# 2012 Poster Abstracts

## 1. N-Photon Wavepackets Interacting with an Arbitrary Quantum System

Ben Baragiola, University of New Mexico

*Abstract.* Traveling nonclassical states of light can be important resources for quantum metrology, secure communication, and quantum networking. A theoretical description of systems interacting with nonclassical states becomes more urgent as the generation of more exotic states of light, such as N-photon states and NOON states, become technologically feasible. We approach this problem with the formalism of input-output theory and derive master equations for an arbitrary quantum system (e.g. harmonic oscillator or a multi-level atom) interacting with wavepackets of definite photon number in one and two polarization modes, which we then generalize to wavepackets with arbitrary spectral density functions. We also obtain equations for output field quantities, such as output homodyne current and photon flux. To illustrate our formalism we consider the problem of efficiently transferring field excitations to the excited state population of a two-level atom. For a single-photon wavepacket, this problem has been studied in detail [1]. We show that, for a given photon number, there is a trade off between wavepacket bandwidth and the population of the excited state.

[1] P. Domokos, P. Horak, and H. Ritsch, Phys. Rev. A {\bf 65}, 033832 (2002); M. Stobinska, G. Alber, and G. Leuchs, EPL {\bf 86}, 14007 (2009); Y. Wang, J. J.Minar, L. Sheridan, and V. Scarani, Phys. Rev. A {\bf 83}, 063842 (2011).

## 2. Integrated Cavity QED in a linear ion trap chip for Enhanced Light Collection

Francisco Benito, Sandia National Laboratories

*Abstract.*

Authors: F.M. Benito, M.G. Blain, K. Fortier, D.L. Moehring, J.D. Sterk, D.L. Stick, B.Tabakov.

Title: Enhancement Light Collection of a single trapped ion in a linear trap chip

Realizing a scalable trapped-ion quantum information processor may require integration of tools to manipulate qubits into trapping devices. We present efforts towards integrating a 1 mm optical cavity into a microfabricated surface trap to efficiently connect nodes in a quantum network. The cavity is formed by a concave mirror and a flat coated silicon mirror around a linear trap where ions can be shuttled in and out of the cavity mode. By utilizing the Purcell effect to increase the rate of spontaneous emission into the cavity mode, we expect to collect up to 13% of the emitted photons.

## 3. Silicon-Based Semiconductor Devices for Quantum Information Science and Technology

Stephen Carr, Sandia National Laboratories

*Abstract.* M.P. Lilly, L.A. Tracy, N.C. Bishop, K.R. Barkley, J.E. Levy, T.M. Lu, K. Nguyen, J.R. Wendt, J. Stevens, R.K. Grubbs, T. Pluym, J. Dominguez, R.W. Young, H.L. Stalford, R. Muller, E. Nielsen, and M.S. Carroll, Sandia National Laboratories.

The semiconductor quantum information team at Sandia National Laboratory includes microfabrication, cryoelectronics, cryogenic measurement, modeling, and architecture of semiconductor devices for adiabatic and non-adiabatic quantum information processing and the quantum engineering of qubit hardware. We have demonstrated silicon-based electrostatically-defined single and double quantum dots using electron transport measurements and integrated electrometry through quantum-point-contact charge sensors. We present an overview of the device fabrication, broadband cryogenic measurement techniques, and modeling for Metal-Oxide-Semiconductor (MOS) devices and Silicon-Germanium (SiGe) heterostructures.

## 4. Reliability of a classical-quantum communication system with noisy feedback

Aman Chawla, University of New Mexico

*Abstract.* We consider a quantum pure-state forward channel used in conjunction with a feedback quantum pure-state channel for the communication of classical messages. The feedback channel is aided by a classical one-way discrete memoryless channel. We derive a lower bound on the reliability function of this communication system in terms of the overlap between the pure states used for communication over the forward channel.

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

Chen-Kuan Chou, University of Washington

*Abstract.* Efficiently collecting ion fluorescence is critical for many aspects of trapped ion quantum computation and information, such as qubit state readout and photon-mediated remote entanglement generation. To address this issue, we developed an ion trap combining a reflective parabolic surface with trap electrodes. This parabolic ion trap design covers a solid angle close to 2 Pi, and allows precise ion placement to focal point of the mirror. With the advantage of little photon blocking and collimated ion photon emission, we can couple the ion fluorescence into fiber in a straightforward way. We expect to reach the diffraction limit for single ion imaging, with which >70% fiber coupling efficiency should be achievable. Owing to its simple design, this trap structure can be easily adapted into more complex trap systems.

## 6. Alternative views for decoherence and discord

Patrick Coles, Carnegie Mellon University

*Abstract.* The theory of decoherence, e.g. [1]-[3], has made major progress in explaining macroscopic phenomena, yet there have been several distinct approaches. For example, decoherence has been defined as (1) the loss of off-diagonal elements of the density matrix, (2) the loss of interference, and (3) the flow of information to the environment. While Hamiltonian models of decoherence in the literature have suggested a connection, here I explicitly give mathematical connections between these three views of decoherence under very general circumstances, i.e. without invoking any sort of Hamiltonian model [4]. The fact that these three seemingly distinct processes scale with each other in a deterministic quantitative way shows, in a sense, that they are three equivalent views of one underlying phenomenon. A similar situation arises when considering the correlation between two systems. Indeed there are several alternative ways to state the “classicality condition” for correlations, and hence there are several ways to construct measures of the “quantumness” of correlations, often called “discord” measures. In addition to emphasizing the alternative perspectives found in the literature, here I give a novel view of what discord is measuring, as the number of secure classical bits (secure from the purifying system) that can be distilled from the bipartite quantum state. This shows that non-classicality is connected to information security. [1] E. Joos, H. D. Zeh, C. Kiefer, D. Giulini, J. Kupsch, and I.-O. Stamatescu, Decoherence and the appearance of a classical world in quantum theory (Springer, 2003), 2nd ed. [2] W. H. Zurek, Rev. Mod. Phys. 75, 715 (2003). [3] M. Schlosshauer, Decoherence and the quantum-to-classical transition (Springer, 2007). [4] P. J. Coles, Unified view of decoherence with application to quantum discord (2011). Eprint arXiv:1110.1664 [quant-ph].

