2007 Poster Abstracts
Quantum information processing using orbital states of neutral donors
Dan Allen, University of California Santa Barbara
Electrons bound to shallow donors in GaAs have a hydrogenic bound state spectrum with a 1S-2P transition ~1THz (4meV). The occupancy of the |0> state (1S orbital) can be detected optically via a rapid (1 ns) light scattering or cycling transition involving the bound exciton state. (Ref. 1) At modest magnetic fields ~5 T the (dark) 2P- orbital state is well isolated and serves as the qubit |1> state, with a ~1us lifetime. Rabi oscillations of an ensemble of neutral donor qubits has been demonstrated using photoconductivity as a measure of the excited state population. (Ref. 2) Recently the optical quantum nondemolition readout technique has been used to measure the qubit lifetime (T1) versus temperature and dopant density. A scanning delay line for free space THz beams has been constructed to enable Hahn echo measurements of the decoherence time T2, which is expected to be much greater than the ensemble dephasing time (T2*) of 50 ps. Concurrent work focuse s of the design and testing of THz cavities to achieve strong coupling of isolated neutral donor qubits. References: 1. Phys. Rev. B 72, 035302 (2005) 2.. Nature 410, 60 (2001)
Multilayer Surface Electrode Ion Traps for Scalable Quantum Processing
Jason Amini, National Institute of Standards and Technology
J. M. Amini, S. Seidelin, J. H. Wesenberg, J. Britton, R. B. Blakestad, K. R. Brown, J. J. Bollinger, R. J. Epstein, J. P. Home, W. M. Itano, J. D. Jost, C. Langer, D. Leibfried, R. Ozeri, N. Shiga, and D. J. Wineland (Time and Frequency Division, NIST, Boulder, Colorado 80305, USA). Microfabricated surface electrode traps for ions are a promising technology for building scalable trapping geometries for quantum information processing. We have expanded upon our single layer gold-on-fused-silica surface electrode trap [1] to include a second patterned conducting layer under the trapping electrodes and have demonstrated the fabrication of this architecture using standard microfabrication techniques. The multilayer approach allows for a significant increase in multi-zone trapping complexity and permits improved trapping structures that are otherwise unattainable in single layer designs without vertical interconnects. Using improved calculational methods [2], we are in the process of optimizing the planar designs to create modular elements that can be joined into larger multi-zone trapping structures. Work supported by DTO and NIST.
[1] S. Seidelin et al., Phys. Rev. Lett. 96, 253003 (2006).
[2] See the abstract by J. H. Wesenberg.
Cloning, broadcasting, disturbance and teleportation in probabilistic theories
Howard Barnum, Los Alamos National Laboratory
This talk summarizes some recent results involving information processing in a very broad class of finite-dimensional convex probabilistic models satisfying a no-signaling criterion, which includes quantum and classical theory as very special cases. In this setting, we prove generic versions of the no-cloning and no- broadcasting theorems, prove that information that can be obtained without disturbance is inherently classical, and characterize theories permitting conclusive probabilistic teleportation. If time permits some cryptographic issues and open questions will be touched on. Many of the results are joint work with Jonathan Barrett, Matthew Leifer, and Alexander Wilce.
Ion Trap Chips with 3D Optical Access for Experiments in Quantum Information
M.G. Blain, C.P. Tigges, D.J. Berkeland (LANL), Sandia National Laboratories
In this poster, we present our recent progress on the microfabrication and packaging of ion trap chips for applications in quantum information experiments. The fabrication process for trap electrodes and air bridge metallic leads, based on a MEMS fabrication technology utilizing molded tungsten, and the engineering of the chip substrate, to provide 3D optical access to the trapping region, is briefly reviewed. We also describe: (1) the development of a custom chip packaging technology that also provides 3D optical access to the traps; and (2) our efforts to metallize the dielectric materials near the trapping region, a key for controlling potentials near the trapping region. We also show some of the initial trapping results in these traps obtained by the NIST group in Boulder.
Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
Simple multi-parameter Heisenberg Limit
Sergio Boixo, University of New Mexico
We consider multi-parameter estimation of a general unitary operation acting on a set of qubits. We show a simple quantum circuit that estimates operators at the optimal Heisenberg limit, i.e., achieving a sensitivity for determining the parameters that scales as 1/N, where N is the number of times the unknown unitary is applied. The circuit makes use of one extra qubit (ancilla) which is initially prepared in a pure state, while the system qubits are initially prepared in the totally mixed state.
Coherent state transfer between a classical pulse and a trapped atom in cavity QED
A. D. Boozer, A. Boca, R. Miller, T. E. Northup, and H. J. Kimble, California Institute of Technology
We demonstrate the coherent mapping of a weak classical state of light (nbar ~ 1) onto the 6S1/2 hyperfine ground states of a single cesium atom trapped within the mode of a high finesse optical cavity. We are able to verify the coherence of this mapping by transferring the atomic state onto a single photon in a way dependent upon the phase of the original field [1]. We present theoretical simulations which address the dependence of efficient coherent state transfer on atom-cavity coupling g and other system parameters. This is an important step towards the realization of a cavity QED-based quantum network, wherein this type of process will serve as means for the storage and exchange of quantum information between individual nodes.
