# 2010 Poster Abstracts

## 1. Scalable Ion Traps for Quantum Information Processing

Jason Amini, National Institute of Standards and Technology

**Abstract**. The basic components for a quantum information processor using trapped ions have been demonstrated in a number of experiments. To perform complex algorithms that are not tractable with classical computers, these components need to be integrated and scaled to larger numbers of qubits. We report the design, fabrication, and preliminary testing of a 150 zone array built in a `surface-electrode' geometry microfabricated on a single substrate. We demonstrate transport of atomic ions between legs of a `Y'-type junction and measure the in-situ heating rates for the ions. The trap design demonstrates use of a basic component design library that can be quickly assembled to form structures optimized for a particular experiment. *Work supported by IARPA, DARPA, NSA, ONR, Sandia, and the NIST Quantum Information Program.

## 2. Synchronization of Barium Ion Qubit Controls

Aaron Avril, University of Washington

**Abstract**. We report on the progress of construction and integration into experiment of a pulse programmer for synchronizing equipment used in Ba+ ion hyperfine qubit control. The hardware includes 3 direct digital synthesizer (DDS) boards for synthesizing wave packets of arbitrary frequency, amplitude, and phase with frequencies up to 800MHz, 28 TTL outputs with rise times below 5ns, and 8 TTL inputs. Together, these features may be used to control acousto-optical modulators, shape laser pulses, trigger lab equipment, read the data, and react to external events. This hardware is synchronized to a single internal clock, and controlled by a sequencer board that distributes commands from user-specified functions. At the time of writing, we are in the process of characterizing the behavior of the DDS boards to ensure reliability. We are developing firmware to count inputs from a photomultiplier tube that will be used to record detection of the qubit state.

## 3. Ultra Smooth Microfabricated Mirrors for Atom Chip Based Cavity QED

Grant Biedermann, Sandia National Laboratories

*Collaborators*: T. Loyd, F. Benito, G. Biedermann, K. Fortier, D. Stick, P. Schwindt, M. Blain, Sandia National Laboratories, Albuquerque, NM 87185

**Abstract**. Microfabricated optical cavities are an attractive system for atomic physics research. When paired with an atom the small mode volume can lead to strong atom-cavity coupling with only a modest finesse. Such systems are of significant interest for applications in quantum information [1]. While experiments using a single cavity or a small number of cavities tend to be tractable, scaling the number of cavities required for a useful quantum network remains speculative [2]. In response, we are blending microfabricated Si mirrors [3] with atom chip technology and its inherent precision [4]. We have demonstrated that our micro-mirror fabrication technique produces ultra smooth mirror surfaces of 2.16 Angstroms rms. Optical cavities formed with these mirrors exhibit a high finesse of 64,000. This performance leads to a calculated single atom cooperativity of over 200 making these cavities attractive candidates for integrated cavity QED experiments and quantum information processing on a chip. [1]. P K. Vahala, ed., Optical Microcavities, (World Scientific, Singapore, 2004). [2]. H. J. Kimble, Nature, 453, 1023 (2008). [3]. M. Trupke, E. A. Hinds, S. Eriksson, E. A. Curtis, Z. Moktadir, E. Kukharenka, and M. Kraft, Appl. Phys. Lett., 87, 211106 (2005). [4]. Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, J. Reichel, Nature, 450, 272 (2007).

## 5. Quantum Information and Simulation with ^{87}Sr

Michael Bishof, JILA/University of Colorado at Boulder

**Abstract**. Quantum Information and Simulation with ^{87}Sr Michael Bishof, Matthew Swallows, Michael J. Martin, Yige Lin, Sebastian Blatt, Travis L. Nicholson, Benjamin Bloom, and Jun Ye Fermionic alkaline earth(like) atoms have recently attracted considerable attention in the context of quantum information science. When trapped in optical lattices, their unique properties offer novel solutions to current challenges in neutral atom quantum information processing. Recent proposals have outlined schemes for quantum computation that employ these atoms as single qubits or few qubit registers. In a broader context, new ideas have emerged on how to use lattice-trapped alkaline earth atoms as quantum simulators of unique many-body phenomena. We present possible implementations of these proposals for the specific case of ^{87}Sr, a fermionic isotope with a 9/2 nuclear spin.

## 6. Arbitrary and Dynamic Painted Potentials for Bose-Einstein Condensates

Malcolm Boshier, Los Alamos National Labs.

Collaborators**: **Changhyun Ryu, Kevin C. Henderson, and Malcolm G. Boshier

**Abstract**. We report on a robust and straightforward method to create potentials for trapping Bose- Einstein condensates which are simultaneously dynamic, fully arbitrary, and sufficiently stable to not heat the ultracold gas. Our technique uses a rapidly-moving laser beam that “paints” a time-averaged optical dipole potential in which we create BECs in a variety of geometries, including toroids, ring lattices, and square lattices. Matter wave interference patterns confirm that the trapped gas is a condensate. As a simple illustration of dynamics, we show that the technique can transform a toroidal condensate into a ring lattice and back into a toroid.

## 7. Atom-chip based tunable optomechanical system

Thierry Botter, UCB

**Abstract**. Ultracold atoms placed inside high-finesse cavities have provided a new perspective on optomechanics. Much like their solid-state counterparts, involving micromechanical membranes and small-scale cavities, these atom-based systems involve strong coupling between the mechanical motion of the atomic ensemble and the circulating light field. However, they have the added benefits of having a low thermal occupation number and little coupling to the surroundings. In our atom-chip based optomechanical system, atoms can be freely positioned relative to the standing wave, leading to both linear and quadratic optomechanical coupling, with contrast as large as 80%. Both the mechanical resonator frequency and the coupling strength can be tuned by varying the intracavity field intensity.We report on recent results from this system, including optical bistability, optomechanical frequency shift and heating in both coupling regimes.