## 7. niversal Quantum Degeneracy Point and Four-wave Mixing Toolbox of Superconducting Qubits

Xiuhao Deng, University of California, Merced

*Abstract.* We present a superconducting circuit that can suppress qubit decoherence due to low-frequency noise and to implement well-controlled quantum operations on superconducting resonators. This circuit contains a universal quantum degeneracy point that protects the encoded qubit from arbitrary low-frequency noise. Universal quantum logic gates can be realized on the encoded qubits. This circuit can also generate various quantum operations on superconducting microwave resonators, including the Bogoliubov-linear operations and nonlinear interactions, by exploiting a dispersive four-wave mixing approach. By adjusting the parameters of the qubits, effective quantum operations on the resonators can be realized from virtual transitions.

## 8. Plug-and-Play Surface Electrode Ion Traps for Scalable Quantum Information Processing

Charlie Doret, 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. Cutting edge experiments are transitioning from a few qubits to a few tens of qubits with many more qubits envisioned for the future. The underlying ion traps need to both grow with the experiments and provide additional features that can simplify and extend these experiments. The Georgia Tech Research Institute (GTRI) is developing modeling and fabrication processes for these new generations of ion traps in surface electrode architectures using silicon VLSI technology. GTRI has demonstrated traps that approach the plug-and-play ideal, featuring reliable ion loading and transport, long dark lifetimes, stable ion chains, and low heating rates, verified by detailed in-house characterization. Several linear geometries have been demonstrated with novel features such as micromirrors for large NA light collection and shaped RF rails for minimizing deformations to the trapping pseudopotential. Testing of additional features is underway, including integrated microwave current guides for global qubit rotations, a 4-way "X" junction, and a monolithic symmetric trapping architecture with large well depth.

## 9. Spatial Search by Non-Linear Quantum Walk

Mahdi Ebrahimi Kahou, Institute for Quantum Information Center

*Abstract.* Authors: Mahdi Ebrahimi Kahou, David L. Feder Affiliation: IQIS, University of Calgary Abstract: One approach to the development of quantum algorithms is the quantum walk. Spatial search can be effected by the continuous-time evolution of a single quantum particle on a lattice or graph containing a marked site. In most conceivable physical applications, however, one would rather expect to have multiple interacting particles. In bosonic systems at low temperatures, the dynamics would be well-described by a discrete non-linear Schr\" o dinger equation. We investigate the role of non-linearity in determining the efficiency of the spatial search algorithm within the quantum walk model, for a variety of graphs including the complete graph, hypercubes, and periodic lattices. The analytical results will be compared with numerical calculations of multiple interacting quantum walkers.

## 10. Ultimate precision limits for measurement of weak forces on noisy harmonic oscillators

Bruno Escher, Universidade Federal do Rio de Janeiro

*Abstract.* We obtain the ultimate precision allowed by the quantum mechanics on the estimation of the amplitude of a resonant weak force acting on a noisy harmonic oscillator, using the general method proposed in References [1,2]. In this case, that method leads to an exact analytical expression for the ultimate precision. REFERENCES: [1] B. M. Escher, R. L. de Matos Filho, and L. Davidovich, General Framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology, Nature Physics, vol. 7, 406 (2011). [2] B. M. Escher, R. L. de Matos Filho, and L. Davidovich, Quantum metrology with noisy systems, Brazilian Journal of Physics, vol. 41, 229 (2011).

## 11. Quantum secret sharing with reduced communication cost

Ben Fortescue, Southern Illinois University

*Abstract.* Standard techniques for sharing a quantum secret among multiple players (such that certain player subsets can recover the secret while others are denied all knowledge) require a large amount of quantum communication to distribute the secret. Two known methods for reducing this are the use of imperfect secret sharing (in which security is sacrificed for efficiency) and classical encryption. I will demonstrate how one may combine these methods to reduce the required quantum communication below what has been previously achieved (in some cases to a provable minimum) without any loss of security. Joint work with Gilad Gour.

## 12. Quantum Information Processing using Scalable Techniques

John Gaebler, National Institute of Standards and Technologies

*Abstract.* Authors: John Gaebler, Ryan Bowler, Yiheng Lin, Ting Rei Tan, David Hanneke, John Jost, Jonathan Home, Adam Meier, Emanual Knill, Dietrich Leibfried, David Wineland We report progress towards improving our previous demonstrations of scalable quantum information processing. In this work we combine all the fundamental building blocks required for scalable quantum information processing using trapped atomic ions. Included elements are long-lived qubits; a laser-induced universal gate set; state initialization and readout; and information transport, including co-trapping a second ion species to reinitialize the quantized motion without qubit decoherence. We are currently studying experimental techniques to efficiently measure the fidelity of quantum sequences involving multiple qubits using randomized benchmarking. To implement the benchmarking we perform quantum information sequences involving as many as 16 two-qubit gates and 50 single-qubit gates. We have also developed an arbitrary waveform generator with an update rate far above the ions' motional frequencies, which is capable of bringing together and then separating the qubit ions each time a two-qubit gate is performed.

## 13. Decoherence in OAM states due to turbulence

Jose Raul Gonzalez Alonso, University of Southern California

*Abstract.* Photons have always been the information carriers of choice in quantum information, with many protocols taking advantage of the polarization degrees of freedom to encode quantum information. Exploiting the photon's orbital angular momentum (OAM) can provide distinctive advantages. The main one is an increased alphabet size for information transmission. Since the Hilbert space of OAM states is infinite dimensional, it can be used to encode more than one bit (or qubit) per photon. However, this potential can only be realized if suitable quantum information can be encoded in the OAM photon states, and if it can be protected from the decohering effect of atmospheric turbulence. In this work, we will numerically simulate the errors induced by weak atmospheric turbulence in OAM states.

