# 2009 Talks Abstracts

### 1. The Role of Coherence in Photosynthetic Energy Transfer

Alan Aspuru-Guzik, Harvard University

(Session 11: Sunday from 9:15-9:45)

**Abstract**. Recently, direct evidence of long-lived coherence has been experimentally demonstrated for the dynamics of the Fenna-Matthews-Olson (FMO) protein complex at 77K [Engel et al., Nature 446, 782 (2007)]. It was suggested that quantum coherence was important for exploring many relaxation pathways simultaneously. I will talk about our recent work in developing methods for exploring that question and analyzing the different contributions of the different processes to the efficiency of energy transfer in the complex. We generalized the concept of continuous-time quantum walks to a Liouville space formalism. This helped us analyze these contributions and report that at room temperature, this complex has contribution of coherent dynamics of about 10%. Relaxation processes are responsible for 80% of the efficiency. The quantum transport efficiency can actually be enhanced by the dynamical interplay of the system Hamiltonian with the pure dephasing dynamics induced by a fluctuating environment. This occurs in an intermediate regime between fully coherent hopping and highly incoherent transport. I will finalize with a short discussion of this environment-assisted quantum transport regime

### 2. Dynamical Decoupling in a Model Quantum Memory

Michael Biercuk, NIST - Ion Storage Group

(Session 10: Saturday from 4:00-4:30)

**Abstract**. We present results on the application of Dynamical Decoupling (DD) pulse sequences for the suppression of phase errors in a qubit array consisting of a laser-cooled crystal of trapped Beryllium ions. We study various DD sequences including CPMG and the recently discovered Uhrig DD sequence. Our results demonstrate the ability of UDD and CPMG to strongly suppress phase errors in the presence of ambient magnetic field noise, and show strong agreement with theoretical predictions for qubit decoherence. We also generate noise artificially and compare the efficacy of these DD sequences in Ohmic, 1/f and 1/f^2 noise environments -- making our qubit array a model quantum system capable of emulating solid state noise environments. Finally, we demonstrate real-time experimental optimization of DD pulse sequences without any required knowledge of the ambient noise environment.

### 3. Quantum computing through decoherence

Sergio Boixo, California Institute of Technology

(Session 10: Saturday from 4:30-5:00)

**Abstract**. A computation in adiabatic quantum computing is achieved by traversing a path of nondegenerate eigenstates of a continuous family of Hamiltonians. We introduce a method that traverses a discretized form of the path: at each step we evolve with the instantaneous Hamiltonian for a random time. The resulting decoherence approximates a projective measurement onto the desired eigenstate, achieving a version of the quantum Zeno effect. For bounded error probability, the average evolution time required by our method is O(L^2 /D), where L is the length of the path of eigenstates and D the minimum spectral gap of the Hamiltonian. The randomization also works in the discrete-time case, where a family of unitary operators is given, and each unitary can be used a finite amount of times. Applications of this method for unstructured search and quantum sampling are considered. We discuss the quantum simulated annealing algorithm to solve combinatorial optimization problems. This algorithm provides a quadratic speed-up (in the gap) over its classical counterpart implemented via Markov chain Monte Carlo.

### 4. Creating and manipulating quantum decoherence-free, or noiseless, systems of qudits

Mark Byrd, Southern Illinois University

(Session 10: Saturday from 3:30-4:00)

**Abstract**. Qudits are promising candidates for many quantum information processing tasks. They can be more entangled than qubits, can share a larger fraction of the entanglement in some cases, and may be required for some quantum information processing tasks. I will show how to make entangled qutrit states using photons which form a decoherence-free subspace and show how, in principle, we can manipulate qudit decoherence-free subspaces comprised of quDits.

### 5. Development of a Silicon Physical Qubit and Single Logical Qubit Design

Malcolm Carroll, Sandia National Laboratories

(Session 1: Thursday from 6:45-7:15)

**Abstract**. An overview will be given of both experimental and theoretical development of a single error corrected logical qubit using silicon based hardware. The physical qubit research centers on demonstrating a basic qubit fabricated in an accumulation mode silicon metal oxide semiconductor (MOS) structure. The experimental component of the logical qubit focuses on the classical-quantum circuit interface and its impact on error correction. The logical qubit effort includes both hardware development, such as cryogenic complementary metal oxide semiconductor (CMOS), and a theoretical component, which examines a quantum error correction circuit architecture. The theoretical analysis accounts for more realistic constraints suggested by the physical qubit research while providing insight and feed-back about choices of lay-out, transport and error code choice. We note that some insight drawn from constraints of working in a cryostat may be more generally useful to other quantum computing architectures using cryogenics. In summary, the goal of this combined engineering effort is to more completely understand the design of a single solid-state logical qubit and work towards development of the required silicon qubit hardware elements (e.g., single qubit and read-out) with which to build it.