## 8. 4.2 K surface electrode trap for Be+ ions

Kenton Brown, National Institute of Standards and Technology

**Abstract**. Ion traps with cryogenic electrodes present several advantages over their room temperature counterparts, including longer ion lifetimes, lower motional heating rates, and the possibility of coupling ions to other systems that function only at cryogenic temperatures. We have recently built a surface electrode ion trap for Be+ ions (ion height 40 microns) that incorporates electrodes cooled to 4.2 K, a bakeable copper vacuum enclosure surrounding the electrodes, and an achromatic, completely reflective, in-vacuum imaging objective. Preliminary results indicate an ion lifetime limited only by the stability of our cooling laser, effective shielding from magnetic field fluctuations, and high trapping frequencies (> 30 MHz). We will present these results as well as initial data on ion heating. We will also discuss our plans for experiments taking advantage of the low heating rates that should be realizable in this apparatus. This work is supported by DARPA, NSA, ONR, IARPA, Sandia and The NIST Quantum Information Program.

## 9. Optical ultra-precise parameter estimation

Hugo Cable, Centre for Quantum Technologies

**Abstract**. I will present the results of collaborative work with Gabriel Durkin on optical ultra-precise parameter estimation [1]. We are investigating the application of multi-photon entangled light generated by parametric down-conversion, and more specifically of singlet states defined in two pairs of polarization modes. The symmetry of these states is maintained under the action of a loss channel, and this suggests the usefulness of the source for quantum sensor applications. We have considered one and two-parameter detection, and also the possibilities for differential measurements between two spatially-separate regions. In a lossless setting, optimal parameter- independent scaling of sensitivity at the Heisenberg limit is possible using number-resolved photodetectors. We find that supra-classical precision is possible for moderate photon losses also. [1] Cable and Durkin arXiv:0910.1957 (2009)

## 10. Scalar and vector differential light shift measurements in optical lattice- trapped ^{87}Rb

Radu Chicireanu, NIST/Joint Quantum Institute

**Abstract**. The existence of „magic wavelengths‟ for hyperfine transitions in alkali atoms is of interest for their applications in quantum information and frequency metrology. Magic wavelength predictions for Rb and Cs have met with some controversy, and it is likely that they do not exist in "traditional" optical lattices. In a state-dependent lattice though, the scalar and vector differential light shifts can have opposite signs, leading to a prospected significant reduction in the sensitivity of the transition frequency to fluctuations in the trapping light field. We investigate this effect, and present preliminary results of a precision measurement of light shifts in lattice-trapped ^{87}Rb, focusing on the differential light shift between the ground-state hyperfine levels F=1,2.

## 11. A fully connected qubit network model for quantum information processing applications

Mark Coffey, Colorado School of Mines

**Abstract**. We describe a fully connected spin network model for quantum information processing applications. This scalable network in the case of spin 1/2 has recently been realized in the laboratory, using Josephson phase qubits, and other solid-state implementations are likely. We have recently jointly developed a rigorous protocol for producing the important maximally entangled generalized GHZ states for this implementation [1]. An exact solution for the eigenstructure of a certain subspace of partial uniform superpositions enables the protocol to be detailed for an arbitrary number of qubits. An investigation of other quantum information processing applications of the spin network is underway. Joint work with Andrei Galiautdinov and Ron Deiotte. [1] A. Galiautdinov, M. W. Coffey, and R. Deiotte, arXiv:0907.2225v2 (2009); to appear in Phys. Rev. A. Work of MWC and RD partly supported by Northrop Grumman.

## 12. Two-party information splitting

Patrick Coles, Carnegie Mellon University

**Abstract**. Consider, for example, a scattering process between particles A and B; it can be viewed abstractly as a partial flow of information from A to B, or alternatively, as an isometric encoding of A‟s initial state into the full space AB followed by a splitting of this information (about A‟s initial state) between the two emerging particles A and B. We treat the more general case of isometric encoding a d-dimensional system into a Hilbert space of dimension dA*dB, which is then split into systems A and B of dimension dA and dB, respectively. We imagine sending different types of information, each type being an orthonormal basis (a particular set of density operators), through the channel. To quantify the local information of each type that the channel outputs have about the input, we construct several information measures that quantify the distinguishability of local density operators. Using these measures, we find trade-off inequalities for an information type in A and a mutually-unbiased type in B. Equations relating complete sets of mutually-unbiased bases are also derived. The most intriguing finding is that, for certain information measures, the information splitting between A and B, I(W,A)-I(W,B), is invariant to the information type W. The fundamental phenomena of measurement and decoherence can be viewed as information splitting processes between the system and the apparatus (or environment), so our results are applicable to these phenomena.

## 13. Control in the Flow

Gregory Crosswhite, University of Washington, Department of Physics

**Abstract**. A classical transistor can be conceptualized as a device through which information flows in such a way that a computation is performed on the information as it moves through it. In this poster we present an analagous quantum system in which information is dragged from one side to the other by means of an adiabatic change to the Hamiltonian, such that when it reaches the other side we see that it is as if we had instantaneously applied a quantum gate to the original information. We furthermore present numerical studies of this system that show the relationship of the energy gap --- a key quantity that tells us how quickly we can do our “dragging” --- to the size of the system.

## 14. Fermionic Resources for Quantum Teleportation

Adam DSouza, Institute for Quantum Information Science, University of Calgary

**Abstract**. The measurement-based quantum computing (MBQC) model requires the creation of a massively entangled "resource state", on which computation proceeds via single-qubit measurements. Although 2D resource states are believed necessary for universal MBQC, 1D states can serve as resources for certain tasks as well, such as quantum teleportation. One possible route to a resource state is to cool a gapped, two-body system whose ground state encodes the resource. This poster describes recent work in which we investigate candidate fermionic systems using the Density Matrix Renormalization Group method and the Matrix Product States description of highly entangled 1D states.