## 14. Quantum Circuit Optimization using Symbolic Gate Identities

Brian Granger, California Polytechnic State University

*Abstract.* Raymond Wong, California Polytechnic State University, San Luis Obispo, CA Addison Cugini, California Polytechnic State University, San Luis Obispo, CA Matt Curry, University of New Mexico, Albuquerque, NM Brian E. Granger, California Polytechnic State University, San Luis Obispo, CA In previous work, we have created an open source software package (SymPy) for simulating quantum computers symbolically. The symbolic manipulation of gates and circuits has many advantages over the traditional numerical approach where gates and qubits are represented as large matrices and vectors. First, extremely large circuits with many gates and qubits can be handled without memory constraints. Second, circuits can be manipulated symbolically using commutation relations, gate decompositions and gate identities. For example, these symbolic manipulations could be used to express a circuit in terms of a different set of universal one and two qubit gates. An important application of this symbolic approach is quantum circuit optimization. For our purposes, quantum circuit optimization consists of taking a known circuit of one and two qubit gates and reducing the overall gate count while taking constraints (for example, CNOT gates are the only allowed two qubit gate) into account. If possible, this type of circuit optimization would be useful for algorithm development as well as for optimizing practical implementations that include quantum error correction. We have started to develop tools for quantum circuit optimization within the context of our open source software. More specifically, we have developed an efficient algorithm for systematically discovering symbolic commutation relations, gate decompositions and gate identities. The algorithm is completely general and works for arbitrary sets of gates and numbers of qubits. We have benchmarked the algorithm by finding known basic gate identities and will report on our ongoing efforts to find additional non-trivial gate identities. We are working to build a library of symbolic gate identities that can be used subsequently for circuit manipulation and optimization. Finally, we will describe our initial work to apply the gate identities to the problem of circuit optimization.

## 15. Adiabatic Quantum Computing with Neutral Atoms

Aaron Hankin, Sandia National Laboratories

*Abstract.* We are developing, both theoretically and experimentally, a neutral atom qubit approach to adiabatic quantum computing (AQC). It has been shown in that neutral atoms trapped in optical far off-resonance traps (FORTs) can be used for two-qubit gates using interactions mediated by electric-dipole coupling of a coherently excited Rydberg state. A similar neutral atom system is attractive for this work due to the long-term coherence of the qubit ground states, the potential of multi-dimensional arrays of qubits in FORT traps and the potential for strong, tunable interactions via Rydberg-dressed atoms. If these arrays can be designed to encode a desirable computation into the system Hamiltonian one could use these tunable interactions along with single-qubit rotations to perform an AQC. Taking full advantage of Sandia's microfabricated diffractive optical elements (DOEs), we plan to implement such an array of traps and use Rydberg-dressed atoms to provide a controlled atom-atom interaction in atomic cesium. We forecast that these DOEs can provide the functions of trapping, single-qubit control and state readout resulting in an important engineering stride for quantum computation with neutral atoms. We will develop this experimental capability to generate a two-qubit adiabatic evolution aimed specifically toward demonstrating the two-qubit quadratic unconstrained binary optimization (QUBO) routine. We are studying the two-qubit QUBO problem to test the immunity of AQC to 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.

## 16. Microfabricated surface ion trap technology development for localized hyperfine qubit control

Clark Highstrete, Sandia National Laboratories

*Abstract.* C. Highstrete, S. Scott, C.D. Nordquist, J.E. Stevens, C.P. Tigges, M.G. Blain - Sandia National Laboratories, Albuquerque, NM. Microwave control of hyperfine ion qubits is a promising technology for quantum information processing. However, for free space microwaves, small field gradients on the atomic scale produce negligible coupling to motional modes used for qubit interaction. Additionally, the long wavelength precludes adequate focusing, causing all qubits to be simultaneously addressed. Recently, two-qubit gates were successfully demonstrated with a surface ion trap using sub-wavelength on-chip electrodes to provide the necessary field gradients.[1] At Sandia, we are working to integrate sub-wavelength microwave electrodes into microfabricated surface ion traps using our four-level-metal technology with the further goal of localizing the microwave fields to specific interaction regions. We will present our nascent efforts toward developing this microfabricated surface ion trap technology for localized hyperfine qubit control. 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. [1] C. Ospelkaus et al., Nature 476, 181 (2011)

## 17. 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 the process 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 one set of FG LDPC codes, where we modeled the noise as a depolarizing channel, and we found that these codes gave good performance only when the noise rate was low. For the set of codes we simulated, only some codes with small block size gave good performance at higher error rates (realistic for QKE), and those had low maximum key rate. Furthermore, it is possible for a classical FG LDPC codes to produce an entanglement-assisted code with negative net rate, further restricting the code selection. However, several other constructions of FG LDPC codes are known, and we continue to work on those constructions to find better codes for QKE, that work better at higher error rates.

## 18. Adiabatic Quantum Computation via the Rydberg Blockade

Tyler Keating, Univeristy of New Mexico

*Abstract.* We study an architecture for implementing adiabatic quantum computation with trapped neutral atoms. Ground state atoms are dressed by laser fields in a manner conditional on the Rydberg blockade mechanism, thereby providing the requisite entangling interactions. As a benchmark we study the performance of a Quadratic Unconstrained Binary Optimization (QUBO) problem whose solution is found in the ground state spin configuration of an Ising-like model. Adiabatic evolution of an ensemble of atoms is achieved by ramping down a fictitious magnetic field along the x-direction while ramping up local magnetic fields along the z-direction together with the Rydberg-dressed qubit-qubit coupling. We model a realistic architecture, including details of the atomic implementation, with qubits encoded into the clock states of 133Cs, effective B-fields implemented through microwaves and light shifts, and atom-atom coupling achieved by excitation to the 100P3/2 Rydberg level. Including the fundamental effects of photon scattering we find the fidelity of two-qubit implementation to be on the order of 0.98, with higher fidelities possible with improved laser sources. The system scales favorably, as seen in our models of three and four qubits.

## 19. Optimal EAQEC Codes of Small Length

Ching-Yi Lai, University of Southern California

*Abstract.* The dual of an entanglement-assisted quantum error-correcting (EAQEC) code is defined from the orthogonal group of a simplified stabilizer group. This duality leads to the MacWilliams identity for EAQEC codes by applying the Poisson summation formula from the theory of orthogonal groups, and the linear programming bounds for EAQEC codes follow in a natural way. We establish a table of upper and lower bounds on the minimum distance of any maximal-entanglement EAQEC code with length up to 15 channel qubits. Maximal-entanglement EAQEC codes can be viewed as a class of classical additive quaternary codes whose generators are pairs of symplectic partners. We improve the upper and lower bounds by discussing the existence of certain EAQEC codes.