### 6. Gapped Two-body Hamiltonian whose Unique Ground State is Universal for One-way Quantum Computation

Xie Chen, Massachusetts Institute of Technology

(Session 9: Saturday from 4:00-4:30)

**Abstract**. Many-body entanglement of quantum states is one of the essential resources which make quantum algorithmic speedup over classical computers possible for certain computational problems. However, generating and maintaining in a controlled way any known type of many-body entanglement that enables quantum computation is usually hard. Here we provide an alternative scheme for quantum computation which protects its entanglement resource in the gapped ground state of a naturally occurring Hamiltonian. We demonstrate how arbitrary quantum computation may be efficiently simulated by measuring each particle in the 'tri-Cluster state', a unique ground state of gapped local Hamiltonian that involves only nearest-neighbor interactions on two-dimensional Hexagonal lattice. In this way we have provided an experimentally more feasible approach for quantum computation.

### 7. The relationship between continuous- and discrete-time quantum walk

Andrew Childs, University of Waterloo

(Session 11: Sunday from 8:30-9:15)

**Abstract**. Quantum walk is one of the main tools for quantum algorithms. Defined by analogy to classical random walk, a quantum walk is a time-homogeneous quantum process on a graph. Both random and quantum walks can be defined either in continuous or discrete time. However, whereas a continuous-time random walk can be obtained as the limit of a sequence of discrete-time random walks, the two types of quantum walk appear fundamentally different, owing to the need for extra degrees of freedom in the discrete-time case. In this talk, I describe a precise correspondence between continuous- and discrete-time quantum walks on arbitrary graphs. This provides a description of continuous-time quantum walk as a certain limit of discrete-time quantum walks, and also leads to improved methods for simulating Hamiltonian dynamics. In particular, there is a simulation whose complexity grows linearly with the total evolution time and that does not necessarily require the Hamiltonian to be sparse.

### 8. Continuous measurement of a quantum phase transition in a collective atomic system weakly coupled to a single optical mode

Robert Cook, University of New Mexico

(Session 7: Saturday from 2:30-3:00)

**Abstract**. We consider an atomic ensemble that is dispersively coupled to a high finesse optical cavity. The application of cavity assisted Raman transitions generate two body interactions that are symmetrically distributed across the entire ensemble. If the cavity mode rapidly decays to an external field, adiabatic elimination of the cavity produces effective atomic dynamics that are equivalent to a dissipative Lipkin-Meshkov-Glick model, which exhibits a zero temperature quantum phase transition. In the framework of quantum stochastic calculus, we derive the propagator that describes the effective coupling between the collective atomic spin and the external field. We then derive a filter that describes the atomic state conditioned on a continuous measurement of the external field. Finally, we simulate this measurement as the system is tuned though its critical parameter range.

### 9. Preparation and detection of a 137Ba+ hyperfine qubit

Matt Dietrich, University of Washington

(Session 6: Saturday from 11:00-11:30)

**Abstract**. We report the initialization and state detection of 137Ba+ hyperfine qubits. We load 137Ba+ into a linear Paul trap by direct photoionization with a Xe discharge lamp. The qubit is initialized by optically pumping into the magnetic field insensitive hyperfine ground state (F=2 m_f=0). State selective shelving to the metastable D5/2 state is accomplished by adiabatic rapid passage using a 1762 nm fiber laser stabilized to a high-finesse cavity, a process which is used for high efficiency state detection. Single qubit rotations are accomplished by RF pulses at the hyperfine splitting (8.037 GHz). Rabi flops excited by individual ultrafast laser pulses have been demonstrated and future plans include using these pulses to generate controlled-phase gates between two ions on sub-microsecond time scale.

### 10. Large Scale Quantum Computation in a Linear Ion Trap

Luming Duan, University of Michigan

(Session 6: Saturday from 8:30-9:15)

**Abstract**. Among the approaches to quantum computation, the trapped ion system remains as one of the leading candidates. The linear Paul trap provides the most convenient architecture for quantum gate operations over a few ions, and the basic requirements for quantum computation have been demonstrated in this setup. However, scaling up this system to a large number of qubits so far remains a formidable challenge because of several obstacles, including the instability of the linear structure and the difficulties of the sideband cooling and addressing for a large ion array. The recent approach to scalable ion trap computation thus has to use a more complicated architecture where the ions are shuttled over different trapping regions. Here, we propose a way to implement large-scale quantum computation in a linear trap by overcoming all the theoretical obstacles. Through excitation of the transverse photon modes in an anharmonic trap, we show that high-fidelity quantum gates can be achieved on ions in a large linear architecture under the Doppler temperature without the requirement of sideband resolving.

### 11. Restrictions on Transversal Encoded Quantum Gate Sets

Bryan Eastin, National Institute of Standards and Technology

(Session 3: Friday from 2:30-3:00)

**Abstract**. Transversal gates play an important role in the theory of fault-tolerant quantum computation due to their simplicity and robustness to noise. By definition, transversal operators do not couple physical subsystems within the same code block. Consequently, such operators do not spread errors within code blocks and are, therefore, fault tolerant. Nonetheless, other methods of ensuring fault tolerance are required, as it is invariably the case that some encoded gates cannot be implemented transversally. This observation has led to a long-standing conjecture that transversal encoded gate sets cannot be universal. In this talk, I discuss new results showing that the ability of a quantum code to detect an arbitrary error on any single physical subsystem is incompatible with the existence of a universal, transversal encoded gate set for the code.