[1] J. McKeever et al., Science 303, 1992 (2004).
Pulse Programming for Qubit Transitions
Ryan Bowler, University of Washington
Ryan Bowler1, Paul Pham2, Boris Blinov1 1University of Washington Department of Physics 2University of Washington Computer Science and Engineering Department We report on the implementation of a homebuilt pulse programmer for high-fidelity qubit transitions. Square-wave signal envelopes commonly used to drive atomic transitions have frequency sidebands to which pulses lose energy and which also can cause unwanted transitions. On the other hand, the Fourier transformation of a Gaussian envelope is also a Gaussian, a much preferred waveform carrier for our pulses. The pulse programmer contains digital-to-analog converter (DAC), variable gain amplifier (VGA), and digital synthesizer circuit boards which are controlled through a programmable pulse sequencer motherboard. The device allows for TTL bit signals to be sent into the digital-to-analog converter to produce any desired waveform (of particular interest is the Gaussian) to modulate the 8.037 GHz microwaves which drive hyperfine transitions in trapped 137Ba+ ions. The TTL bits have a 10ns minimum duration for 32 simultaneously switching outputs. The digital synthesizer enab les direct control of the microwave phase. The pulse programmer has 8 input triggers to be able to cycle through various programs based on user input and 2 waveform output channels. Future improvement will include a pulse counter to allow triggering based on the quantum state, more sophisticated clock control, and remote internet control of the programmer.
Multi-Photon Quantum Interference Effects in Sensor Technologies
Todd A. Brun (University of Southern California), Ivan Deutsch (University of New Mexico), Marc C. Welliver, Ned Allen, Lockheed Martin Coherent Technologies
Use of quantum interference phenomena in sensor technologies offers the potential for dramatic improvement in resolution and sensitivity. Measurement protocols have been conceived in which multi-photon interference effects can be used to improve spatial resolution (beating the diffraction limit), improve temporal resolution of interferometric systems, achieve noiseless amplification of images, and improve measurement precision beyond the standard quantum limit. Other areas of potential sensor improvement include access to additional target or scene characterization and classification information, improved efficacy of automated feature algorithms in imaging applications, and low-probability-of-intercept operation of sensing and communication equipment. We describe a technique by which multi-photon interference between a coherent state and a nonclassical ``cat'' state allows us to improve resolution without using higher frequency light. The two-photon version of this protocol should be practical in near-term demonstration experiments.
Computing entanglement of Mixed States
Kate Carlisle, Haverford College
Computation of entanglement of mixed states of more than two qubits requires minimization over the set of ensembles which realize the mixed state. This convex roof construction can be implemented using a theorem of Schroedinger's which identifies the set of ensembles with a set of unitary transformations. We present results on the computation of mixed state entanglement using random matrix methods to sample from the set of ensembles.
Teleportation depth as a measure of quantum gate complexity
Xie Chen, Bei Zeng, and Issac L. Chuang, Massachusetts Institute of Technology
Teleportation as a computational primitive is important for fault tolerant quantum computation. However, multiple teleportation steps must typically be performed in order to implement a desired quantum gate. Assuming that arbitrary ancilla states are free and there is no limit to the number of Clifford operations applied, how many teleportation steps are necessary, on average, to approximate a given gate to a certain error? For classical circuits, a similar measure of gate complexity, such as the minimal number of Toffoli gates, is typically intractable. Surprisingly however, the measure we introduce here for quantum gate complexity, which we call teleportation depth, can be bounded in a useful way for some important quantum circuits, such as the Quantum Fourier Transform. Fascinatingly, certain classical reversible gates have a teleportation depth lower than that obtained by decomposition into standard gates and teleportation.
Local unitary versus local Clifford equivalence of stabilizer and graph states
Hyeyoun Chung, Massachusetts Institute of Technology
Bei Zeng, Hyeyoun Chung, Andrew W. Cross, and Isaac L. Chuang (Massachusetts Institute of Technology) The equivalence of stabilizer states under local transformations is of fundamental interest in understanding properties and uses of entanglement. Two stabilizer states are equivalent under the usual stochastic local operations and classical communication criterion if and only if they are equivalent under local unitary (LU) operations. More surprisingly, under certain conditions, two LU equivalent stabilizer states are also equivalent under local Clifford (LC) operations, as was shown by Van den Nest et al. [1]. Here, we broaden the class of stabilizer states for which LU equivalence implies LC equivalence (LU <=> LC) to include all stabilizer states represented by graphs with neither cycles of length 3 nor 4. To compare our result with Van den Nest et al., we show that any stabilizer state of distance d = 2 is beyond their criterion. We then further prove that LU <=> LC holds for a more general class of stabilizer states of d = 2. We also explicitly construct gr aphs representing d > 2 stabilizer states which are beyond their criterion: we identify all 58 graphs with up to 11 vertices and construct graphs with 2m+/-1 vertices using quantum error correcting codes which have non-Clifford transversal gates. [1] M. Van den Nest, J. Dehaene, B. De Moor, Phys. Rev. A71, 062323 (2005)
Silicon Based Solid State Quantum Computing Development Leveraging a CMOS Platform at Sandia National Laboratories
M. S. Carroll, M. P. Lilly, Sandia National Laboratories
Sandia National Laboratories is in a unique position to assist in the science and engineering of scalable silicon qubit development, in collaboration with the quantum computing community. Current internally supported solid state qubit development is intended to demonstrate feasibility at SNL. In this poster we will discuss: (1) our capabilities that can contribute to scaling of a silicon solid state approach and (2) approaches that we are considering for qubits that might be scalable in the future. Initial experiments (e.g., Si/oxide interface state measurements) and simulations are in progress to examine the feasibility of different silicon approaches, which will be discussed in the poster.
Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.
Effect of correlated noise on a fault-tolerant quantum error correction protocol
James Clemens, Miami University
We consider the effect of correlated noise in the context of a fault-tolerant quantum error correction protocol. The noise is represented by a set of classical fluctuating fields with partial spatial and temporal correlations. We explicitly account for the propagation of errors in the implementation of quantum circuits for ancilla verification and syndrome extraction. Errors arising from single-bit and two-bit gates are considered separately. The performance of the error correction protocol is characterized by means of the probability for an uncorrected error to occur calculated from numerical simulations of the error propagation. For errors on single-bit gates, using the [[7,1,3]] code, we find that in the limit of strong correlations the crash probability is enhanced roughly by a factor of three. For the two-bit gates we find that the effect of correlated noise can be minimized by choosing an appropriate sequence of operations which takes advantage of th e correlations with an order of magnitude difference between the best and worst cases.
Feasibility of the controlled-NOT gate from certain model Hamiltonians
Mark W. Coffey and Gabriel G. Colburn, Department of Physics, Colorado School of Mines
There has been much interest of late in characterizing two-qubit operations, optimizing the number of quantum logic gates in small circuits, and developing minimal universal bases of quantum gates. The controlled-NOT (CNOT) gate is widely used in quantum circuits and in current and proposed quantum computing technologies. We investigate the feasibility and minimal implementation of CNOT from specific model Hamiltonian operators that have appeared in the literature. We first address the question whether certain parameterized Hamiltonians can generate a CNOT up to single-qubit gates in a definite time. If so, we determine the time for this unitary evolution. We follow an algebraic approach that provides an analytic solution. Our method has direct relevance to two-qubit Hamiltonians currently being considered for spin-based and superconductivity-based-systems for quantum computing as well as to other implementations. Work supported by Air Force contract numbers FA870-04-1-0298 and FA8750-06-1-0001.
Entanglement and correlations in mixed-state quantum computation
Animesh Datta, University of New Mexico
A very intriguing model of mixed-state quantum computation is the `power of one qubit' [E. Knill and R. Laflamme, Phys. Rev. Lett. 81, 5672 (1998)], which has one pure qubit and n qubits in the completely mixed state. This model is known to evaluate the normalized trace of a unitary matrix with fixed accuracy efficiently, and offers an exponential speed-up over the best known classical algorithm. We show that this model involves entangled states. We also show that, on one hand, these states have no more than a constant amount of entanglement (as measured by the negativity), while on the other, they have an exponentially high operator Schmidt rank. Since quantum systems with limited Schmidt rank are known to be simulatable classically in an efficient manner, this suggests that the advantage of mixed-state quantum computation may stem not from the amount of entanglement but the degree of correlations (as quantified by the operator Schmidt rank) the system possesses.
Efficiently distinguishing Borel conjugates of PSL(2;F_q)
Aaron Denney, University of New Mexico
An efficient quantum Fourier transform (QFT) is not known for the family of simple groups PSL(2;F_q), preventing the standard method of analyzing a coset state in the Fourier basis. However, some sets of subgroups are still efficiently distinguishable by doing partial Fourier transforms over partial coset states.
Barium Ions for Quantum Computation
Matthew Dietrich, University of Washington
We report progress on investigating 137Ba+ as a trapped ion qubit candidate. The hyperfine structure and visible spectrum cooling transitions of 137Ba+ make it an excellent qubit candidate. Here we report trapping 138Ba+, an even isotope of barium, in a linear Paul trap. Cooling is provided by two diode lasers, one at 650 nm and the other at 493 nm is generated by a doubled infrared laser. To create the sidebands necessary for trapping 137Ba+, an EOM is applied to the blue light, while the red is modulated directly using a bias-T on the diode's operating current. Shelving to the D5/2 state from the ground S1/2 state has been accomplished with a 1792 nm fiber laser and during qubit readout direct adiabatic rapid transfer will shelve the state with high fidelity. Rabi flops between the ground hyperfine levels will be performed using microwave pulses whose waveforms can be shaped using a homebuilt pulse sequencer. A 400 fs pulsed Ti:sapphire laser is doubl ed in a single pass of BBO to 455 nm, and can be used for coherent population transfer and single photon production, using the S1/2 to P3/2 transition.
THz Gain without Inversion from a Bloch Oscillator
Gregory C. Dyer, University of Calgary
Superlattices with periodically interspersed n+ doped regions, or super-superlattices, have the potential to supply terahertz gain at frequencies below the Bloch frequency. Because a Bloch oscillator does not require a population inversion like a traditional laser, a super-superlattice under current bias is especially promising as a room temperature terahertz laser. We anticipate that the n+ doped layers will suppress electric field domain formation, which otherwise inhibits Bloch gain. Our recent work has demonstrated potential terahertz cross-over from loss to a gain, with electrical bias as well as room temperature terahertz photon assisted transport in test super-superlattice devices. This suggests that with the appropriate geometry, a terahertz oscillator can be achieved. We focus on two such geometries, super-superlattice ring and disk resonators. Calculations indicate that gain should overcome intrinsic resonator losses due to leakage as well as due to materials. We will show typical super-superlattice material structures and device geometries as well as the experimental setup we have developed to explore terahertz emission.