## 15. Simulating Concordant Computations Composed of Two-qubit Gates

Bryan Eastin, National Institute of Standards and Technology

**Abstract**. A quantum state is called concordant if it has zero quantum discord with respect to any part. By extension, a concordant computation is one such that the state of the computer, at each time step, is concordant. In this presentation, I describe a classical algorithm that, given a product state as input, permits the efficient simulation of any concordant computation composed of gates acting on two or fewer qubits. This shows that a quantum computation composed of two-qubit gates must generate quantum discord if it is to efficiently solve a problem that requires super-polynomial time classically. While I employ the restriction to two-qubit gates sparingly, a crucial component of the simulation algorithm appears not to be extensible to gates acting on higher dimensional systems. Collaborators: Emanuel Knill, Carlton Caves, Vaibov Madhok, Anil Shaji, Adam Meier

## 16. Polarized atoms in a far-off-resonance YAG laser optical dipole trap

Fang Fang, Los Alamos National Lab

**Abstract**. Optical trapping of radioactive atoms has a great potential in precision measurements for testing fundamental physics such as electric dipole moment (EDM), atomic parity non- conservation (PNC) and parity violating beta-decay correlation coefficients. One challenge that remains is to polarize the atoms to a high degree and to measure the polarization of the sample and its evolution over time. We report on the polarization study of Rb atoms in a yttrium - aluminum-garnett (YAG) laser optical dipole trap using resolved Zeeman spectroscopy techniques. We have prepared a cold cloud of polarized atoms to 97% by optical pumping in the YAG dipole trap. The spin polarization is further purified to 99% and maintained when the two- body collision loss rate between atoms in mixed spin states is greater than the one-body trap loss. These advancements are an important step towards a new generation of precision measurement with polarized trapped atoms. LA-UR: 09-07784

## 17. Most entangled states cannot be locally cloned

Vlad Gheorghiu, Carnegie Mellon University

**Abstract**. We derive a set of necessary conditions for the local cloning by separable operations of a set S of full Schmidt rank partially entangled states using a blank state of the same Schmidt rank, not necessarily maximally entangled. We first prove that no information about which state was cloned can be present at the output of the cloning machine, and conclude that in general local cloning cannot be accomplished by local discrimination with preservation of entanglement (see PhysRevA.75.052313). We further show that the states in S must have equal G- concurrence, and explain why our result is not a consequence of PhysRevA.73.012343, the latter being based on an incorrect proof. In addition, we prove that the states in S which are inter- convertible under separable operations must share the same set of Schmidt coefficients.

## 18. Multipartite Nonlocality in N-qubit Generalized GHZ states

Shohini Ghose, Wilfrid Laurier University

**Abstract**. We analyze genuine multipartite nonlocality in the class of pure N-qubit generalized GHZ states that are of interest for various quantum information processing applications. For the case of 2 qubits, bipartite entanglement leads to violations of Bell inequalities, showing that no local hidden variable theory can account for the correlations between certain measurement outcomes. We show here that the connection between multipartite entanglement and tests of genuine multipartite nonlocality is quite diﬀerent from the 2-qubit case. We use the Svetlichny inequality to test for N-partite nonlocality in the N-qubit generalized GHZ states and an analytical formula for the maximum value of the Svetlichny parameter for these states. Our results conﬁrm and generalize previous numerical studies of these states and show that not all N-qubit generalized GHZ states can violate the Svetlichny inequality. Our work is a step towards understanding the complex nature of entanglement and nonlocality in multiqubit states.

## 19. Micro-fabricated surface ion traps for quantum computation

Clark Highstrete, Sandia National Laboratories

**Abstract**. This poster will present results of the design, operation, and performance of surface ion micro-traps fabricated at Sandia. Microfabrication of linear and junction traps will be described, including recent improvements in the controlled etching of oxide insulators and incorporation of on-chip filters. Recent results in testing of the micro-traps will also be highlighted, including successful motional control of ions and the validation of simulations with experiments. We will also highlight the progress we have made in integrating micro-optical components, and addressing other obstacles to the development of ion traps suitable for performing quantum computations.

## 20. Universal quantum processing using a complete scalable methods set*

Jonathan Home, National Institute of Standards and Technology

*Collaborators: *J. P. Home, D. Hanneke, J. D. Jost, R. Bowler, J. Amini, D. Leibfried, and D. J. Wineland

**Abstract .** A major challenge in quantum information technology is to scale up from systems performing fixed tasks on small numbers of qubits to a large scale device which could perform general computations on large numbers of qubits. Here we describe experiments which demonstrate the combination of all of the fundamental building blocks required for large-scale quantum information processing using trapped atomic ions [1]. We store qubit information robustly using a magnetic-field insensitive transition in 9Be+ and transport information by moving the ions themselves using time-varying potentials applied to the electrodes of a multi-zone Paul trap. Both ambient heating and imperfect control of the ions during transport lead to motional excitation of the ions, impeding our ability to perform subsequent two-qubit gates. We counter this effect by trapping 24Mg+ "refrigerant" ions along with the 9Be+, allowing us to sympathetically cool the 9Be+ ions to the ground state without disturbing the stored quantum information. We characterize the repeatability of a multi-qubit operation involving a combination of single- and two- qubit gates and transport of trapped-ion qubits over macroscopic distances, and demonstrate no loss of gate performance due to transport. The ability to concatenate operations allows us to realize a universal two-qubit quantum information processor capable of performing any unitary transformation in SU(4)[2]. We have programmed this device with 160 operations chosen at random and characterized its performance using state and process tomography. * supported by DARPA, NSA, ONR, IARPA and the NIST Quantum Information Program [1] J. P. Home et al. Science 325, 1227 (2009) [2] D. Hanneke et al. Nature Physics, doi:10.1038/nphys1453 (2009)

## 21. Optical Feshbach Resonances in Ytterbium 171

Krittika Kanjilal, University of New Mexico

**Abstract**. Feshbach resonances are a very powerful tool in atomic physics to control the interaction between ultracold atoms. Whereas magnetic Feshbach resonances (MFRs) are widely used for alkaline atoms, they rely on ground-state hyperfine structure, not available in the alkaline-earth-like atoms. Here we explore optical Feshbach resonances (OFRs), obtained through laser coupling to excited molecular bound states. OFRs provide a possible alternative to MFRs, particularly in the case of alkaline-earth-like atoms, due to their very narrow 3S0 -> 3P1 intercombination line. In addition OFRs provide unique features in that one can turn interactions on and off much more rapidly than MFRs and spatially modulate the interaction strength through local variations in laser intensity. Moreover, one can independently tune even and odd partial wave resonances through absorption selection rules, opening possibilities to study, e.g., p-wave superfluidity. We study OFRs in the context of Yb-171, a fermionic species with spin-1/2 nucleus, making it an interesting candidate for quantum information processing.