### 12. Resource Requirements for Fault-Tolerant Quantum Simulation: The Transverse Ising Model Ground State

Samuel Gasster, The Aerospace Corporation

(Session 9: Saturday from 5:00-5:30)

**Abstract**. Craig R. Clark, Kenneth R. Brown, Tzvetan S. Metodi, Samuel D. Gasster The cost, in both computational space and time, of calculating the energy of the ground state of the transverse Ising model on a fault-tolerant quantum computer is estimated using the Quantum Logic Array (QLA) architecture model. The QLA is a homogeneous, scalable, tile-based quantum architecture design employing concatenated quantum error correction for the construction of logical qubits and gates, based on experimentally viable ion-trap device technology parameters and components. The error correction requirements for calculating the energy on the QLA architecture are comparable to those for factoring large integers via Shor's quantum factoring algorithm number due to the exponential scaling of the computational time steps with the precision. As a result, a fault-tolerant QLA-based quantum computer which can factor 1024-bit integers can also be used to calculate the Ising ground-state energy with precision of up to 7 decimal digits.

### 13. Strong NP-Hardness of the Quantum Separability Problem

Sevag Gharibian, Institute for Quantum Computing, University of Waterloo

(Session 8: Saturday from 4:00-4:30)

**Abstract**. Quantum entanglement is generally believed to be a valuable resource in the theory of quantum computing. The problem of determining whether an arbitrary quantum state is entangled, dubbed the Quantum Separability problem, has hence received much attention over the past decade. In 2003, Gurvits showed that the Quantum Separability problem is NP-hard, with one caveat - one must allow instances in which the input quantum state is exponentially close (with respect to dimension, and in Euclidean distance) to the border of the set of separable (equivalently, unentangled) quantum states. This leaves open the question - is the Quantum Separability problem "weakly" NP-hard, i.e. can it be solved efficiently if one is promised that the input state is at least an inverse polynomial distance away from the border of the separable set? In this talk, we answer this question negatively by showing that the Quantum Separability problem is in fact "strongly" NP-hard. This is accomplished by combining previous work by Gurvits and a recent non-ellipsoidal reduction of Liu to show that the Weak Membership problem over the set of separable quantum states is strongly NP-hard. Based on this result, we observe an immediate lower bound on the maximum distance possible between a bound entangled state and the separable set (assuming P != NP). Time permitting, we also demonstrate that determining whether a completely positive trace-preserving linear map (i.e. a quantum channel) is entanglement-breaking is NP-hard.

### 14. Relationship between 3-qubit entanglement and nonlocality

Shohini Ghose, Wilfrid Laurier University

(Session 4: Friday from 4:00-4:30)

**Abstract**. Multiqubit entanglement is a crucial ingredient for large-scale quantum information processing and has been the focus of several recent studies. Entanglement between qubits can lead to violations of Bell-type inequalities that are satisfied by local hidden variable models, indicating the nonlocal nature of the correlations between qubits. For 2-qubit pure states, bipartite entanglement is simply related to the Bell-CHSH nonlocality parameter. No such analytical relation between multipartite entanglement and nonlocality has yet been obtained for systems of three or more qubits. We have derived relationships between genuine tripartite entanglement and nonlocality for families of 3-qubit GHZ-class pure states. We quantify tripartite entanglement by the 3-tangle and derive its relationship to the Svetlichny inequality for testing tripartite nonlocality. For the class of generalized GHZ states, although the 3-tangle is always non-zero, we identify some states that do not violate the Svetlichny inequality. Furthermore, we show that states known as the maximal slice states always violate the Svetlichny inequality and analogous to the 2-qubit case, the amount of violation increases with the 3-tangle. We find that the generalized GHZ states and the maximal slice states have unique tripartite entanglement and nonlocality properties in the set of all pure states.

### 15. Optomechanical systems

(Session 1: Thursday from 6:00-6:45)

**Abstract**. Very sensitive mechanical detectors are rapidly approaching a regime in which either the mechanical device itself or its readout should demonstrate quantum behavior. The main technical barrier to reaching this regime has been the difficulty of integrating ultrasensitive micromechanical devices with high-finesse optical cavities. Recently we have developed a robust means for addressing this issue, and have integrated a 50 nm-thick membrane (with a quality factor > 1,000,000) into an optical cavity with a finesse ~ 200,000. Although the membrane is nearly transparent, it couples to the optical cavity dispersively. This coupling is strong enough to laser-cool the membrane from room temperature to 7 mK. In addition, the dispersive nature of the optomechanical coupling allows us to realize a sensitive "displacement squared" readout of the membrane. Such a readout is a crucial requirement for measuring quantum jumps in a mechanical oscillator. We will describe these results, as well as our progress towards observing quantum effects in this system.

