, Army Research Laboratory

*Abstract.* Entanglement between remotely situated quantum memories may be accomplished through single photons transmitted through telecom fibers. Single photons can be emitted and entangled with quantum memories based on atomic gases. However, for long-haul transmission, these photons must be quantum frequency converted into the telecom regime. We review the status of our setup to convert single photons, emitted by a cold Rb87 gas, into a telecom photon via four-wave mixing and then, after fiber transmission, frequency up-covert into an IR photon using a periodically-poled lithium niobate waveguide. This scheme would allow for a long-distance and scalable quantum network.

## 51. Quantum Process Tomography of Superconducting Qubit Circuits via Compressed Sensing

Andrey Rodionov, University of California, Riverside

*Abstract.* Andrey Rodionov, Alexander N. Korotkov (University of California, Riverside); Robert L. Kosut (SC Solutions, Sunnyvale, California); Matteo Mariantoni, Daniel Sank, James Wenner, John M. Martinis (University of California, Santa Barbara). We analyze quantum circuits based on superconducting phase qubits using the Compressed Sensing (CS) method of Quantum Process Tomography (QPT). Applying the CS method allows us to estimate the process matrix $\chi$ from a strongly reduced set of initial states and/or measurement configurations. Using experimental data for 2-qubit controlled-Z gate, we show that the CS-QPT method gives an estimate of the $\chi$-matrix with reasonably high fidelity, compared with full QPT, even when the amount of used data is so small, that the standard QPT would have an underdetermined set of equations. The CS-QPT method is also applied to the analysis of a three-qubit Toffoli gate with numerically added noise. Similarly, we show that the method works reasonably well for a strongly reduced set of data, including the underdetermined case.

## 52. Dual Species Trapped Ion Quantum Logic Gates

Tomasz Sakrejda, University of Washington

*Abstract.* Working towards a scalable quantum computation architecture within the MUSIQC collaboration we discuss co-trapping Yb-171 and Ba-138 in a microfabricated surface trap. Ytterbium ions would be used for local quantum gates, while barium ions would be used for remote entanglement generation and sympathetic cooling. A demonstration toward this protocol is two-species trapping of Ba-137 and Ba-138 isotopes and quantum logic gates between these using stimulated Raman transitions. We plan to use a frequency-doubled Ti:Sapphire laser near 470nm initially, and move to a high power Raman beams at 532nm pulsed laser shortly thereafter to achieve ultrafast operation. The two Barium isotopes do not share cooling laser frequencies and this allows us to demonstrate the functionality and feasibility of a Barium-Ytterbium system.

## 53. Coherent state manipulation in a surface-electrode ion trap with integrated microwave elements

Chris Shappert, Georgia Tech Research Institute

*Abstract.* We present the development of a microfabricated surface-electrode ion trap with integrated microwave elements. The trap was engineered to control the internal state of the ^{171}Yb^{+} hyperfine qubit and produce highly uniform gate operations along the trapping axis. The design also incorporates magnetic field polarization control to reduce off-resonant coupling outside the qubit manifold while generating a Rabi frequency of Ω/2π ≈0.5 MHz on the qubit clock transition. Gates were executed using composite pulse sequences that reduce sensitivity to external noise sources and also compensate for the small amplitude variation intrinsic to the control field standing wave. The ability to maintain coherent quantum superpositions of internal states during ion transport was also demonstrated.

## 54. Experimental progress with Sandia micro-fabricated ion traps with integrated diffractive optic elements

Boyan Tabakov, University of New Mexico and Sandia National Laboratories

*Abstract.*

Experimental progress with Sandia micro-fabricated ion traps with integrated diffractive optic elements Boyan Tabakov^{1}, Matthew Blain, Francisco Benito, Chin-wen Chou, Craig Clark, Mike Descour, Rob Ellis, Ray Haltli, Edwin Heller, Shanalyn Kemme, Jon Sterk, Chris Tigges, Peter Maunz, Daniel Stick

Sandia National Laboratories

^{1}Center for Quantum Information and Control, University of New Mexico, MSC 07-4220,Albuquerque, NM 87131-0001

In ion trap quantum computing there are many technical challenges which still need to be addressed for scalable quantum information processing to be viable. One of those challenges is to perform accurate state detection via the fluorescence of an ion or multiple ions in a scalable fashion. One solution is to integrate diffractive optic elements (DOEs) with surface electrode traps. In this talk, I will discuss recent results using a linear trap with an integrated DOE for light collection. I will show data in which we employ an experimental method for determining the collection efficiency, one that is insensitive to micro-motion and is not dependent on fully characterizing the atomic physics. A result for micro-motion compensation and heating rate measurement with the ion away from the exposed dielectric of the DOE is compared to results with the ion sitting above the DOE. Preliminary results from our newest High Optical Access (HOA) trap will also be presented.