Graphical description of the action of Clifford operators on stabilizer states
Matthew Elliott, University of New Mexico
We introduce a graphical representation of stabilizer states, which reduces to standard graphs for graph states. The effects of Clifford operators on stabilizer states are then translated into graph operations on the corresponding stabilizer state graphs, and we find that they are completely described in terms of loop complementation and local complementation.
Characterization of scalable ion traps for quantum computation
Ryan J. Epstein, National Institute of Standards and Technology
R. J. Epstein, J. J. Bollinger, D. Leibfried, S. Seidelin, J. Britton, J. H. Wesenberg, N. Shiga, J. M. Amini, R. B. Blakestad, K. R. Brown, J. P. Home, W. M. Itano, J. D. Jost, E. Knill, C. Langer, R. Ozeri, and D. J. Wineland Time and Frequency Division, NIST, Boulder, Colorado 80305, USA Abstract: We discuss the experimental characterization of several scalable ion trap architectures for quantum information processing. We have developed an apparatus for testing planar ion trap chips [1,2], which features: a standardized chip carrier for ease of interchanging traps, a single- laser Raman cooling scheme, and photo-ionization loading of Mg+ ions. A primary benchmark for a given trap is the heating rate of the ion motional degrees of freedom, which can reduce multi-ion quantum gate fidelities. As the heating rate depends on the ion trap geometry and materials, our testing apparatus allows for efficient iteration and optimization of trap parameters. For planar traps made of gold on fused quartz [1], we aim to compare heating rates measured via Raman cooling to those obtained from time-resolved fluorescence during Doppler re-cooling [1]. Work supported by DTO and NIST.
[1] S. Seidelin et al., Phys. Rev. Lett. 96, 253003 (2006).
[2] J. Kim et al., Quantum Inf. Comput. 5, 515 (2005).
On the evaluation of the Potts partition function for a class of graphs
Joseph Geraci, University of Southern California/Toronto
We present a scheme based on classical coding theory to compute the exact q-state Potts partition function for a certain class of graphs (co-cycle graphs of irreducible cyclic codes). The scheme requires a method to obtain the weights of code words. This can be done, e.g., via the approximation of Gauss sums or via the evaluation of Zeta functions. We show that using quantum computational resources for this weight evaluation step provides a speed up over the best current classical algorithms for this class of graphs. The speed up is polynomial in the number of vertices and exponential in the Potts q parameter. This work is part of an ongoing project to identify instances of classical statistical physical models for which quantum computers show a marked improvement in performance over classical machines.
Quantum chaos, entanglement and decoherence in the kicked top
Shohini Ghose, Wilfrid Laurier University
An understanding of the quantum behavior of systems with a chaotic classical limit is a central focus of fundamental studies of quantum mechanics. In recent years, the emergence of the field of quantum information science has sparked an interest in signatures of chaos in entanglement and decoherence of quantum systems. We present theoretical studies of entanglement, decoherence and chaos in the quantum kicked top. The ideal kicked top is analyzed as well as a realistic system of cold atoms interacting with lasers and magnetic fields. We describe a feasible experiment to study the kicked top with cold atoms including state preparation, manipulation and measurement. Signatures of chaos can be identified in the entanglement between the atom\'s electron and nuclear spin in a deeply quantum regime that is achievable in current experiments. We show that measuring the expectation values of the collective spin operators is sufficient to study the dynamical entanglement between the atom\'s electron and nuclear spin. The signatures of chaos in the evolution of the entanglement can be understood by examining the support of the initial state on regular versus chaotic Floquet eigenstates. In a strongly chaotic regime, decoherence due to photon scattering becomes significant. We perform accurate simula tions of the cold atom system and analyze the effect of decoherence on the entanglement dynamics. Although decoherence causes the overall purity of the nuclear+electron spin state to decay, the signatures of chaos identified in the entanglement between nuclear and electron spin can persist for times much longer than the photon scattering time. Furthermore, we show that chaos affects the decoherence rate even in a deeply quantum regime.
Purification of graph states
Kovid Goyal, California Institute of Technology
We present new recursive protocols for the purification of graph states. These protocols are designed to tolerate noisy purification operations and their performance is independent of the size of the state being purified. We develop new analytical techniques that allow us to derive simple recursion relations characterizing the protocols as well as rigorous estimates of thresholds for various noise models.
Super-fluid assisted quantum computation with group II atoms
David Hayes, University of New Mexico
We investigate the possibility of using super-fluid immersion in order to suppress diabatic transitions in a system governed by a time-dependent Hamiltonian. A simple model has been used to study the question where quantum information is stored in the nuclear spin of a group II atom which is trapped in a harmonic oscillator that is traveling at a constant velocity inside of a stationary BEC. While the motion of the trap acts to heat the atom in the trap to higher vibrational levels, the motion of the trapped atom creates excitations in the BEC and carries the energy away in the form of phonons and decreases the effective heating.