### 16. The Classically-Enhanced Father Protocol

Min-Hsiu Hsieh, Quantum Computation and Information Project, Solution Oriented Research for Science and Technology

(Session 12: Sunday from 11:45-12:15)

**Abstract**. The classically-enhanced father protocol is an optimal protocol for a sender to transmit both classical and quantum information to a receiver by exploiting preshared entanglement and a large number of independent uses of a noisy quantum channel. We detail the proof of a quantum Shannon theorem that gives the three-dimensional capacity region containing all achievable rates that the classically-enhanced father protocol obtains. Points in the capacity region are rate triples consisting of the classical communication rate, the quantum communication rate, and the entanglement consumption rate of a particular coding scheme. The classically-enhanced father protocol is more general than any other protocol in the family tree of quantum Shannon theoretic protocols. Several previously known quantum protocols are now child protocols of the classically-enhanced father protocol. Interestingly, the classically-enhanced father protocol gives insight for constructing optimal classically-enhanced entanglement-assisted quantum error-correcting codes.

### 17. Quantum Control of Large Atomic Hyperfine Manifolds

Poul Jessen, University of Arizona

(Session 2: Friday from 9:15-9:45)

**Abstract**. Laboratory techniques to manipulate and observe ultracold atoms make these an attractive platform for testing new ideas in quantum control and measurement. I will review a series of experiments in which we have used tensor AC Stark shifts and magnetic fields to drive non-trivial quantum dynamics of a large spin-angular momentum associated with an atomic hyperfine ground state. The nonlinear spin Hamiltonian is sufficiently general to achieve universal quantum control over the 2F+1 dimensional state space, and allows us to generate arbitrary spin states and perform a full quantum state reconstruction of the result. We have implemented and verified time optimal controls to generate a broad variety of spin states, as well as an adiabatic scheme to generate spin-squeezed states for metrology. Most recently we have used our control and measurement tools to realize a common paradigm for quantum chaos known as the quantum kicked top. Direct observation of the phase space dynamics of this system has given an unprecedented look at quantum/classical correspondence. We are now implementing a new scheme for quantum control of an entire ground hyperfine manifold, based solely on interaction with DC, radiofrequency and microwave magnetic fields. The longer coherence times available with this approach will allow us to explore new ideas related to robust control and constructive design of unitary transformations.

### 18. Ion Motional Entanglement and Quantum Information Experiments at NIST*

John Jost, National Institute of Standards and Technology, Boulder

(Session 6: Saturday from 9:15-10:45)

**Abstract**. I will summarize current trapped-ion quantum information processing (QIP) experiments at NIST. Quantum entanglement has been the subject of considerable research, in part due to its non intuitive nature and ubiquitous presence in QIP. For this reason it is of interest to study entanglement in a variety of systems. We demonstrate deterministic entanglement in a system pervasive in nature: mechanical oscillators. Here, the mechanical oscillators are composed of the vibrations of two Be+ - Mg+ ion pairs in spatially separate locations. The techniques demonstrated in this experiment are likely to form core components of large-scale trapped-ion QIP. Other work at NIST includes characterization of ion transport dynamics in a trap array that includes a 2-D junction, recent developments in micro-fabricated surface traps, and studies of dynamic decoupling. * supported by IARPA and the NIST Quantum Information Program

### 19. Simplifying quantum double Hamitonians using perturbative gadgets

Robert Koenig, California Institute of Technology

(Session 11: Sunday from 9:45-10:15)

**Abstract**. Perturbative gadgets were originally introduced to generate effective k-local interactions in the low-energy sector of a 2-local Hamiltonian. Extending this idea, we present gadgets which are specifically suited for realizing Hamiltonians exhibiting non-abelian anyonic excitations. At the core of our construction is a perturbative analysis of a widely used hopping-term Hamiltonian. We show that in the low-energy limit, this Hamiltonian can be approximated by a certain ordered product of operators. In particular, this provides a simplified realization of Kitaev's quantum double Hamiltonians.

### 20. Recent Progress in Quantum Computing with Optically Controlled Semiconductors

Thaddeus Ladd, Stanford University

(Session 1: Thursday from 7:45-8:15)

**Abstract**. I will present two recent experimental results from the Yamamoto group at Stanford. The first is the rapid initialization and subsequent coherent manipulation of a single electron spin qubit in a self-assembled InAs quantum dot using ultra-fast laser pulses. This result demonstrates a complete single qubit gate set at the highest possible clock speed for the system. The second is the generation of indistinguishable single photons from two separate semiconductor sources based on isolated donor-bound excitons in ZnSe/ZnMgSe quantum wells. This result demonstrates a tool of great importance for linear optics quantum computing; it also shows promise for mass-production of homogeneous, optically connected semiconductor qubits. I will also briefly indicate some theoretical work on implementing all-optical quantum logic and designing a complete quantum computer architecture around these elements.

### 21. Exploring exotic matter through the quantum manipulation of dipolar atoms

Benjamin Lev, University of Illinois at Urbana-Champaign

(Session 2: Friday from 10:15-10:45)

**Abstract**. Highly magnetic atoms such as dysprosium offer the ability to create strongly correlated matter in both atomic physics and quantum optics settings. In addition, these atoms will form the key ingredient in novel devices possessing unsurpassed sensitivity and resolution for the microscopy of condensed matter materials. Our group aims to develop technology to perform laser cooling---and subsequent trapping in atom chips and optical lattices---of dysprosium. This will lead to three research projects: the investigation of quantum liquid crystal physics in 2D fermoinic dipolar lattices; the exploration of non-equilibrium quantum phase transitions in many body cavity QED; and the development of atom chip microscopy at the 10^-10 magnetic flux quantum level.