## 22. Quantum Frustration of Ising Spins with Trapped Ions

Kihwan Kim, Joint Quantum Insitute and University of Maryland

**Abstract**. Spin systems exhibit frustration when the spins cannot satisfy all of their mutual interactions in a simple ordered configuration, which gives rise to a large ground state degeneracy, with analogues in liquids and ice [1,2]. In quantum spins, the frustrated ground states are expected to be highly entangled. Here we report experimental simulations of three quantum Ising spins in a textbook example of triangular geometrical frustration. We study the ground state properties through adiabatic evolutions from simple polarized states, and also measure correlations and entanglement witnesses of these ground states. We directly observe that such ground states are accompanied by an added degree of degeneracy and entanglement when the underlying Hamiltonian features frustration. [1] H. T. Diep, Frustrated Spin Systems (World Scientific Publishing Company, 2005). [2] R. Moessner and A. P. Ramirez, Phys. Today

59, 24 (Feb 2006).

## 23. Quantum computing with trapped barium ions

Nathan Kurz, University of Washington

**Abstract**. Barium is a very favorable candidate for trapped ion quantum computation, with a simple cooling scheme accessible at diode wavelengths, high natural abundance of two useful isotopes and easily accessible, long-lived D-states for readout via electron shelving. Recently in our lab we have demonstrated qubit rotations between the hyperfine levels of the ground state in the odd isotope, as well as improved state-selective shelving on the narrow S-D dipole-forbidden transition with a microcontroller cavity-locked fiber laser at 1762 nm. We have demonstrated the ability to generate single photons with spontaneous decay and gained an order of magnitude increase in ion fluorescence collection for ion-photon entanglement generation through integration of in-vacuum reflective elements. Work in progress includes entangling remote ions with fluorescence from the pair mode-matched on a beam splitter, development of a second repump at 614 nm to generate single photons from both excited P states, further improving shelving efficiency with an OPA-based system, implementing new trap designs to further increase fluorescence and perhaps improve scalability, and implementation of an pulse programmer for greater RF pulse switching control.

## 24. Progress in Controlling the Quantum Mechanical Motion of Cs Atoms in an Optical Lattice using Microwaves

Jae Hoon Lee, University of Arizona

**Abstract**. Quantum coherent transport is an important requirement for many methods of quantum information processing in optical lattices. We are studying new schemes for which we can do such transport in a more robust and controllable fashion using microwave transitions. First, in order to understand the physics of this system we calculated the band structure and Bloch states, and then integrated the Schrodinger equation in the Bloch basis. With this model we can simulate Rabi oscillations between spin up and spin down states for various lattice configurations. Finally, we were able to accurately model experimental data from arbitrary lattice configurations by including in our model the inhomogeneous broadening from variations in the lattice depth and magnetic field across the atomic ensemble.

## 25. Types and Location of Information

Shiang Yong Looi, Carnegie Mellon University

**Abstract**. Imagine having some input quantum information encoded in n carrier qubits. We are interested in the question of how much information is present in a subset of the carrier qubits. In the case where the encoding is done using a stabilizer code, we have a precise and complete answer. The two extreme cases of having too small a subset whereby no information is present versus having a large subset of almost all n qubits from which all the information can be extracted are already well understood. In this talk we focus on the intermediate situation where partial information is present. For this purpose we define different ``types" of information, where the presence of a type of information on a subset of carrier qubits implies the ability to distinguish a particular set of encoded states associated to that type. With this we can determine how much and what types of information are present in any given subset of carrier qubits. With the help of some simple examples, we will show how sometimes only ``classical" information is present and sometimes both quantum and classical information are simultaneously present. We also found that the presence/absence of types of information on a subset strongly restricts what types of information can be present in the complement of the subset. Our results can also be generalized to higher dimensional qudit stabilizer codes.

## 26. Quantum-enhanced measurement using trapped ions

Warren Lybarger, Los Alamos National Laboratory

*Collaborators*: Warren Lybarger (LANL), Malcolm Boshier (LANL), and John Chiaverini

**Abstract**. The application of algorithms and techniques from the realm of quantum information processing to the problem of metrology can enable better precision than is possible with traditional measurement protocols using similar resources. We describe plans for the use of trapped ion quantum processors to surpass the shot-noise limit to precision for measurements of various quantities of interest. In particular, the motional states of ions trapped in a 3D harmonic well may be put into superposition states (Schroedinger-cat-type states) that are more sensitive to displacements than classical-like coherent states. These states may be created using operations similar to those employed for trapped-ion quantum computing gates. Also, superpositions of internal atomic states may be used to more quickly achieve a prescribed precision in the measurement of external fields through use of a bit-by-bit phase estimation algorithm via conditional coherent operations applied to an individual ion. There is also the possibility to use nonlinear interactions among many-body probe systems to surpass the standard quantum limit for measurement; trapped-ion arrays may be exploited to achieve this kind of enhanced sensitivity to external fields of interest.

## 27. Using and Extending Randomized Benchmarks

Adam Meier, National Institute of Standards at Boulder and University of

Colorado at Boulder

**Abstract**. Randomized benchmarking is a procedure that extracts a "typical" error probability for an experimental quantum computer. This number describes the failure rate of a typical gate in the middle of a long computation and is a worthwhile figure of merit for quantum control demonstrations. I will present a practical, systematic approach to randomized benchmarking using examples from planned experiments in ion traps. I will discuss ways to extend the data analysis to reveal information about individual gates. Finally, I will look at the simplifying assumptions made regarding the error models and randomness of the experimental gates and how they could be generalized. This work has been done in collaboration with E. Knill, K. Brown, D. Hanneke, and J. Home.

## 28. Benchmarking the Krotov Algorithm

Seth Merkel, Institute for Quantum Computing (University of Waterloo)

**Abstract**. A remarkable feature of quantum open-loop control is the ability to find high fidelity control functions using very simple search techniques. While complicated protocols such as simulated annealing and genetic algorithm techniques have been explored, the current standard for optimizing quantum controls, such as the GRAPE algorithm, are based on gradient searches. Gradient searches are generally easy to implementation and for the case of quantum control converge very quickly to an optimal answer. Even simpler than gradient searches, however, are greedy searches, which one can view as the basis for the Krotov algorithm. In this poster we describe an implementation of the Krotov algorithm and look at benchmarking its performance versus that of a GRAPE implementation.