Entanglement-assisted quantum error correction
Min-Hsiu Hsieh, Todd A. Brun and Igor Devetak, University of Southern California
We show how entanglement shared between encoder and decoder can simplify the theory of quantum error correction. The entanglement-assisted quantum codes we describe do not require the dual-containing constraint necessary for standard quantum error correcting codes, thus allowing us to ``quantize'' all of classical linear coding theory. In particular, efficient modern classical codes that attain the Shannon capacity can be made into entanglement-assisted quantum codes attaining the hashing bound (closely related to the quantum capacity). We can also incorporate operator quantum error correction into entanglement-assisted quantum error correction formalism. This new scheme, which we call entanglement-assisted operator quantum error correction, is the most general quantum error-correcting technique known today.
Mesoscopic entanglement of atomic ensembles through non-resonant SRS
Wenhai Ji, Oregon Center for Optics, University of Oregon
We propose a scheme of generating and verifying mesoscopic- level entanglement between two atomic ensembles using non-resonant stimulated Raman scattering. Entanglement can be generated by direct detection or balanced homodyne detection of the Stokes fields from the two cells, after they interfere on a beam splitter. The entanglement of the collective atomic fields can be transferred to the anti-Stokes fields in a readout process. By measuring the operator moments of the anti-Stokes fields, we can verify the presence of entanglement. We model the effects of practical factors such as Stokes field detector quantum efficiency and additive thermal noise, anti-Stokes losses in the verification process, and find achievable regimes in which entanglement can be verified at the levels of tens to hundreds of atomic excitations in the ensembles.
Quantum undemolition measurement of a solid-state qubit
Alexander N. Korotkov (University of California Riverside) and Andrew N. Jordan (University of Rochester)
We propose an experiment which demonstrates the undoing of a weak continuous measurement of a solid-state qubit, so that any unknown initial state is fully restored. The undoing procedure has only a finite probability of success because of the non-unitary nature of quantum measurement, though it is accompanied by a clear experimental indication of whether or not the undoing has been successful. The probability of success decreases with increasing strength of the measurement, reaching zero for a traditional projective measurement. Measurement undoing (``quantum un-demolition'') may be interpreted as a kind of a quantum eraser, in which the information obtained from the first measurement is erased by the second measurement, which is an essential part of the undoing procedure. The experiment can be realized using quantum dot (charge) or superconducting (phase) qubits.
Symmetry and hitting time for quantum walks on graphs
Hari Krovi, University of Southern California
Quantum walks on graphs are analogues of classical random walks, and can be defined as the repeated application of a unitary evolution operator on a Hilbert space corresponding to the graph. Hitting times are the average time it takes a walk to reach a given final vertex from a given starting vertex. On certain graphs, quantum walks can have much shorter hitting times than classical random walks. We demonstrate that symmetries (automorphisms) of the graph have a large effect on the evolution of a quantum walk, and hence on its hitting times. The symmetries of the graph induce symmetries in the unitary evolution operator, by virtue of which the state can be confined to a subspace. In this case, the system in the subspace behaves like a different quantum walk on a smaller quotient graph. For certain graphs, the size of the quotient graph is much smaller than the original graph, and this can lead to fast hitting times. However, symmetry can also play a negative role: the symmetries of the graph can cause degeneracies in the unitary evolution operator, which in turn permit the existence of initial states with infinite hitting times. This is very different from the classical case, where the hitting time for a classical random walk on a finite connected graph will always be finite. Infinite hitting times are a purely quantum phenomenon.
Master equation for spin-density matrix
Sharif Kunikeev, University of Southern California
Many solid-state proposals for quantum computation make use of the spin of an electron localized in a quantum dot (QD) or by a donor ion as a qubit. In this talk, we consider a scenario where interacting QD\'s electrons either are too close to be resolved, or we do not wish to apply measurements that resolve them. Then the physical observable is an electron spin only (one cannot unambiguously ascribe a spin to a QD) and the system state is fully described by the spin-density matrix. Our aim is to test whether a Hamiltonian description of the spin-only degrees of freedom is valid. We show that as long as there is no B-field inhomogeneity this is indeed the case, but with B-field inhomogeneity there are open systems effects, i.e., the dynamics is non-unitary even without coupling to a true bath. Our primary focus in the presentation will be an investigation of non-unitary effects, based on the derived master equation for the spin-density matrix, and its implication for quantum computation.
Feasibility of Hybrid Quantum Repeaters and Qubus Quantum Computers
Thaddeus D. Ladd, Stanford University
Several recent schemes for quantum entanglement distribution and quantum computation rely on phase shifts imparted on a pulse of light that depend on the state of a matter qubit. In some schemes these phase shifts are very small, and in others they may be as large as pi. These schemes may all be realized by the reflection of a light pulse from a cavity loaded with a single Lambda-type emitter. The fidelity of this operation depends on the Q of the cavity, the efficiency of the emitter, and the length of the pulse. Critically, the overlap of the input and reflected pulse shape in the continuum outside the cavity must be considered. We present detailed simulation results exploring all of these parameters, and address the feasibility of these schemes.