## 20. Trapped Atoms with an Evanescent Field for Hybrid Quantum Systems

Jongmin Lee, Joint Quantum Institute, University of Maryland

*Abstract.* We explore uses of atoms trapped in evanescent optical fields for hybrid quantum information. A first system consists of an ensemble of Rb atoms trapped in the evanescent field of a nanofiber [1] coupled to the magnetic field in a lumped-element superconducting resonator [2] operating near the Rb ground state hyperfine frequency (6.8 GHz) as a step towards coupling atoms to a SQUID qubit. A second avenue explores uses of silicon waveguides instead of nanofibers and optical-to-microwave interfaces [3-5] for coherent communication. We will report on the parameter design and possible system performance as well as our experimental. Work supported by the NSF through the PFC at JQI and the ARO Atomtronics MURI. [1] E. Vetsch, D. Reitz, G. Sagué, R. Schmidt, S. T. Dawkins, and A. Rauschenbeutel, Phys. Rev. Lett. 104, 203603 (2010). [2] Z. Kim, C. P. Vlahacos, J. E. Hoffman, J. A. Grover, K. D. Voigt, B. K. Cooper, C. J. Ballard, B. S. Palmer, M. Hafezi, J. M. Taylor, J. R. Anderson, A. J. Dragt, C. J. Lobb, L. A. Orozco, S. L. Rolston, and F. C. Wellstood, AIP Advances 1, 042107 (2011) [3] M. Hafezi, Z. Kim, S. L. Rolston, L. A. Orozco, B. L. Lev., J. M. Taylor, arXiv:1110.3537v1 [quant-ph] (2011). [4] Mankei Tsang, Phys. Rev. A 84, 043845 (2011). [5] C. A. Regal and K. W. Lehnert, J. Phys.: Conf. Ser. 264 012025 (2011).

## 21. Quantum signatures of chaos in quantum tomography

Vaibhav Madhok, University of New Mexico

*Abstract.* Authors: Vaibhav Madhok, Carlos Riofrio, Ivan H. Deutsch. Abstract: We study the connection between quantum chaos and information gain in the time series of a measurement record used for quantum tomography. The record is obtained as a sequence of expectation values of a Hermitian operator evolving under repeated application of the Floquet operator of the quantum kicked top on a large ensemble of identical systems. We find an increase in information gain and hence higher fidelities in the process when the Floquet maps employed increase in chaoticity. We make predictions for the information gain using random matrix theory in the fully chaotic regime and show a remarkable agreement between the two. Finally we discuss how this approach can be used in general as a benchmark for information gain in an experimental implementation based on nonlinear dynamics of atomic spins measured weakly by the Faraday rotation of a laser probe.

## 22. Role of quantum discord in quantum communication.

Vaibhav Madhok, University of New Mexico

*Abstract.* We establish the role of quantum discord in quantum information theory. Firstly we show that discord is a measure of how coherently the mother protocol is performed in the presence of decoherence. Since the mother protocol is a unification of an important class of problems (those which are bipartite, unidirectional and memoryless), we show discord to be a measure of how coherently any of these protocols can be performed. We explicitly demonstrate the role quantum discord plays in quantum state merging, noisy super-dense coding, entanglement distillation and noisy teleportation. We also describe a similar role for quantum discord in quantum computation and correlations erasure. Thus quantum discord can be regarded as the advantage of quantum coherence in quantum information theory as a whole.

## 23. Can the Heisenberg limit be surpassed?

Ruynet Matos Filho, Universidade Federal do Rio de Janeiro

*Abstract.* The error in the estimation of parameters characterizing dynamical process decreases with the number N of resources employed in the measurement. Quantum strategies may improve the precision for noiseless processes, by an extra factor that depends on the inverse of the square root of N, leading to the so-called Heisenberg limit. Recently, questions have been raised on whether this limit could be surpassed. Here a general framework to tackle this problem is presented. It involves the consideration of corrections to the quantum Cramér-Rao bound that arise when the number of repetitions of the measurement is finite, and it leads to analytical expressions of lower bounds for this number so that these corrections become negligible. These results are used to challenge recent claims that the Heisenberg limit can be beaten.

## 24. Neutral atom quantum computing with the dipole traps formed behind a circular aperture

Danielle May, California Polytechnic State University, San Luis Obispo

*Abstract.* The field of neutral atom quantum computing has made encouraging progress towards creating a quantum computer. The neutral atom quantum computing community has experimentally demonstrated the initialization, the readout, and a universal set of quantum gates for neutral atoms trapped in optical dipole traps. Neutral atoms have long decoherence times due to their weak coupling with the environment in their ground state. One remaining problem for neutral atom quantum computing is to create an array of trapped atoms that can be individually addressed for initialization, readout, single, and two qubit gates. Our research team has created a cloud of cold 87Rb atoms in a Magnet-Optical Trap (MOT). The next step is to trap the cold atoms in the dipole traps formed by the bright or dark regions produced in the diffraction pattern formed immediately behind a circular aperture. The atoms can be trapped in the intensity minima for blue laser detuning, or the intensity maxima for red laser detuning. The position of the trapped atoms can be manipulated by tilting the beam incident on the circular aperture. Exploiting the light polarization dependence of the magnetic substates of the atoms allows two trapped atoms to be brought together or apart to facilitate two qubit gates without significant losses due to tunneling or Raman scattering. This system can be scaled up to many dipole traps by creating a 2D array of circular apertures. The center-to-center distance between adjacent circular apertures determines the distance between the trapped atoms. This technique potentially has the ability to produce a scalable system of qubits while allowing each qubit to be individually addressed. We anticipate demonstrating these dipole traps by projecting the diffraction pattern with a lens onto the cloud of cold atoms in the MOT. Once this is accomplished we will measure the trap properties and compare them to our computational results. In this presentation we summarize our computational results for these traps and will report our experimental progress to date. This work was performed in collaboration with Travis Frazer, Sara Monahan, David Roberts, Jennifer Rushing, 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.