## 29. Implementation of a Quantum Computer Compiler

Tzvetan Metodi, The Aerospace Corporation

**Abstract**. A full-scale quantum computer will be a complex interaction of both classical computer and quantum subsystems. Their realization will require significant advances in both the underlying quantum technologies that implement the qubits and gates and in the overall system level design and analysis. The implementation of a full-scale quantum application (complete with error correction) will require the orchestration of many millions of qubit interactions at each cycle of execution. In order to better understand both the system design and physical implementation we have developed a Quantum Compiler. The quantum compiler allows us to analyze the transformation and performance of a high-level quantum program that is mapped into a specific physical architecture of qubits and gates. The compiler can be applied to trade studies for optimizing reliability and latency of the program execution and to determine the error correction resources required to implement the quantum program. We describe the quantum compiler design and software implementation. The quantum compiler consist of three stages:

- A pre- compiler that translates a human readable high-level specification of a quantum circuit into a machine readable quantum intermediate representation (QIR)
- An assembler that maps the QIR representation of the circuit into an equivalent low-level quantum assembly representation composed of a universal set of logic gates
- Assembly legalization which maps each quantum assembly-level instruction to corresponding machine instructions. The machine instructions are based on the specific technology-dependent physical architecture of the quantum computer

## 30. Tools for planar ion trap development

Soenke Moeller, University of California, Berkeley

**Abstract**. We are pursuing experiments to address scalability of ion-trap based quantum information processing. In a first direction, we concentrate on planar ion trap development to facilitate scalable ion trap quantum computing. We present a set of tools which allow convenient control of planar trap potentials, as well as tools to characterize planar traps in terms of stray electrostatic fields and electromagnetic noise. We show an implementation of these tools in characterizing microfabricated gold-on-sapphire traps. A second direction focuses on using a transmission-line interface to transfer quantum information between distant ions. We present a cryogenic ion trap setup based on a closed cycle cryostat which will be used in this effort.

## 31. A Numerical Quantum and Classical Adversary

Mike Mullan, National Institute of Standards and Technology

**Abstract**. The Quantum Adversary Method has proven to be a successful technique for deriving lower bounds on a wide variety of problems. However, its application can be difficult as one must understand the detailed combinatorial properties of the problem under consideration. In addition, it assumes perfect quantum computation, which in most modern devices, is unrealistic. Here, we develop a generalization of this technique which allows it to be applied to arbitrary small problems automatically. To do this, we reformulate the spectral adversary such that the objective value of the semidefinite program corresponds to the probability that a quantum computer will output the correct value after a specified number of queries. This technique is naturally extended to include decoherence. In particular, the optimum probability of success can be determined for any probability of phase error. In the limit of complete phase decoherence, we recover the semidefinite programming formulation of a classical adversary, and so are able to automatically compute optimal classical success probabilities for small problem sizes. This work is in collaboration with E. Knill.

## 32. Quantum Control of Collective Spin Ensembles

Leigh Norris, University of New Mexico

**Abstract**. Trapped atomic ensembles have emerged as important tools in quantum information processing, with a range of applications including the production of spin squeezed states and the development of light-atom interfaces. We investigate the effects of collective entangling interactions and local unitary control on a large ensemble of atomic spins. In particular, we explore the nature of multi-body entanglement in this ensemble, the relationship between spin squeezing and entanglement, and the possible enhancement of existing squeezing protocols through entangling interactions.

## 33. Micro Ion Frequency Standard

Heather Partner, Sandia National Laboratories and University of New Mexico

**Abstract**. We are developing a highly miniaturized trapped ion clock to probe the 12.6 GHz hyperfine transition in the 171Yb+ ion. Our goals are to develop a clock that is less than 5 cm^3 in size, consumes <50 mW of power, and has a long-term frequency stability of 10^-14 at one month. Realizing a clock of this size requires advanced technologies to create a miniaturized vacuum package with an integral linear ion trap, Yb source, and pump. Integrated light sources for photoionization, state preparation and detection and a low-phase-noise micro resonator for use as a local oscillator must also be developed. We report on our design for this frequency standard and our progress toward its realization. P. D. D. Schwindt, R. Olsson, K. Wojciechowski, D. Serkland, T. Statom, H. Partner, G. Biedermann, L. Fang, A. Casias, R. Manginell, Y.Y. Jau.

## 34. Quantum emulation with trapped ions

Thaned Pruttivarasin, University of California Berkeley, Haeffner Group

**Abstract**. Crystal interfaces play an important role in condensed matter physics. In particular, if the lattice constants of the crystals are incommensurate, interesting phenomena such as crystal dislocations and dry friction arise. The so-called Frenkel-Kontorova model captures the essential physics of these phenomena and is therefore investigated in great detail by theorists. Here we propose to study the Frenkel-Kontorova model experimentally by placing an ion crystal in a periodic optical lattice potential formed inside a resonator. The goal of the experiment is to observe the so-called analyticity breaking transition from the pinned phase to the sliding (unpinned)phase of the ion chain which is prominent in both the classical and quantum regimes. By look at the crystal deformation and the phonon spectrum, our preliminary numerical calculations of the of the ion chain show that such a transition is observable with our experimental parameters. Moreover, the effective dimensionless Planck constant for our system can be varied from 0.1 to 2 by changing the axial trapping frequency, hence allowing us to investigate the physics of this particular model in the quantum regime.

## 35. A new class of optimal entanglement witnesses

Justyna Pytel, Nicolaus Copernicus University

**Abstract**. We provide a new class of indecomposable entanglement witnesses. In 4 x 4 case it reproduces the well know Breuer-Hall witness. We prove that these new witnesses are optimal and atomic, i.e. they are able to detect the "weakest" quantum entanglement encoded into states with positive partial transposition (PPT). Equivalently, we provide a new construction of indecomposable atomic maps in the algebra of 2k x 2k complex matrices. It is shown that their structural physical approximations give rise to entanglement breaking channels. This result supports recent conjecture by Korbicz et. al. [Phys. Rev. A <b> 78 </b>, 062105 (2008)].