### 22. Optical lattice-based addressing and control of long-lived neutral-atom qubits

Nathan Lundblad, Joint Quantum Institute/NIST/Univ. of Maryland

(Session 2: Friday from 10:45-11:15)

**Abstract**. Quantum computational platforms are driven by competing needs: the isolation of the quantum system from the environment to prevent decoherence, and the ability to control the system with external fields. For example, neutral-atom optical-lattice architectures provide environmental isolation through the use of "clock" states that are robust against changing external fields, yet those same external fields are inherently useful for qubit addressing. Here we demonstrate a technique to address a spatially dense field-insensitive qubit register. A subwavelength-scale effective magnetic-field gradient permits the addressing of particular "marked" elements of the lattice register, leaving unmarked qubits unaffected, with little worry about crosstalk or leakage. We demonstrate this technique with rubidium atoms, and show that we can robustly perform single-qubit rotations on qubits located at addressed lattice sites. This precise coherent control is an important step forward for lattice-based neutral-atom quantum computation, and is applicable to state transfer and qubit isolation in other architectures using field-insensitive qubits.

### 23. Ion Trap Photonic Quantum Networks

Christopher Monroe, JQI and University of Maryland

(Session 6: Saturday from 10:15-11:00)

**Abstract**. The local manipulation and entanglement of nearby atomic ion qubits through their Coulomb interaction is now established as one of the most reliable ways to build entangled states. Trapped ions can also be coupled through a photonic channel, allowing for various remote probabilistic ion-ion entanglement protocols. Recent experiments have shown entanglement, a Bell inequality violation, teleportation, and operation of a two-qubit quantum gate between two ions separated by 1 meter. Despite the probabilistic nature of this ion/photon network, it can be efficiently scaled to much larger numbers of ions for distributed large-scale quantum computing and long-distance quantum communication, especially when accompanied by local Coulomb-mediated deterministic quantum gates. Future work will couple photons emitted from trapped ions into optical cavities, and perhaps interface trapped ion qubits with other optically-active qubits such as quantum dots.

### 24. Quantum Fidelity and Thermal Phase Transitions

Haitao Quan, Los Alamos National Laboratory

(Session 1: Thursday from 8:15-8:45)

**Abstract**. We study the quantum fidelity approach to characterize thermal phase transitions. Specifically, we focus on the mixed-state fidelity induced by a perturbation in temperature. We consider the behavior of fidelity in two types of second-order thermal phase transitions (based on the type of non-analiticity of free energy), and we find that usual fidelity criteria for identifying critical points is more applicable to the case of $\lambda$ transitions (divergent second derivatives of free energy). Our study also reveals that for fixed perturbations, the sensitivity of fidelity at high temperatures (where thermal fluctuations wash out information about the transition) is reduced. From the connection to thermodynamic quantities we propose slight variations to the usual fidelity approach that allow us to overcome these limitations. In all cases we find that fidelity remains a good pre-criterion for testing thermal phase transitions, and we use it to analyze the non-zero temperature phase diagram of the Lipkin-Meshkov-Glick model.

### 25. Two-qubit quantum logic gates via optical Feshbach resonances in alkaline-earth-like atoms

Iris Reichenbach, University of New Mexico

(Session 2: Friday from 11:15-11:45)

**Abstract**. The ability to implement quantum information processing in neutral atoms hinges critically on the ability to coherently control both the internal states and the interactions between two such atoms. We show that alkaline-earth-like atoms are uniquely suited to the task of quantum computing, due to their rich but controllable internal structure, including the nuclear spin, and their very narrow 1S0 -> 3P1 intercombination transition, which makes the application of optical Feshbach resonances possible. Optical Feshbach resonances allow for fine tuning of the interaction strength over a wide range, even making it possible to completely turn off the interaction, thus improving the coherence time. Theoretical modeling of the optical Feshbach resonance on the example of 171Yb shows their potential in the implementation of two qubit gates through nuclear spin exchange.

### 26. Measurement-Based Quantum Computation in Realistic Spin-1 Chains

Joseph Renes, Technical University of Darmstadt

(Session 9: Saturday from 3:30-4:00)