## 25. Design and Construction of a Nanofiber-based Quantum Interface

Pascal Mickelson, University of Arizona

*Abstract.* We describe the design and construction of 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 producing cold atom samples and loading them into these nanofiber traps.

## 26. 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 loaded cesium atoms into a ~50 uK deep optical dipole trap, and we observe Faraday rotation of the probe light as it passes through this cloud of atoms. Work is ongoing to increase the optical depth of the atom sample and to optimize the atom-light coupling by mode-matching the probe beam to the atom sample.

## 27. Surface studies of microfabricated ion traps

Oliver Neitzke, University of California at Berkeley

*Abstract.* Miniaturization of ion traps may be a suitable approach to scalable quantum information processing if the excessive noise of ion traps is understood and controlled. In recent years, with the increased use of micro fabricated surface traps, the excessive heating of trapped ions has come to the attention and ideas about its possible sources have been proposed. Electric field noise created by surface effects is thought to be one possible cause. Our work will relate the trap electric field noise to its surface properties. With a newly developed design of a ion trap vacuum chamber with integrated surface science tools, we can analytically characterize and modify our trap composition. The apparatus is in the final construction stage. It consists of an annealing lamp, an ion gun, and a UV lamp to alter the structure and composition of our trap surfaces. An Auger spectrometer with LEED capability can analyze these variations of the trap surface. In addition, we have developed micro fabrication methods allowing us to explore a variety of novel trap materials, such as refractory metals and surfaces passivated with graphene.

## 28. Toward Ion-Photon Entanglement

Thomas Noel, University of Washington

*Abstract.* We present work toward ion-photon entanglement in a trapped barium ion system. The work is being done in a newly fabricated linear Paul trap, which has an integrated spin-flip electrode for coherent control of the ion's electronic ground state. We excite 138Ba+ on the 6S1/2-6P1/2 dipole transition with frequency doubled light from a Ti:Sapph laser tuned to 986 nm. The polarization state of the subsequent spontaneously emitted photon is entangled with the resulting ionic ground state. This work is an initial step toward long-distance remote entanglement of ions. Barium is a good candidate for such work due the relatively long wavelengths of the transitions involved.

## 29. Complete characterization of linear amplifiers including the quantum limits for nongaussian noise

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

*Abstract.* We characterize the quantum limitations on the entire probability distribution of added noise in a phase-preserving linear amplifier. Previously the quantum limits on amplifiers have been given entirely in terms of second moments. As Josephson parametric amplifiers approach fundamental quantum limits on noise temperature, it becomes important to investigate the limits on higher moments of the amplifier noise. We prove that all phase-preserving linear amplifiers with arbitrary noise are formally equivalent to a parametric amplifier ,i.e. a two-mode squeeze operator with a physical state of an ancillary mode whose quantum noise determines the noise properties of the amplifier. We also discuss generalizations to the nondeterministic linear amplifiers proposed by Ralph and Lund.

## 30. Manipulation of small atom clouds in a microscopic dipole trap

Joseph Pellegirno, Laboratoire Charles Fabry

*Abstract.* Ronan Bourgain, Joseph Pellegrino, Yvan R.P. Sortais and Antoine Browaeys Laboratoire Charles Fabry, Groupe Optique Quantique - Atomes, Institut d�Optique, Avenue de la Vauve 91127 Palaiseau Cedex, France Recent years have seen a growing interest in the study of small, but dense cold atomic ensembles. Here we present our progress on the manipulation of cold atomic clouds in a regime where they contain only a few tens of atoms. In our case we use 87Rb atoms, trapped in a microscopic optical dipole trap, to study this mesoscopic regime. We use a single atom to measure the resolution of our imaging system [1]. This provides a calibration of our detection scheme which is useful to understand the regime where a few atoms are trapped [2]. In particular it was applied to the measurement of dipole trap losses due to the presence of near resonant light [3]. These results indicate that the loading, in presence of two body losses leads to a subpoissonian atomic number distribution.We also perform a lossless state preparation, and detection on single atom [4]. All these tools should be useful for the realisation of a BEC with a few atoms only. [1] A. Fuhrmanek, A. Lance, C. Tuchendler, P. Grangier, Y.P.R. Sortais and A. Browaeys, "Imaging a single atom in a time-of-flight measurement.�, NJP 12, 053028 (2010). [2] A. Fuhrmanek, Y. R. P. Sortais, P. Grangier, and A. Browaeys, "Measurement of the atom number distribution in an optical tweezer using single-photon counting�, PRA 82, 023623 (2010). [3] A. Fuhrmanek, R. Bourgain, Y.R.P. Sortais, A. Browaeys, "Large light-assisted collision rates between cold atoms in amicroscopic dipole trap", ArXiv 1107.5781 (2011). [4] A. Fuhrmanek, R. Bourgain, Y. R. P. Sortais, and A. Browaeys, "Free-Space Lossless State Detection of a Single Trapped Atom", PRL 106, 133003 (2011).

## 31. Backaction of Microwave Photon Detection by a Strongly Coupled Josephson Junction

Emiy Pritchett, Saarland University

*Abstract.* We analyze the functionality of on-chip Josephson junctions as single microwave photon detectors, as has been demonstrated recently in Chen, et al., arXiv:1011.4329. The Josephson junction device, which we refer to as a Josephson Photomultiplier (JPM), acts as a nearly perfect binary detectors of microwave photons by undergoing an observable switching event when there are one or more photons in an incident cavity. We analyze the backaction of this switching event on the state of incident light, including the energy dissipation and dephasing affecting an imperfect JPM. This analysis improves the efficiency and fidelity with which a JPM reconstructs the state of light in an incident transmission line `cavity', which are commonly used to store and transfer quantum states in implementations of circuit-QED.