## 36. Echo quench and its application in adiabatic quantum computation

Haitao Quan, Los Alamos National Laboratory

**Abstract**. The quantum adiabatic theorem has aroused a lot of debate in recent years. How to ensure the adiabaticity of a quantum dynamic process remains an open problem. We propose a simple method to test the adiabaticity of a quantum quench process when we know only the eigenstates of the initial Hamiltonian. This method promises important applications in implementing adiabatic quantum computation algorithm.

## 37. Quantum state reconstruction of the 16 dimensional hyperfine manifold in cesium via continuous measurement and control

Carlos Riofrio, University of New Mexico

**Abstract**. Quantum state reconstruction techniques based on weak continuous measurement have the advantage of being fast, accurate, and almost non-perturbative. Moreover, they have been successfully implemented in experiments on large spin systems (PRL 97, 180403 (2006)). In this poster, an application of the reconstruction algorithm developed by Silberfarb et al. (PRL 95, 030402 (2005)) is presented for the reconstruction of quantum states stored in the 16 dimensional ground-electronic hyperfine manifolds (F=3, F=4) of an ensemble of 133Cs atoms controlled by microwaves and radio- frequency magnetic fields. Simulations showed that

randomly generated control fields produce informationally complete measurement records and thus give high fidelity reconstructed states. Furthermore, exploration of appropriate operation regimes is shown for possible experimental implementation.

## 38. Atom Chip Matter Wave Interferometer

Rob Sewell, The Institute of Photonic Sciences (ICFO)

**Abstract**. We have fabricated and tested an atom chip that operates as a matter wave interferometer. We coherently split a single Bose Einstein condensate (BEC) in two using a radio- frequency field to deform a magnetic trap smoothly from a single to a double well. We read out the relative phase between the two modes from the interference pattern that is produced when they are released from the trap and allowed to overlap in free fall. The interferometer has good phase stability and a coherence time limited by phase spreading due to atom-atom interactions. We have tested it as a measurement device by introducing a known small energy difference between the two minima of the trapping potential and reading out the resulting phase difference from the interference pattern. We discuss our results and future plans to increase the sensitivity of the interferometer by exploiting atom-atom interactions during the splitting process to induce number squeezing and increase the phase coherence time.

## 39. Compressed Quantum Process Tomography

Alireza Shabani, Princeton University

**Abstract**. The characterization of a decoherence process is among the central challenges in quantum physics. A major difficulty with current quantum process tomography methods is the enormous number of experiments needed to accomplish a tomography task. Here we present a highly efficient method for tomography of a quantum process that has a small number of significant elements. Our method is based on the compressed sensing techniques being used in information theory. In this new method, for a system with Hilbert space dimension n and a process matrix of dimension n^2 x n^2 with sparsity s, the required number of experimental configurations is O(s log n^4). This heralds a logarithmic advantage in contrast to other methods of quantum process tomography. More specifically, for q-qubits with n=2^q, the scaling of resources is O(sq) linear in the product of sparsity and number of qubits.

## 40. Classical communication using quantum states in the absence of a shared reference frame

Michael Skotiniotis, Institute for Quantum Information Science, University of Calgary

**Abstract**. We address the problem of quantum communication between two parties who lack a requisite shared reference to decode classical information encoded in quantum systems. Specifically, we develop a theory for quantum encoding and decoding protocols utilizing relative parameters, whereby information is encoded in relational properties of quantum systems such as the angle between two spins. If the reference frames are related by finite group transformations, we develop an encoding strategy and optimize the choice of measurements for decoding. Our method obviates the need to perform tasks requiring significant use of resources, such as reference frame alignment. Consider the case where Alice and Bob lack a shared reference frame for ascertaining which way is up in the other party's locale. Such a reference frame is associated with the SO(3) symmetry group. When a reference frame is lacking, parties wishing to communicate can either expend precious resources to establish a shared reference frame or use physical properties of systems that are independent of a reference frame. The latter approach has been studied for the case where the associated symmetry group is SU(2). Following a similar recipe, and using techniques from quantum estimation theory, we determine the optimal encoding states and decoding measurements for the cases where the requisite reference frame is associated with a general, finite group of transformations.

## 41. Silicon surface-electrode ions traps for quantum information processing*

Dick Slusher, Georgia Tech Research Institute

**Abstract**. The Georgia Tech Research Institute (GTRI) is designing, fabricating, and testing scalable surface-electrode ion traps for quantum information applications with a wide range of trap architectures fabricated in scalable silicon VLSI technology. We will present designs and initial test results for several of our traps, including a linear trap that holds long chains of equally spaced ions, a 90-degree X-junction, and an integrated micromirror with collection efficiency up to

20%. We will also present results on fabrication features that can be integrated with the surface electrode designs such as multilayer interconnects, optics for enhanced light collection, flexible optical access through beveled slots extending through the substrate, and recessed wire bonds for clear laser access across the trap surface. Traps are designed at GTRI using in-house codes that calculate the fields, compute the full motion of ions confined in the trap including the micromotion, and optimize the electrode shapes and transport waveforms using genetic algorithms. *Support for this work provided by IARPA through the Army Research Office award W911NF081-0315 and by DARPA through award W911NF-07-1-0576.

## 42. Controlled interactions between ultracold Lithium and Cesium atoms in optical lattices for quantum information processing

Kathy-Anne Soderberg, The University of Chicago

**Abstract**. We present progress on a quantum information processing experiment using degenerate gases of bosonic 133Cs and fermionic 6Li, each confined in an independently controlled, overlapping optical lattice. An insulating state of 6Li will prepare an initial state with exactly one atom per lattice site. These atoms serve as quantum bits (qubits). 133Cs atoms are sparsely loaded into a second lattice, and act as messenger bits to carry entanglement between distant qubits. Qubit operations are mediated through magnetic dipole transitions to a 6Li-133Cs molecular state that is formed only when qubit and messenger are overlapped. The 133Cs messenger atom can interact with (multiple and distant) 6Li qubits through translation of the Cs lattice using an electro-optic modulator array, making this implementation scalable. We present progress on the first spectroscopy experiments of the 6Li 133Cs molecular states. These findings will guide the best strategies for implementing qubit operations using messenger atoms.