Efficiently implementable codes for quantum key expansion
Zhicheng Luo, University of Southern California
The Shor-Preskill proof of the security of the BB84 quantum key distribution protocol relies on the theoretical existence of good classical error-correcting codes with the ``dual-containing'' property. A practical implementation of BB84 thus requires explicit and efficiently decodable constructions of such codes, which are not known. On the other hand, modern coding theory abounds with non-dual-containing codes with excellent performance and efficient decoding algorithms. We show that the dual-containing constraint can be lifted at a small price: instead of a key distribution protocol, an efficiently implementable key expansion protocol is obtained, capable of increasing the size of a pre-shared key by a constant factor. (new version of quant-ph/0608029)
Quantum Simulators, Spin Systems, and Trapped Ions
Warren Lybarger, Los Alamos National Laboratory
Many quantum spin systems cannot be efficiently simulated on classical computers as they require exponentially large resources. Yet many such systems can be simulated efficiently with quantum simulators (QS) that do not require universal control like quantum computers. Following the work of Porras and Cirac [Phys. Rev. Lett. 92, 207901-1 (2004)] we discuss current theoretical and experimental efforts at Los Alamos to implement a QS for Ising-like and Heisenberg- like models with trapped ion qubit ``spins". The states of the QS systems follow nearly the same equations of motion as the systems of interest and, unlike with real materials, the experimenter has the advantage of direct access to and control over the spins. We will discuss progress towards proof-of-principle investigations of two ion simulations in a single-well trap, in which we use state- selective optical forces to induce ion-ion interactions.
Optimal Control of Large Spin Systems
Seth Merkel, University of New Mexico
A quantum system is said to be controllable if the accessible Hamiltonians (as a Lie algebra) generate all unitary operators on Hilbert space. Optimal quantum state control seeks a time-dependent sequence of Hamiltonians that maximize the fidelity with an arbitrary target state given a fixed initial state. We consider optimal control of the spin of a cesium atom restricted to its F=3 ground state hyperfine manifold, with a Hilbert space of dimension 2F+1=7. Control is implemented through time varying magnetic fields in two orthogonal directions along with a quadratic AC-Stark shift created by an off-resonant laser probe. The optimization is performed under several constraints, most importantly a temporal limitation determined by dephasing due to photon scattering and parameter inhomogeneity. The fidelity of state preparation is verified through both a full density matrix simulation and experimental data.
Controlled Interaction of Cs Atoms in Optical Lattices
Brian Mischuck, University of New Mexico
A necessary step to develop neutral atom quantum computation in optical lattices is to demonstrate controlled interaction of pairs of neutral atoms. We describe a scheme to detect the controlled interaction of pairs of Cs atoms in the presence of a large background of single Cs atoms. It should be possible to detect the interaction between pairs of atoms by measuring the modifications to the spectral response caused by the interactions in a low density sample of atoms trapped in a lattice.
Characterization of (In,Ga)As Quantum Posts for Terahertz Quantum Information Processing
C. M. Morris, D. G. Allen, J. He, C. Pryor (University of Iowa), P. M. Petroff and M. S. Sherwin, University of California Santa Barbara
Quantum posts (QPs) are a new kind of self-assembled semiconductor nanostructure which may be suitable for quantum information processing using terahertz frequencies.1 A QP is a roughly cylindrical In-rich region embedded in a GaAs matrix whose height can be controlled with monolayer resolution. For a single electron trapped in a 40 nm high QP, the orbital transition between the ground and first excited state is predicted to occur near 1 THz. Since this is well below the optical phonon frequency (9 THz), decoherence is expected to arise primarily from very weak interactions with acoustic phonons. QPs grown in the insulating region of a metal-insulator-semiconductor structure allow voltage-controlled charging, which is measured by capacitance-voltage spectroscopy. Terahertz absorption spectra are also measured by Fourier-transform infrared spectroscopy. Work supported by the NSF NIRT grant No. CCF 0507295
[1] M. S. Sherwin, A. Imamoglu and C. Montroy, PRA 60, 3508 (1999)
Continuous Quantum Error Correction for Non-Markovian Decoherence
Ognyan Oreshkov and Todd A. Brun, University of Southern California
We study the effect of continuous quantum error correction in the case where each qubit in the code is subject to general hamiltonian interaction with an independent bath. We first consider the simple model of the bit-flip code with each qubit being coupled to an independent bath qubit, and analyze its analytical solution. We show that for sufficiently large error-correction rates, the encoded state follows an effective evolution which is identical to that of a single decohering qubit but with a decreased coupling constant. We find that the factor by which the coupling constant is decreased scales quadratically with the error-correction rate. This is compared to the case of Markovian noise, where the decoherence rate is effectively decreased by a factor which scales only linearly with the rate of error correction. It is shown that the quadratic increase is due to the existence of a Zeno regime in the hamiltonian evolution, which is absent in the case of purely Markovian dynamics. We analyze the ranges of applicability of the present approach and identify two relevant time scales. Finally, we extend this result to more general codes and argue that there the performance of continuous error correction exhibits the same qualitative characteristics.