## 32. Trapping atoms around nanofibers

Sylvain Ravets, University of Maryland

*Abstract.* Coupling atomic and superconducting qubits in a hybrid quantum platform is a promising option for quantum information. To build such a system, drastic experimental conditions have to be met: in our project, classical atom-light techniques used to control atoms must fit in the millikelvin temperature environment necessary to work with superconducting qubits. To limit the heating induced by the trapping light, we take advantage of nanofiber traps [1]: by superposing the repulsive and attractive potentials induced by the evanescent blue-detuned and red-detuned light fields propagating around a tapered nanofiber, it is possible to create a potential well to trap atoms. In this poster, we present recent results on long tapered fibers from our fiber puller. We can reliably produce tapered optical fibers with a waist up to 10 cm in length and down to 500 nm in diameter. By controlling the geometry of the tapered region, we can reach the adiabatic regime and minimize losses given our size constraints. Work supported by the NSF through the PFC at JQI and SR thanks the Fulbright Fellowship. [1] E. Vetsch, D. Reitz, G. Sagué, R. Schmidt, S. T. Dawkins, and A. Rauschenbeutel, Phys. Rev. Lett. 104, 203603 (2010).

## 33. Continuous measurement quantum state tomography of atomic spins

Carlos Riofrio, University of New Mexico

*Abstract.* C. Riofrío and I. H. Deutsch, Department of Physics and Astronomy, Center for Quantum Information and Control , University of New Mexico. A. Smith, B. E. Anderson, H. Sosa, and P. Jessen, College of Optical Sciences, Center for Quantum Information and Control, University of Arizona. Quantum state tomography is a fundamental tool in quantum information science and technology. It requires estimates of the expectation values of an "informationally complete" set of observables. This is, in general, a very time-consuming process that requires a large number of measurements to gather sufficient statistics. There are, however, systems in which the data acquisition can be done more efficiently. An ensemble of quantum systems can be prepared and controlled by external fields while being continuously and collectively probed, producing enough information in the time-evolving measurement record to estimate the initial state [1]. Such protocol has the advantage of being fast and robust. In this poster, we present a study of a continuous-measurement quantum-state tomography protocol and its application to controlling large spin ensembles. We perform reconstruction of quantum states prepared in the 16 dimensional ground-electronic hyperfine manifolds of an ensemble of 133Cs atoms, driven by microwaves and radio-frequency magnetic fields and probed via polarization spectroscopy [2]. We present theoretical and experimental results of its implementation and discuss two estimation methods: constrained maximum likelihood and compressed sensing. We show the exquisite level of control achieved in the lab and the excellent agreement between theory and experiment. Moreover, we are able to achieve fidelities >95% for low complexity quantum states, and >92% for arbitrary random states. [1] A. Silberfarb and I. H. Deutsch, "Quantum-state reconstruction via continuous measurement", Phys. Rev. Lett. 95, 030402 (2005). [2] C. A. Riofrío, P. S. Jessen, and I. H. Deutsch, "Quantum tomography of the full hyperfine manifold of atomic spins via continuous measurement on an ensemble", J. Phys. B: At. Mol. Opt. Phys. 44 (2011) 154007.

## 34. Entanglement quantification with finite data

Lucia Schwarz, Oregon Center for Optics, University of Oregon

*Abstract.* In recent experiments, more and more qubits have been entangled in a GHZ state. We simulated a measurement on a noisy GHZ state with fixed measurement settings. Thanks to information criteria, we can simulate states with up to 52 qubits. The question is, how often do we have to repeat those measurements in order to get a reliable estimate of entanglement? And how does this depend on the number of qubits?

## 35. Towards building hybrid quantum systems out of wires, ions, and solid-state devices.

Sankaranarayanan Selvarajan, University of California, Berkeley

*Abstract.* Oscillating trapped ions induce currents in nearby electrodes. These currents can be send either to electrical devices such as tank circuits or to another ion. Here we discuss progress towards both goals. We developed a high-quality tank circuit with a resonance frequency of approximately 1 MHz. Winding the coil from niobium wires, we find for the fundamental and higher order modes quality factors between 27,000 and 160,000 at temperatures around 5 K. For the fundamental mode (Q=27,000 at 1.1 MHz) we find a damping time of 3.5 ms. Connecting the resonator to trap electrodes and assuming an ion 50 μm above a surface trap, we expect an ion-resonator coupling of 2π*450 Hz, entering the strong coupling regime. Initial experiments will use multiple ions to increase the coupling strength. We also discuss progress in coupling ions through a macroscopic wire. With two ions trapped close to either end of a gold wire about 1mm in length, we estimate that the ions can coherently exchange a motional quantum in about 1ms, significantly faster than the estimated T1 times at cryogenic temperatures. By determining the capacitance between the wire and the trap electrodes, we have modified our electrostatic trap simulations to include the effect of the electrically floated wire on the trapping potentials. Both the ion-resonator coupling and the wire mediated coupling between two ions can be used to construct hybrid quantum systems out of ions and solid state devices.

## 36. Quantum control of spin correlations in an atomic ensemble

Robert Sewell, Institute of Photonic Sciences

*Abstract.* We report on an an experimental project designed to measure and control spin correlations in an ensemble of laser cooled rubidium atoms. Through a combination of spin-squeezing via quantum-non-demolition (QND) measurement, and real-time incoherent feedback (optical pumping), we aim to generate a macroscopic singlet state in an ensemble of up to 1 millions atoms. The singlet state is characterized by a generalized spin-squeezing inequality, ξ=Σi(ΔFi)^2/Nf ≤ 0, where ξ<0 implies non-classical spin correlations and entanglement amongst the atoms. It has potential application in quantum memories for storing information in decoherence-free subspaces, and in quantum metrology for magnetic field gradiometry, and is an example of real-time engineering of quantum correlations in a macroscopic atomic ensemble. We conditionally squeeze the quantum noise in each angular momentum component below the standard quantum limit via projection-noise limited QND measurement. Real-time optical pumping feedback based on the measurement outcome restores the average angular momentum to zero. In this way, by working with an unpolarised atomic ensemble, we avoid back-action and are able to simultaneously squeeze all three angular momentum components. In the experimental apparatus, micro-second pulses of polarised light interact with an elongated atomic cloud and are detected by a shot-noise-limited polarimeter. The experiment achieves projection-noise limited sensitivity, as calibrated against a thermal spin state, and we have recently demonstrated spin squeezing of atoms in the F=1 hyperfine ground state. We have developed an FPGA-based detection and feedback device for real-time control of quantum correlations. Here we report preliminary results towards generating a macroscopic singlet state.