**Abstract**. The excitement surrounding measurement-based quantum computation comes not just from the intriguing theoretical result that the power of a quantum computer can be attributed to the nature of the initial state, but also the more practical feature that it might be possible to find or engineer physical systems which would naturally provide such initial states as ground states. Since no system can be controlled or engineered perfectly, it is therefore vital to develop methods which characterize how suitable a given physical system is for this purpose. Moreover, this must be done in a way which circumvents the apparent need to evaluate the result for arbitrary computational measurement sequences, as these grow exponentially in number. We study this problem at the single-qubit level for the hybrid scheme recently introduced by Brennen and Miyake [1] using gapped one-dimensional spin-1 AKLT chains. Here individual qubit gates are performed by measurement while two-qubit gates are performed by dynamically coupling different chains. Brennen and Miyake describe a implementations using either atoms or polar molecules in optical lattices, where the gap is expected to help suppress decoherence. We show that the approach taken by Doherty and Bartlett to characterize the computational power of nearly-cluster state quantum computers [2] can be profitably adapted to this case, avoiding the exponential counting trap mentioned above. By numerical and perturbative analysis we find that arbitrary single-qubit operations can be faithfully executed over a reasonably wide parameter range of bilinear-biquadratic Hamiltonians near the AKLT point. Furthermore, we find that the Doherty-Bartlett approach leads directly to the use of string order parameters, showing a connection between computational questions and the traditional theoretical study of condensed matter, where these parameters arise. Joint work with Stephen Bartlett, Gavin Brennen, and Akimasa Miyake. [1] Brennen and Miyake, Phys. Rev. Lett. 101, 010502 (2008). [2] Doherty and Bartlett, arXiv:0802.4314v1 [quant-ph].

### 27. Comparison between continuous wave and pulsed laser EQKD

Patrick Rice, Los Alamos National Lab

(Session 12: Sunday from 11:15-11:45)

**Abstract**. Entangled quantum key distribution (EQKD) is a secure protocol that is based on fundamental quantum mechanics and is not vulnerable to these threats. The primary figure of merit for QKD systems is the ability to generate secret bits. However, to date, methods that have been developed to simulate the secret bit rate generation for EQKD systems have been limited by techniques that do not provide a complete description of the quantum state produced by the source. In this talk, I show a complete description and comparison of the secret bit rate for continuous-wave and pulsed laser EQKD systems. In particular, I highlight the relevant Poissonian and thermal photon statistics that affect the EQKD secret bit rate and use practical system parameters and configurations to show regimes where one expects optimal performance for each case.

### 28. Non-Markovian Environmental Contributions to the Efficiency of Energy Transfer

Cesar Rodriguez-Rosario, Harvard University

(Session 10: Saturday from 5:00-5:30)

**Abstract**. Non-Markovian environmental effects have been experimentally observed in the Fenna-Matthews-Olson photosynthetic complex, but their role is not understood. We study the dynamical contribution of the environment to the efficiency of energy transfer by considering a non-Markovian environment and its interplay with the system Hamiltonian. We focus on the role of memory effects of different orders in time, and their competition that affect the energy transfer by defining the efficiency of the non-Markovian process. This efficiency measure has applications to the study of the quantum transport efficiency and engineering of light-harvesting devices.

### 29. Heisenberg limited phase estimation with mode-entangled coherent states

Anil Shaji, The University of New Mexico

(Session 7: Saturday from 1:00-1:30)

**Abstract**. We investigate phase estimation in a Mach-Zehnder type interferometer using the ``0BB0" state which is a mode-entangled state formed by superposing a state with the vacuum in the first arm of the interferometer and a coherent state in the second arm and another state with the coherent state in the first arm and the vacuum in the second. The quantum Cramer-Rao bound on the measurement uncertainty in the estimate of an unknown phase shift between the two arms of the interferometer scales inversely with the mean photon number in the 0BB0 state (Heisenberg limited scaling). We discuss how 0BB0 states can be created and also the measurements that must be performed on the output state of the interferometer in order to find the phase shift. We compare the performance of the 0BB0 states in phase estimation with that of ``N00N" states. In the presence of photon loss, using 0BB0 states instead of N00N states, lead to lower measurement uncertainties.

### 30. Renewing and Uniting Two Challenges of John von Neumann and Richard Feynman: Atomic-Resolution Biomicroscopy and Simulating Quantum Physics with Computers

John Sidles, University of Washington

(Session 7: Saturday from 1:30-2:00)

**Abstract**. In two renowned lectures, Richard Feynman (in 1959) challenged mathematicians, scientists, and engineers to "see the individual atoms" in biological molecules and (in 1982) to "make a simulation of nature [that is] quantum mechanical." An earlier statement of these same challenges can be found in a 1946 letter from John von Neumann to Norbert Weiner. The status of these two challenges is reviewed. Atomic-resolution biomicroscopy is treated as a problem in quantum communication whose fundamental quantum limits can be calculated by combining Feynman's formalism for quantum measurement with Shannon's formalism for information channel capacity. Modern advances in quantum information theory and simulation science suggest avenues for further analysis. The assessment concludes that both of von Neumann's and Feynman's challenges are rapidly approaching scientific and technological feasibility.

### 31. Channel-Optimized Quantum Error Correction

Soraya Taghavi, University of Southern California

(Session 8: Saturday from 4:30-5:00)

**Abstract**. We develop a theory for finding quantum error correction (QEC) procedures which are optimized for given noise channels. Our theory accounts for uncertainties in the noise channel, against which our QEC procedures are robust. We demonstrate via numerical examples that our optimized QEC procedures always achieve a higher channel fidelity than the standard error correction method, which is agnostic about the specifics of the channel. Our main novel finding is that in the setting of a known noise channel the recovery ancillas are redundant for optimized quantum error correction. We show this using a general rank minimization heuristic and supporting numerical calculations. Therefore, one can further improve the fidelity by utilizing all the available ancillas in the encoding block.