Sideband cooling while preserving quantum information
Iris Reichenbach, University of New Mexico
We propose a scheme that makes it possible to do resolved sideband cooling on alkaline-earth atoms without changing the state of the nuclear spin, thus preserving coherences which are usually destroyed due to optical pumping during laser cooling. This makes it possible for the first time to laser-cool neutral atom qubits without destroying the quantum information, if the quantum information is stored in the nuclear spin of the atom.
Decoy States in Quantum Key Distribution
Pat Rice, Los Alamos National Lab
Quantum Key Distribution (QKD) is a cryptographic protocol that allows two remote parties (Alice and Bob) to generate a random key (a string of bits) so that only Alice and Bob have any information about the key. In many current implementations, Alice sends Bob a sequence of highly attenuated coherent laser pulses. If we allow an eavesdropper (Eve) to carry out any attack consistent with quantum mechanics, then weak coherent pulses possess a vulnerability that Eve can exploit by means of a photon number splitting (PNS) attack. One way to handle a PNS attack is to scale the mean photon number with the transmission efficiency. Decoy state protocols provide a more efficient countermeasure. Decoy states allow the signal state to remain at a constant order of magnitude as the transmission efficiency decreases. The poster will focus on decoy state protocols in fiber optical implementations and the numerical analysis I have performed to determine the best QKD protocol as a function of channel and device characteristics.
Atom(s)-Field Entanglement in Cavity QED
Perry Rice, Miami University
Entanglement is essentially a quantum correlation between two systems, as such a cross-correlation function can be shown to indicate, or witness, entanglement between two parts of a system. If the state of the system is a product state, with no entanglement, then any cross-correlation function factorizes and is unity. If any cross correlation is not equal to one, then the two modes are entangled. Previously, we have shown that entanglement between a two- level atom and a field mode can be characterized by correlations between transmitted and fluorescent light, in particular the measure of entanglement is proportional to a homodyne measurement of the transmitted field conditioned on detection of a fluorescent photon. This is problematic experimentally, as the collection efficiency of the fluorescent light will be quite low. Here we exploit a trick suggested by Birnbaum et. al., that relies on using a multi-level atom, and two orthogonal polarization modes of the cavity. The atom is driven with polarization a (vertical polarization say). The atom can spontaneously emit into either the a mode, or the b mode. As the b mode is undriven, light of that polarization can only arise from spontaneous emission. Hence perhaps one can measure the entanglement between the atom and field mode by a cross-correlation of the two modes a and b. The problem with this is that we now have an atom and two field modes, and hence a tripartite system. In such systems, measures of entanglement are not well defined. While a measure of entanglement is hard to define, we find that cross-correlations can be entanglement witnesses. We make comparisons with experiments underway in the group of Luis Orozco at the Universi ty of Maryland.
Quantum Error Correction Beyond Completely Positive Maps
Alireza Shabani, University of Southern California
By introducing an operator sum representation for arbitrary linear maps, we develop a generalized theory of quantum error correction (QEC) that applies to any linear map, in particular maps that are not completely positive (CP). This theory of \"linear quantum error correction\" is applicable in cases where the standard assumption of a factorized system-bath initial state does not apply. For linear maps that preserve positivity and/or Hermiticity, we find that standard QEC based on CP recovery maps still applies. Other linear maps generally require non-CP recovery operations. The stabilizer formalism of the theory describes a standard way to find these new operations. We illustrate our findings with examples of QEC for non-CP maps. We also identify a broad class of entangled initial states leading to CP maps.
Quantum projection noise and squeezing with ions in a Penning-Malmberg trap
Nobuyasu Shiga, W.M. Itano and J.J. Bollinger, National Institute of Standard and Technology
We describe plans and summarize initial progress towards making spin squeezed states with up to $\\sim$100 $^{9}$Be$^{+}$ ions in a Penning-Malmberg trap. We use the ground-state electron spin- flip transition, which in the 4.5 T magnetic field of the trap has a transition frequency of 124 GHz, as the ion qubit. With a 30 mW Gunn diode oscillator we have observed Rabi flopping rates as high as $\ \sim$7 kHz. We have realized projection noise limited spectroscopy on this transition, which is a prerequisite for demonstrating spin squeezing. For entangling the ions we plan to use a generalization of the few ion qubit phase gate developed at NIST [1] to generate an \exp{(i chi J_z^2 t) interaction between all of the ion qubits. This interaction can be implemented on a single plane of ions [2] with a motional sideband, stimulated Raman transition. Supported by a DOD MURI program administrated by ONR.
[1] D. Leibfried, et al., Nature 38, 639 (2005).
[2]T.B. Mitchell, et al., Science {\\bf 282}, 1290 (1998).
Generation of squeezed light from spin squeezed Bose-Einstein Condensates
Sulakshana Thanvanthri, Louisiana State University
Generation of squeezed light from spin squeezed Bose- Einstein Condensates Sulakshana Thanvanthri(1) and Zachary Dutton(2) (1)Louisiana State University, Baton Rouge, LA 70803. (2)Naval Research Laboratory, Washington, DC 20375. Non-classical states of light fields are key ingredients in the implementation of most quantum computation schemes and show promise in improved precision measurements beyond shot noise limits. Squeezed states have traditionally been produced using nonlinear crystals, which are inefficient and have limited flexibility. The phenomenon of spin- squeezing in two-component Bose-Einstein Condensates (BEC) coupled with stimulated Raman Scattering may be used to generate squeezed light more efficiently. We present a novel theoretical treatment of the development of spin squeezing in two-component Bose-Einstein condensates, including the spatial dynamics, using a second order cumulant approach. We find that the spin squeezing is robust in the presence of spatial dynamics. We then present a study of the generation squeezed light generation from the spin squeezed BECs, using a Stimulated Raman Scattering (SRS) type scheme. We expand upon the scope of previous studies of SRS squeezed light generation [1] by quantizing and including the nonlinear propagation of both the write and generated light fields. This allows us to study generation of squeezed light with larger intensities. [1] U. V. Poulsen and K. Molmer, Phys. Rev. A 87, 123601 (2001).