## 37. Quantum Control and Quantum State Tomography in the Hyperfine Ground Manifold of Atomic Cesium

Hector Sosa-Martinez, University of Arizona

*Abstract.* Aaron Smith, Brian E. Anderson, Hector Sosa Martinez, Poul Jessen Center for Quantum Information and Control (CQuIC), College of Optical Science and Department of Physics, University of Arizona Carlos Riofrio, Ivan H. Deutsch Center for Quantum Information and Control (CQuIC), Department of Physics and Astronomy, University of New Mexico. Quantum systems with Hilbert space dimension greater than two (qudits) provide an alternative to qubits as carriers of quantum information, and may prove advantageous for quantum information tasks if good laboratory tools for qudit manipulation and readout can be developed. We have successfully implemented a protocol for arbitrary quantum state-to-state mapping in the 16 dimensional hyperfine ground manifold of Cesium 133 atoms, using only static, radio frequency (rf) and microwave magnetic fields to drive the atomic evolution. This system is controllable given rf and microwave fields with constant amplitude and frequency, and piecewise constant phase modulation. Control waveforms (rf and microwave phases versus time) are found by numerical optimization, and can be designed to work well in the presence of errors in the driving and background magnetic fields. Experimentally, we achieve an average state mapping fidelity of 99% for a sample of randomly chosen target states. To perform quantum state tomography, we drive an ensemble of identically prepared atoms with phase modulated rf and microwave magnetic fields, and simultaneously probe them by coupling an atomic spin observable to the polarization of a near-resonant optical probe field. A measurement of the probe polarization then yields an informationally complete measurement record that can be inverted to obtain an estimate of the unknown quantum state. We have reconstructed the full density matrix for a set of randomly chosen test states, using computer algorithms based either on least squares fitting or compressed sensing. The latter approach reconstructs our test states with an average fidelity above 90%, limited primarily by errors in applied drive fields.

## 38. Trapping 40Ca+ in a segmented annular (ring) trap

Boyan Tabakov, University of New Mexico, Sandia National Laboratories

*Abstract.*

Authors: B. Tabakov, F. Benito, M. G. Blain, M. Descour, L. Fang, K. M. Fortier, R. A. Haltli, C. Highstrete, T. L. Lindgren, D. L. Moehring, M. E. Smith, J. D. Sterk, D. L. Stick, C. P. Tigges

Abstract: We report on operating and characterizing a surface ion trap with segmented annular (ring) geometry under the Multi-Qubit Coherent Operations MUSIQC collaboration. We describe a surface trap technology that utilizes four metal level technology allowing for leadless electrodes. Other key advances implemented in the ring trap fabrication are precision backside loading holes and low profile wire bonds. Robust loading and shuttling of single 40Ca+ has been demonstrated. Efforts towards loading multiple ions, micromotion compensation, and heating rate measurements are underway.

## 39. Towards understanding thermodynamics and energy transport in strings of trapped ions.

Ishan Talukdar, University of California, Berkeley

*Abstract.* We report experiments on laser induced heating of ions confined in a linear Paul trap. Specifically, we investigate the mechanism of melting of a crystallized ion chain due to heating by light detuned blue from an atomic resonance. In these experiments, we observe the decay of ion fluorescence as we shine laser light on either the entire ion string or a small subset. From these measurements we hope to extract information on the thermodynamic properties of such Coulomb crystals. Understanding these properties, together with the ability to address individual ions will facilitate the study of excitation transfer dynamics along the chain.

## 40. Effect of the basis-dependent flaw on the security of quantum key distribution system

Kiyoshi Tamaki, NTT Basic Research Laboratories

*Abstract.* In this presentation, we study the effect of the basis-dependent flaw on the security of quantum key distribution system, especially in the context of measurement device independent quantum key distribution (MDIQKD). We propose two schemes for the phase encoding scheme for MDIQKD, the first one employs a phase locking technique with the use of non-phase-randomized coherent pulses, and the second one uses conversion of standard BB84 phase encoding pulses into polarization modes. We prove the unconditional security of these schemes and we also simulate the key generation rate based on simple device models that accommodate imperfections. Our simulation results show the feasibility of these schemes with current technologies and highlights the importance of the state preparation with good fidelity between the density matrices in the two bases. Since the basis-dependent flaw is a problem not only for MDIQKD but also for standard QKD, our work highlights the importance of an accurate signal source in practical QKD systems.

## 41. Magically, negativity of the Wigner function is useful

Victor Veitch, Institute for Quantum Computing

*Abstract.* It is possible to represent d-dimensional quantum states as probability distributions over a phase space of d^2 points. However, to encompass the full quantum formalism we must allow negative representations. The well known magic state model of quantum computation gives a recipe for universal quantum computation using perfect Clifford operations and repeated preparations of a noisy ancilla state. It is an open problem to determine which ancilla states enable universal quantum computation in this model. In this paper we show that for systems of odd dimension a necessary condition for a state to enable universal quantum computation is that it have negative representation in a particular quasi-probability representation which is a discrete analogue to the Wigner function. This condition implies the existence of a large class of bound states for magic distillation: states which cannot be prepared using Clifford operations but which are not useful for quantum computation. This settles in the negative the conjecture that all states not representable as a convex combination of stabilizer states enable universal quantum computation.

## 42. The approach to typicality in many-body quantum systems

Sai Vinjanampathy, University of Massachusetts, Boston

*Abstract.* The recent discovery that for large Hilbert spaces, almost all (that is, typical) Hamiltonians have eigenstates that place small subsystems in thermal equilibrium, has shed much light on the origins of irreversibility and thermalization. Here we give numerical evidence that many-body lattice systems generically approach typicality as the number of subsystems is increased, and thus provide further support for the eigenstate thermalization hypothesis. Our results indicate that the deviation of many-body systems from typicality scales as an inverse power of the number of systems, and we compare this with the equivalent scaling for random Hamiltonians.