### 32. No-Go Results for a 2D Quantum Memory Based on Stabilizer Codes

(Session 3: Friday from 1:15-2:00)

**Abstract**. We study the possibility of a self-correcting quantum memory based on stabilizer codes with geometrically-local stabilizer generators. We prove that the distance of such stabilizer codes in D dimensions is bounded by O(L^{D-1}) where L is the linear size of the D-dimensional lattice. In addition, we prove that in D=1 and D=2, the energy barrier separating different logical states is upper-bounded by a constant independent of L. This shows that in such systems there is no natural energy dissipation mechanism which prevents errors from accumulating. Our results are in contrast with the existence of a classical 2D self-correcting memory, the 2D Ising ferromagnet.

### 33. Designing Optimal States and Transformations for Quantum Optical Communication and Metrology

(Session 9: Saturday from 4:30-5:00)

**Abstract**. Entangled states of light are in great demand in quantum technology today. Photonic quantum communication, information processing, and metrology are all based on exploiting special properties of non-classical multipath entangled states. Generation of such states and quantum operations on them require effective photon-photon interaction which may be produced using ancilla modes and projective measurements. We will report on our study of optimal implementations of optical measurement-assisted transformations of non-classical photonic states, by performing numerical optimization of the fidelity, success probability, and Fisher-information functions. For the first time, we have provided convincing numerical evidence that for the basic CNOT (CS) gate the maximal success probability is S = 2/27. We have numerically verified a hypothesis that maximal success probability is achieved using a minimal level of ancilla resource (for NS, CS and Toffoli gates). As a proof of principle, we demonstrated that heuristic methods of constructing optimal optical schemes are quite limited when it comes to complicated 3- and more qubit gates: using the Toffoli gate, we found a scheme that uses fewer ancilla photons and provides better success probability than the best previously known scheme.The numerical optimization method was used to address the error-correction problem. For a particular error-correction scheme, the encoding-decoding gates required construction of a CS gate coupling hyper-entangled qubits. The solution found numerically requires only three ancilla photons while providing maximal success probability. We will also report on our numerical results for optimization of Heisenberg-limited quantum phase metrology.

### 34. Verifying multi-partite mode entanglement of W states

Steven van Enk, University of Oregon

(Session 4: Friday from 3:30-4:00)

**Abstract**. We construct a method for verifying mode entanglement of N-mode W-states. The ideal W-state contains exactly one excitation symmetrically shared between N modes, but our method takes the existence of higher numbers of excitations into account, as well as the vacuum state and other deviations from the ideal state. Moreover, our method distinguishes between full N-party entanglement and states with M-mode entanglement with M

### 35. Resource Handling for Quantum Networks of Arbitrary Topology

Rodney Van Meter, Keio University

(Session 8: Saturday from 3:30-4:00)

**Abstract**. To date, research on entangled quantum networks has primarily focused on an abstract model consisting of a linear chain of repeaters, with a power of two number of hops of identical length and quality. We are analyzing the behavior of more complex network topologies, with more than two end nodes competing to communicate across shared links. We compare three resource management disciplines, hop-by-hop teleportation, nested entanglement swapping, and graph state-based bipartite communication. We discuss quantum equivalents to the classical network concepts of spatially and temporally multiplexed circuit switching, and packet switching. We show cases in which multiplexing raises the aggregate communication rate, and cases in which graph states help the system reach the bisection bandwidth.

### 36. Quantum computing with atoms in a 3D optical lattice

(Session 2: Friday from 8:30-9:15)

**Abstract**. We have demonstrated trapping and imaging of 250 single atoms in a 3D optical lattice. The 5 micron lattice spacing is large enough that individual atoms can be addressed using lasers and microwaves in a way that does not affect the quantum coherence of other atoms. Our goal is to use these trapped atoms as qubits. So far, we fill a random half of the lattice sites, but a combination of site-selective state changes and state-selective lattice translations should allow us to verifiably fill all vacancies. We will describe our experiments to date and our plans for entangling atoms and implementing a neutral atom quantum computer.

### 37. Quantum communication with zero-capacity channels

Jon Yard, Los Alamos National Laboratory

(Session 12: Sunday from 10:45-11:15)

**Abstract**. A quantum channel models a physical process in which noise is added to a quantum system via interaction with its environment. Protecting quantum systems from such noise can be viewed as an extension of the classical communication problem introduced by Shannon sixty years ago. A fundamental quantity of interest is the quantum capacity of a given channel, which measures the amount of quantum information which can be protected, in the limit of many transmissions over the channel. In this talk, I will show that certain pairs of channels, each with a capacity of zero, can have a strictly positive capacity when used together, implying that the quantum capacity does not completely characterize a channel's ability to transmit quantum information. As a corollary, I will show that a commonly used lower bound on the quantum capacity - the coherent information, or hashing bound - is an overly pessimistic benchmark against which to measure the performance of quantum error correction because the gap between this bound and the capacity can be arbitrarily large. This is joint work with Graeme Smith (IBM), published in the Sept. 26 issue of Science.