## 43. Macroscopic two-state system with cold atoms: towards BEC flux qubit

Dmitry Solenov, Los Alamos National Laboratory

**Abstract**. We investigate macroscopic properties of Bose-Einstein condensate of interacting neutral (spin-0) atoms confined in a ring with weak Josephson tunneling link. We show that, similar to superconducting Josephson ring, cold atom BEC system of such geometry can be tuned to create macroscopic two-state system. We analyze its many-body wave function and derive an effective low energy Schrodinger equation to the leading order as an expansion in the number of particles. We determine the range of parameters in which quantization of the macroscopic variable adequately describes low-energy physics and predicts measurement. Finally, we outline signatures of the time-of-flight experiment expected for neutral atom Josephson ring systems in two-state regime.

## 44. Optimized Entanglement Assisted Quantum Error Correction

Soraya Taghavi, University of Southern California

**Abstract**. Using convex optimization, we propose entanglement assisted quantum error correction procedures which are optimized for given noise channels. We demonstrate through numerical examples that such an optimized error correction method achieves a higher channel fidelity than existing methods. This outperformance, which leads to perfect error correction for a larger class of error channels, is interpreted by quantum teleportation.

## 45. Mixed state quantum reference frame resources

Borzumehr Toloui, Institute for Quantum Information Science at the University of Calgary

**Abstract**. Situations where the operations of a noisy channel used for the transmission and retrieval of quantum states belong to a specific group of transformations give rise to resources beside entanglement that allow us to overcome the ensuing constraints, such as when shared reference frames (RF) associated with symmetry groups are lacking between the nodes of a quantum channel. So far, most work on this new kind of resource, dubbed "frameness", has been focused on pure state transformations even though almost all states and operations in the lab involve some degree of mixedness. Here we address the problem of quantifying the frameness of mixed states. We introduce a new family of pure state frameness measures associated with Abelian Lie groups in a Hilbert space of arbitrary but finite dimensions, whose convex roof

extensions remain monotonic. In particular, we show that this family of frameness monotones are closely related to generalized concurrence functions of the reduced density operators of entangled states. This highlights interesting and deep links between frameness and entanglement resource theories, and provides a new way of classifying all frameness monotones as functions of the "twirled" state that results from tracing out the RF, where the state plus the RF are treated as a joint entangled system. Finally, we use a member of this family of frameness monotones to determine the explicit analytical form of a qubit's frameness of formation. The frameness of formation denotes the minimum average cost of preparing the ensemble of pure states that realize a given mixed state, and can be used to quantify the frameness of that state under certain conditions. Our results thus extends Wootter's formula for the entanglement of formation of bipartite qubit states to a whole new and different class of resources.

## 46. Quantum Interferometric Metrology in the Presence of Photon Loss

Dmitry Uskov, Tulane University and Hearne Institute for Theoretical Physics

**Abstract**. I will report on our recent progress [1] in solving the problem of optimization of the interferometric phase measurement with two-mode entangled photon states in the presence of loss, and optimization of quantum operations on such states [2]. Our main result is that in the presence of photon loss one can single out two distinct regimes: 1) a low-loss regime, favoring purely quantum states, akin the |N00N> states and 2) a high-loss regime, when the generalized coherent SU(2) states become the optimal ones. [1] T. Lee et al, Phys. Rev. A 80, 063803 (2009). [2] D. Uskov et al, arXiv:0908.2482.

## 47. Generic two-qubit photonic gates implemented by number-resolving photodetection

Dmitry Uskov, Tulane University

**Abstract**. We use numerical techniques [Uskov et al., Phys. Rev.A79, 042326 (2009)] to obtain optimal implementations of generic linear-optical Knill-Laflamme-Milburne-type two-qubit entangling gates inside the whole volume of the Weyl chamber. We find that while any two-qubit controlled-U gate can be implemented using only two ancilla resources a generic SU(4) operation requires three ancilla photons. We show that single-shot implementation of a generic SU(4) gate offers more than an order of magnitude increase in the success probability and a two-fold reduction in overhead ancilla resources compared to standard triple-CNOT and double-B gate decompositions. Some applications for photonic quantum information processing and metrology with lossy modes are also discussed.

## 48. Quantum Search by Quantum Cellular Automata

Kevin Van De Bogart, University of Calgary

**Abstract**. Quantum Cellular Automata provide a description of quantum systems whose evolution is periodic in space and time. The drawing feature of QCA is that evolution is described by global operations that can be decomposed into periodic components, instead of operations on individual data registers. While it has been demonstrated that QCA can be constructed that are equivalent to the circuit model, these constructions do not lend themselves easily to a physical system. However it is possible to create QCA that, while they do not correspond to a fully programmable quantum computer, can nevertheless implement quantum algorithms. By drawing on the connection between quantum walks and QCA, I demonstrate that it is possible to implement Grover's algorithm on a system that may be readily translated to a physical implementation.

## 49. Fiber Optics in Surface Ion Traps

Aaron VanDevender, National Institute of Technology

**Abstract**. Fiber optics provide a more scalable and resource efficient means of delivering light to and collecting fluorescence from a trapped ion than bulk optics. We demonstrate trapping of a 24Mg+ ion in a gold-on-quartz surface-electrode trap with an integrated high numerical-aperture

photonic-crystal multi-mode fiber 100 microns from the ion, and observe fluorescence photons through the fiber. The trap features multiple RF electrodes whose potentials can be adjusted to vary the height of the pseudopotential zero from 30 to 50 microns above the electrode surface (80 to 100 microns from the fiber). This demonstrates the ability to trap ions very near dielectrics, an important step toward trapping ions in small volume fiber optic cavities useful for the strong coupling of ions and photons. * supported by DARPA, NSA, ONR, IARPA, Sandia and The NIST Quantum Information Program

## 50. Generalized X-states for N-qubits

Sai Vinjanampathy, Louisiana State University

**Abstract**. X-states of a pair of qubits are density matrices whose non-zero elements lie along its diagonal and anti-diagonal. Such states have been useful in the study of the sudden death of entanglement and in understanding quantum correlations in spin chains. We present the generalization of X-states to N-qubits and characterize the algebra of the operators involved. We will present connections between N-qubit X-states and N-simplexes and discuss some applications.