This work was supported by Sandia's Laboratory Directed Research and Development (LDRD) and the Intelligence Advanced Research Projects Activity (IARPA). Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the US Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

## 55. Progress on Trapped-ion-based Quantum Information Processing using Scalable Technique

Ting Rei Tan, National Institute of Standards and Technology

*Abstract.* T. R. Tan, J. P. Gaebler, R. Bowler, Y. Lin, J. D. Josty, D. Leibfried, and D. J. Wineland National Institute of Standards and Technology, 325 Broadway, Boulder, CO 80305, USA November 26, 2012 The fundamental building blocks required for large-scale quantum information processing (QIP) using trapped atomic ions can be comprised of qubits stored in magnetic field-insensitive states for long coherence times, a universal logic gate set consisting of single-qubit rotations and two-qubit entangling gates, motional state initialization without destroying qubit memory by sympathetic cooling with 'refrigerant' ions, and information transport by shuttling and distributing ions across different trap zones. Integration of these blocks has previously been demonstrated. One limitation of previous experiments was the fidelity of two-qubits logic gate. Here we demonstrate a trapped-ion-based entangling gate scheme proposed by Bermudez et al. [Phys. Rev. A. 85, 040302 (2012)] and improved gate fidelity. This scheme takes advantage of dynamic decoupling which protects the qubit against dephasing errors. It can be applied directly on magnetic-field-insensitive states, and is robust against thermal excitations. Furthermore, this new scheme provides a number of simplifications in experimental implementation compared to some other entangling gates with trapped ions. Another limitation of our previous work was the extended time required for ion transport and separation/recombination followed by lengthy sympathetic cooling required to re-initialize the ions' motional state. We report a speed-up of ion shuttling to a time scale comparable to that of logic gates, with reduced motional excitation. We also report sympathetic electromagnetically-induced-transparency cooling which requires smaller laser intensities than our previous resolved sideband cooling protocols and increases the cooling speed by roughly an order-of-magnitude. These improvements should lead to substantial speed-up in future demonstrations of scalable quantum information processing. Supported by IARPA, ARO contract No. EAO139840, ONR, and the NIST Quantum Information Program. [1] D. J. Wineland, et al., Phil. Trans. R. Soc. Lond. A 361, 1349 (2003). [2] J. P. Home, et al., Science 325, 1227 (2009). [3] D. Hanneke, et al., Nature Physics 6, 13 (2009). [4] J. P. Gaebler, et al., Phys. Rev. Lett. 108, 260503 (2012). [5] R. Bowler et al., Phys. Rev. Lett. 109, 080502 (2012)

## 56. Quantum Circuit Fault Tracer: an efficient tool to calculate logical failure rates of concatenated FTQEC circuits

Yu Tomita, Georgia Institute of Technology

*Abstract.* Quantum Circuit Fault Tracer is our new tool created to efficiently compute level-k logical failure rates of concatenated FTQEC codes. This tool is based on the idea of fault paths which was introduced to calculate thresholds of distance-3 concatenated FTQEC codes by Aliferis, Gottesman, and Preskill [1]. Our implementation supports inhomogeneous error channels and improves the computational complexity. To improve the accuracy of the output logical failure rate, we separate errors into X-type and Z-type, and propagate them on the circuit independently. The computational complexity of our tool is improved in two ways. First, the circuit is traversed from output qubits to input qubits. This assures the program collects only fatal fault point sets. Second, the level-k circuit is calculated recursively and dynamically from the physical level. This keeps the computational cost to O(kn^2) where n is the number of physical gates in the level-1 logical circuit. Finally, we compare the performance with that of the Monte Carlo simulation. [1] P. Aliferis, D. Gottesman, and J. Preskill, Quant. Inf. Comput. 6 (2006) 97-165