## 43. Coupling Neutral Atoms to Superconducting Circuits

Kristen Voigt, Joint Quantum Institute, Department of Physics, University of Maryland and National Institute of Standards and Technology, College Park, MD 20742, United States

*Abstract.* We have developed a lumped-element thin-film superconducting resonator [1] for coupling to the hyperfine transition of 87Rb at 6.834683 GHz. The resonator operates on the cold stage of a dilution refrigerator. It is made by photolithographic patterning of Al that has been deposited on a sapphire substrate. By moving a carefully machined Al pin towards the inductor of the resonator using a piezoelectric stage, we can to tune the resonance frequency, in situ at 15mK, over a range of 35 MHz and within a few kHz of the Rb resonance while maintaining a quality factor greater than 60,000. We will discuss our tuning results and an initial design for coupling the resonator to 87Rb atoms trapped on a tapered optical fiber.

Work supported by NSF through the Physics Frontier Center at the Joint Quantum Institute.

[1] Z. Kim et al., AIP ADVANCES**1**, 042107 (2011)

## 44. TIQC-SPICE: a simulator for trapped-ion quantum computing

Shannon Wang, Massachusetts Institute of Technology

*Abstract.* Quantum computing experiments are growing in capability and complexity; to realize algorithms, the effects of noise on long computations need to be predicted, understood and minimized. TIQC-SPICE is a modelling system for trapped ion quantum computing experiments. It simulates practical pulse sequences for realizing quantum algorithms by numerically evolving the system Hamiltonian in the presence of various noise sources corresponding to physical errors and technical imperfections in the experiment. These noise sources are modelled by making close correspondence between physically relevant parameters and theoretical noise models, and are simulated via Monte-Carlo methods. Simulated and experimentally measured gate fidelities for a pulse sequence that realizes the Quantum Fourier Transform on 3 ions show good agreement. Finally, we propose and evaluate the in-circuit fidelity of a number of single- and two-qubit gates; this fidelity measure bounds individual gates given a limited set of measurements on a complete pulse sequence and provides a practical alternative to full process tomography.

## 45. Heating studies with an in-situ-cleaned surface-electrode ion trap

Andrew Wilson, National Institute of Standards & Technology

*Abstract.* Anomalous heating is a major obstacle to the development of scalable quantum information processors based on trapped atomic ions. Miniaturized traps can achieve high trap frequencies for fast gate operations and quick transport, but the ions are confined in close proximity to surfaces where motional decoherence is rapid. Suppression of motional heating has been demonstrated at cryogenic temperatures, but fabrication issues appear to cause variable results. Moreover, motional decoherence remains substantially more rapid than expected from Johnson electric field noise. Despite investigations by many groups, the physical origin of the electric field noise that causes this motional heating has not yet been identified. However, a number of studies suggest that it might be caused by electrode surface effects. We describe a micro-fabricated, surface-electrode, 9Be+ ion trapping apparatus with an integrated ion-bombardment cleaning capability that allows us to remove contaminant layers from the surfaces of the trap's gold electrodes. We report characterization of the surface properties of our traps (including Auger spectroscopy analysis), results of our cleaning procedures, as well as heating measurements performed before and after cleaning. Work in the laboratory is on-going, but to date the observed heating rate has been unaffected by the surface cleaning. The observed electric field noise is amongst the lowest measured in a room-temperature ion trap with an ion-electrode distance comparable to ours, but still more than three orders of magnitude higher than the Johnson electric field noise calculated for this apparatus. We characterized the heating under a variety of trapping conditions, and describe our efforts to test for and eliminate sources of externally injected noise. * Supported by IARPA, NSA, DARPA, ONR, and the NIST Quantum Information Program

## 46. Towards a quantum-limited, broadband microwave parametric amplifier

Emma Wollman, California Institute of Technology

*Abstract.* It is well known that a phase-preserving linear amplifier must add, at minimum, a half-quantum of noise. For microwave signals, however, commonly-used cryogenic HEMT amplifiers operate more than 50 times above this limit. Recently demonstrated Josephson parametric amplifiers are now operating near the quantum limit, but are fundamentally narrowband due to their standing-wave design. We have developed parametric amplifiers that use the non-linear kinetic inductance of a superconducting NbTiN transmission line to amplify microwave signals with a wide bandwidth. Due to the low-loss properties of NbTiN, these amplifiers should be able to operate near the quantum limit for a large range of input powers. In addition, by utilizing a traveling-wave rather than a standing-wave configuration, these devices can have bandwidths of several octaves and can be designed to operate at frequencies from the microwave to the submillimeter-wave band. These amplifiers are expected to have many applications in low-temperature fields such as sub-millimeter astronomy, precision measurement, quantum information, and tests of fundamental quantum physics. We present initial results that demonstrate wide-bandwidth gain and low added noise values.

## 47. PCB-based Ion Chip Trap Mounting

John Wright, University of Washington

*Abstract.* Planar ion chip traps are good quantum computer candidates because DC control electrodes placed within hundreds of microns of the trapping region allow fine control over multiple trapped ions simultaneously. Recently fabricated chips include mounted optical cavities or fabricated mirrors for photon collection and printed microwave coils for driving hyperfine transitions. In order to facilitate easily mounting and frequently upgrading these traps, we have designed a UHV-compatible printed circuit board that connects CPGA-100 socket chip trap carriers to four DB-25 vacuum feedthroughs. The board incorporates low-pass filters on the DC control pins approximately 1 cm from the chip to quickly route capacitive RF pickup to ground. The PCB should provide more stable DC control voltages than the more common method of routing individual wires for each control pin to filters outside the vacuum chamber. We have reached UHV with the assembled system without significant problems, and are currently attempting to trap Barium ions.

## 48. Fast controlled unitary protocols using group or quasigroup structures

Li Yu, Carnegie Mellon University

*Abstract.* A nonlocal bipartite unitary gate can sometimes be implemented using prior entanglement and only one round of classical communication in which the two parties send messages to each other simultaneously. This cuts the classical communication time by a half compared to the usual protocols, which require back-and-forth classical communication. We introduce such a fast protocol that can implement a class of controlled unitaries exactly, where the controlled operators form a subset of a projective representation of a finite group, which may be Abelian or non-Abelian. We also introduce a modified version of the protocol for the approximate implementation of controlled unitaries. This protocol makes use of quasigroups, which are closely related to Latin squares. We then show that by using enough entanglement, this fast protocol can implement all controlled unitaries approximately. The entanglement cost of our protocols is compared with other fast unitary protocols in the literature. The cost is quite small when the form of the unitary is relatively simple.