### 38. Duality theorem and topological properties in local stabilizer codes

Beni Yoshida, Massachusetts Institute of Technology

(Session 8: Saturday from 5:00-5:30)

Topological codes offer the possibility of a naturally fault-tolerant quantum memory, and significant progress has been made with theoretical constructions in four dimensions. However, recent work (Bravyi and Terhal; Kay and Colbeck) has ruled out the possibility of such memories in two-dimensions, and left an open question about three-dimensional topological codes. Specifically, Bravyi and Terhal show that the distance of geometrically local stabilizer codes in a D-dimensional lattice of volume L^{D} is bounded above by O(L^{D - 1}).

Here, we present a new approach to the problem, which sharpens these bounds, by limiting consideration to topological codes whose stabilizers are geometrically local and have translational symmetry. Using this physically reasonable assumption, and assuming that the number of logical qubits is a small number which is independent of the lattice size, we find that the logical qubits must obey a duality theorem, whereby each logical qubit may be described by a pair of weight O(L^{a}) and O(L^{D - a}) logical operators. This gives a full set of relations between all logical operators. It follows from this theorem that the distance of such codes is bounded above by O(L^{n}) for 2n- and (2n+1)-dimensional lattices.

This non-trivial duality clearly distinguishes systems of even and odd dimension. One surprising consequence is that for certain definitions of topological protection, encodings are possible only in systems of even dimension. This is consistent with a fact in topological quantum field theory, that the quantum Hall effect can occur only in systems of even dimension. We illustrate the implications of this observation by showing that on a two-dimensional Bravais lattice with a small number of encoded qubits, all the logical operators have O(L) weight, such that all the logical qubits are topologically protected from local errors. This also allows us to directly relate the number of encoded qubits with the topological entropy, providing insights which will be useful in designing gapped Hamiltonians with topological properties which may be useful for quantum memories.

[1] Sergey Bravyi and Barbara M. Terhal, "A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes", arXiv:0810.1983 (2008)[2] Alastair Kay and Roger Colbeck, "Quantum Self-Correcting Stabilizer Codes", arXiv:0810.3557 (2008)

### 39. Optimal experiment design for parameter estimation as applied to dipole- and exchange-coupled qubits

Kevin Young, University of California - Berkeley

(Session 7: Saturday from 2:00-2:30)

**Abstract**. We consider the problem of quantum parameter estimation with the constraint that all measurements and initial states are separable. Two qubits are presumed coupled through the dipole and exchange interactions. The resulting Hamiltonian generates a unitary evolution which, when combined with arbitrary single-qubit operations, contributes to a universal set of quantum gates. However, while the functional form of the Hamiltonian is known, a particular experimental realization depends on several free parameters - in this case, the position vector relating the two qubits and the magnitude of the exchange interaction. We use the Cramer-Rao bound on the variance of any point estimator to construct an optimal series of experiments to estimate these free parameters. Our method of transforming the constrained optimal estimation problem into a convex optimization is powerful and widely applicable to other systems.

### 40. Generalized Concatenated Quantum Codes

Bei Zeng, Massachusetts Institute of Technology

(Session 3: Friday from 2:00-2:30)

Quantum error-correcting codes play a central role in quantum computation and quantum information. While considerable understanding has now been obtained for a broad class of quantum codes, almost all of this has focused on stabilizer codes, the quantum analogues of classical additive codes. Nevertheless, there are a few known examples of nonadditive codes which outperform any possible stabilizer code. In previous work (a talk given at SQuInT 2008), my colleagues and I introduced the codeword stabilized ('CWS') quantum codes framework for understanding additive and nonadditive codes. Within this framework we found good new nonadditive codes using exhaustive or random search. However, these new codes have no obvious structure to generalize to other cases -- no nonbinary nonadditive code which outperforms any additive code has ever been found since the search space is getting too large. A systematical understanding of constructing good nonadditive CWS codes is still lacking.

In this work we provide a systematical method of constructing nonadditive CWS codes by introducing the concept of generalized concatenated quantum codes. Compared to the usual concatenated quantum code construction, the role of the basis vectors of the inner quantum code is taken on by subspaces of the inner code.

Using this generalized concatenation method, we systematically construct families of single-error-correcting nonadditive CWS codes, in both binary and nonbinary cases, which outperform any stabilizer codes. Particularly, we construct a ((90,2^{81.825},3)) qubit code as well as a ((840,3^{831.955},3)) qutrit code, which is the first known nonbinary nonadditive code that outperforms any stabilizer codes. For large block lengths, we show that these families of nonadditive codes asymptotically achieve the quantum Hamming bound. What is more, our new method can also be used to construct stabilizer codes. We show that many good stabilizer codes, e.g. quantum Hamming codes, can be constructed this way. Moreover, we found new stabilizer codes with better parameters than previously known, e.g. a [[36,26,4]] qubit code.

Based on joint work with Markus Grassl, Peter Shor, Graeme Smith, and John Smolin.