## 57. Stability of Ion Chains in a Cryogenic Surface-Electrode Ion Trap

Grahame Vittorini, Georgia Institute of Technology

*Abstract.* Ion trap development in recent years has been motivated by the pursuit of scalable ion trap technologies for quantum computation and simulation applications. Surface-electrode traps are amenable to microfabrication using standard processes, making this geometry scalable while also enabling creation of small electrodes capable of generating complicated, high spatial resolution potentials. This fine control makes possible the tailoring of potentials to hold long, many-ion chains. Unfortunately, large anomalous heating rates associated with the small ion-electrode distances in microfabricated traps combine with the reduced trap depth of planar trap geometries to decrease the stability of trapped ion chains. These two drawbacks can be ameliorated through the use of a cryogenic ion trapping chamber. The combination of reduced outgassing and high pumping speed in a cryogenic environment dramatically improves vacuum. The low temperature suppresses ion heating and reduces the thermal energy of colliding background gas to reduce ion loss. We have developed a modular cryostat for trapping in surface-electrode traps, allowing us to investigate how ion chain stability is affected by factors such as vacuum, laser cooling parameters, and modifications to RF and DC trapping potentials.

## 58. **Stabilizer Formalism for Generalized Concatenated Quantum Codes**

Yun-Jiang Wang, Institute for Quantum Information Science

*Abstract.*

Error-correcting codes are necessary to overcome restrictions in computation and communication due to noise, but constructing algorithms for finding good

codes is generically an intractable problem and evidently the central question of coding theory. Good codes

are special in that they have good trade-off among rate, distance, encoding and decoding costs, thereby reducing requisite space and time resources. In classical settings, constructing generalized concatenated codes, which incorporate multiple outer codes concatenated with multiple inner codes, is a promising approach for realizing good trade-off among those parameters. Recently, generalized concatenation has been introduced into quantum scenarios providing a systematically way to construct good quantum codes, but the stabilizer formalism of generalized concatenated quantum codes has not been investigated so far.

As the stabilizer formalism plays a central role in almost all branches of quantum information science, we attack the problem by developing the stabilizer formalism for generalized concatenated quantum codes, thereby providing a new code interpretation for generalized concatenated stabilizer codes and also a powerful and systematic technique for constructing good stabilizer codes. Using this method, we derive a lower bound on the achievable distance for generalized concatenated stabilizer codes. We show that our stabilizer formalism enables construction of generalized concatenated stabilizer codes, no matter the outer codes being stabilizer codes or classical linear codes, and the resultant codes being binary codes or non-binary codes.

“Collaboration with Barry C. Sanders and Bei Zeng”.

“This research has been supported by CIFAR, AITF, PIMS, MITACS, and USARO.”

## 59. Stability and Relaxation Oscillations in a Superradiant Raman Laser

Joshua Weiner, JILA/University of Colorado at Boulder

*Abstract.* We experimentally study the relaxation oscillations and amplitude stability properties of an optical laser operating deep into the bad-cavity regime using a cold atom Rb-87 Raman laser. By combining measurements of the laser light field with non-demolition measurements of the atomic populations, we infer the response of the the gain medium represented by a collective atomic Bloch vector. The results are qualitatively explained with a linearized model. Measurements and theory are extended to include the effect of intermediate repumping states on the closed-loop stability of the oscillator and the role of cavity feedback on stabilizing or enhancing relaxation oscillations. This experimental study of the stability of an optical laser operating deep into the bad-cavity regime will guide future development of superradiant lasers with ultranarrow linewidths.

## 60. Superradiant Raman Laser Magnetometer

Joshua Weiner, JILA/University of Colorado at Boulder

*Abstract.* Superradiant or "bad cavity" lasers rely on collective atomic coherence to sustain coherent light emission, with the phase of the emitted light corresponding to the atomic phase. We employ a cold atom Raman laser with a tunable emission rate to demonstrate non-destructive measurement of atomic phase via heterodyne detection of the light phase in both active and Ramsey-like passive modes, and arbitrary fast transitions between the two modes. By operating the superradiant emission on a magnetic field-sensitive transition, the superradiant laser acts as a variable bandwidth magnetometer with sensitivity ~200 pT/sqrt(Hz) at 10 kHz.

## 61. Fast and concise decoder for topological quantum surface codes

Arman Zaribafiyan, University of British Columbia

*Abstract.* Local architecture of Qbits in two dimensional lattices is known as one of the candidates to do fault tolerant quantum computation with high threshold. Topological quantum error correcting codes, such as surface codes, are used to make this architecture robust against various quantum error models. In this research we present a very fast, concise, operationally inexpensive and highly parallelizable decoding algorithm for surface codes without using concatenation. The operational cost without any parallelization is of order O(l^2*log(l)) where l is the lattice size. Using proper parallelization and without significant decrease in threshold, our algorithm scales logarithmically with l, in terms of time complexity which is much more efficient than the common minimum weight perfect matching method.