## 51. Continuous quantum non-demolition measurement of Fock states of a nanoresonator using feedback-controlled circuit QED

Matthew Woolley, University of Queensland

**Abstract**. An important benchmark for quantum control is the ability to prepare and detect a harmonic oscillator in a Fock state, an energy eigenstate. Meanwhile, a major goal of the study of nanomechanical systems near the quantum limit is to prepare quantum states of the nanomechanical resonator. We propose a scheme for the quantum non-demolition (QND) measurement of Fock states of a nanomechanical resonator via feedback control of a coupled circuit QED system. A Cooper pair box (CPB) is coupled to both the nanoresonator and microwave cavity. The CPB is read-out via homodyne detection on the cavity and feedback control is used to effect a non-dissipative measurement of the CPB. This realizes an indirect QND measurement of the nanoresonator via a second-order coupling of the CPB to the nanoresonator number operator. The phonon number of the Fock state may be determined by integrating the stochastic master equation derived, or by processing of the measurement signal.

## 52. Multipartite entanglement verification

Jun Yin, University of Oregon

**Abstract**. We propose a general data analysis scheme for multipartite entanglement verification under limited number of measurements, making use of several information criteria. We show that in most situations, models can be simplified according to the measurement performed, without the entanglement verification process being compromised. We also show that some entanglement related properties are sensitive to these criteria while others are not.

## 53. Stroboscopic Generation of Topological Protection

Kevin Young, University of California - Berkeley

**Abstract**. Trapped neutral atoms oﬀer a powerful route to robust simulation of complex quantum systems. We present here a stroboscopic scheme for realization of a Hamiltonian with n-body interactions on a set of neutral atoms trapped in an addressable optical lattice, using only 1- and 2-body physical operations together with a dissipative mechanism that allows thermalization to ﬁnite temperature or cooling to the ground state. We demonstrate this scheme with application to the toric code Hamiltonian, ground states of which can be used to robustly store quantum information when coupled to a low temperature reservoir.

## 54. Efficient local implementation of bipartite quantum gates

Li Yu, Carnegie Mellon University

**Abstract**. Any bipartite nonlocal unitary operation can be carried out by teleporting a quantum state from one party to the other, performing the unitary locally, and teleporting a state back again. This paper investigates unitaries which can be carried out using less prior entanglement than needed for teleportation. In particular large families of such unitaries are constructed using (projective) representations of finite groups. Among the tools employed are: a diagrammatic approach to the analysis of quantum circuits, a theorem on the necessary absence of information at certain locations, and a representation of bipartite unitaries based on a generalized Fourier transform.

## 55. Computable and asymptotically optimal lower bounds on confidence for rejecting local realism given experimental data

Yanbao Zhang, University of Colorado at Boulder

**Abstract**. Because of the fundamental importance of Bell's theorem, loophole-free demonstrations of violations of local realism (VLR) are highly desirable. Besides the locality and detection loopholes in current experimental tests of VLR, there is another loophole--the memory loophole, which concerns the time dependence of the local hidden variables on the previous measurement settings and outcomes. This loophole affects the confidence at which local realism is (hopefully) rejected by a finite number of experimental data. We suggest the use of a prediction-based likelihood ratio to lower-bound the rejection confidence. The method gives a strict lower bound with no assumptions on memory, experimental stability or independence of each data point from previous ones. If the prepared state does not vary in time, the bound is asymptotically optimal. We demonstrate our method with simulated data for the configuration used in conventional Bell tests with balanced or unbalanced Bell states. Collaborators: Emanuel Knill and Scott Glancy

## 56. Quantum Darwinism in hazy environments

Michael Zwolak, Los Alamos National Laboratory

**Abstract**. Quantum Darwinism provides an information-theoretic framework for the emergence of the classical world from the quantum substrate. It recognizes that we - the observers - acquire our information about the "systems of interest" indirectly from their imprints on the environment. Objectivity, a key property of the classical world, arises via the proliferation of redundant information into the environment where many observers can then intercept it and independently determine the state of the system. After a general introduction to this framework, we demonstrate how non-ideal initial states of the environment (e.g., mixed states) affect its ability to act as a communication channel for information about the system. The environment‟s capacity for transmitting information is directly related to its ability to increase its entropy. Therefore, environments that remain nearly invariant under the Hamiltonian dynamics, such as very mixed states, have a diminished ability to transmit information. However, despite this, the environment almost always redundantly transmits information about the system.

## 57. Recent Experiments with Phase Qubits at UCSB

Radek Bialczak, Max Hofheinz, Mike Lenander, Erik Lucero, Matteo Mariantoni, Matthew Neeley, Aaron A. O'Connell, Daniel Sank, Haohua Wang, Martin Weides, James Wenner, Yi Yin, Andrew Cleland, John Martinis – University of California, Santa Barbara

**Abstract**. We present new experimental results in quantum information processing using Josephson phase qubits and superconducting microwave resonators. We have used a coupled qubit-resonator system to demonstrate deterministic arbitrary state preparation in the resonator with terms up to the tenth Fock state. We confirmed these state preparations by measuring the Wigner function of the resonator. In another experiment, we showed that higher energy states in the phase qubit can be used to simulate geometric phase effects typically discussed in the context of spin particles. By driving the various qubit level transitions at the appropriate relative strengths, the dynamics of spin operators were experimentally simulated for spins 1/2, 1, and 3/2, and various geometric phases were measured. In a third experiment we used entanglement of two qubits to demonstrate a violation of Bell's inequality. Underlying these results are qubits with high enough energy (T1) and phase (T2) coherence times to allow for complex algorithms to be executed. More interesting and complex information processing will demand qubits with longer lifetimes. To achieve this, we need a more complete understanding of the physical processes that cause decoherence. We report on recent advances in our understanding of decoherence from magnetic flux fluctuations, radiative loss in resonators, and quasiparticle tunneling effects in the Josephson junctions.

Work supported by: IARPA, ARO, NSA, NSF, CNSI

## 58. Verification of Entanglement for HOM-like States

Megan Ray, University of Oregon

**Abstract**. We propose a simple method of verifying the entanglement of two mode states similar to Hong- Ou-Mandel states 1/ √ 2 (|02> - |20>). While full state tomography can be used to verify the entanglement of such states, it is measurement intensive. Our method relies on a bounding scheme that requires far fewer measurements than required for full state tomography.