Chaos and Entanglement with Two Coupled Spins
Collin M. Trail, University of New Mexico
Collin Trail and Ivan Deutsch, University of New Mexico Leigh Norris, Parin Sripakdeevong, and Arjendu Pattanayak, Carleton College Shohini Ghose, Wilfrid Laurier University We explore the relationship between chaos and entanglement in a system of two spins, coupled by a hyperfine-like interaction and driven by a time-varying external magnetic field. Here, chaos arises via the coupling between subsystems, in contrast with previously studied cases where two coupled subsystems are independently chaotic (e.g. coupled kicked tops). Using a common Hamiltonian to generate quantum and classical dynamics, we study how the entanglement generated by initially uncoupled spin-coherent states correlates with the mixed nature of the underlying the classical phase space consisting of regular islands and a chaotic sea. Entanglement provides a quantum signature of classical chaos. We explain the dependence of our long time entanglement averages on the entanglement of the eigenstates of the dynamical map, and study how entanglement scales with spin size which defines the classical limit.
Modelling Generalized Measurements with Stochastic Processes
Martin Varbanov, University of Southern California
One of the abstract concept of a measurement in Quantum Information Theory is known under the name of generalized measurement, a special subclass of which is the positive-operator value measurement. Another separate paradigm of a measurement comes from Quantum Optics when one considers measurements continuous in time. Their natural description involves the concept of a stochastic process --- a time-dependent random variable. In this paper we construct a continuous stochastic process which simulates a generalized measurement --- in the long time limit it gives the same outcomes with the right probabilities as the measurement being simulated.
Analytical methods for design of surface-electrode ion traps
Janus H. Wesenberg, Natl. Inst. of Standards and Technology
J. H. Wesenberg, J. M. Amini, R. B. Blakestad, J. Britton, K. R. Brown, R. J. Epstein, J. P. Home, W. M. Itano, J. D. Jost, C. Langer, D. Leibfried, R. Ozeri, S. Seidelin, and D. J. Wineland. Surface-electrode ion traps [1,2] are promising candidates for large scale multi-zone ion traps, as required for large scale quantum information processing. In particular, surface-electrode ion traps are well suited for micro-fabrication with integrated control electronics [3], and ion heating rates compatible with quantum information processing have been demonstrated for a trap made with gold electrodes on a fused quartz substrate [2]. Electrode design for surface-electrode traps is complicated by the low symmetry and the large exposed electrode area. We apply a simple method [4] to obtain analytical expressions for the field of arbitrarily shaped surface- electrodes. The efficiency of this method compared to traditional boundary (BEM) or finite (FEM) element methods has allowed us to use numerical optimization techniques to help in the design of advanced trap structures, such as intersections and ion separation zones. Work supported by DTO and NIST. J.H.W. acknowledges support from the Danish Research Agency.
[1] J. Chiaverini et al., Quantum Inf. Comput. 5, 419 (2005).
[2] S. Seidelin et al., Phys. Rev. Lett. 96, 253003 (2006).
[3] J. Kim et al., Quantum Inf. Comput. 5, 515 (2005).
[4] M. H. Oliveira et al., Eur. J. Phys. 22, 31 (2001).
Path-Entangled Number States Violate a Bell's Inequality
Christoph F. Wildfeuer, Louisiana State University
Path-Entangled Number States Violate a Bell's Inequality Christoph F. Wildfeuer, Austin P. Lund, and Jonathan P. Dowling The nonlocality of the maximally path-entangled states |N,0> +exp(i theta)|0,N> (often abbreviated to NOON states) is a very controversial and frequently discussed topic. On one hand, these states are investigated in the context of the foundations of quantum mechanics. On the other hand there are many important applications to quantum imaging, metrology, and sensing. The single photon case (N=1) has been the subject of several theoretical and experimental publications, but there have been no published results devoted to the nonlocality of NOON states for arbitrary N. We propose an experiment that explicitly shows that NOON states violate a Clauser-Horne Bell's inequality for any finite photon number N. The correlation functions we calculate are related to well-known phase space distributions, the two-mode Q function and the two-mode Wigner function. The marginals of these phase space distributions are used to display some of the correlations and discuss the violation as a function of the photon number N. This clarifies the true nature of the entanglement and nonlocality of NOON states. The presented setup is very promising for demonstrating nonlocal correlations of NOON states with low photon numbers N experimentally. For further details see: quant-ph/0610180
Universal quantum computation in deocoherence-free subspace with neutral atoms
Peng Xue, Institute for Quantum Information Science
We have proposed a scheme for a universal set of deterministic quantum gates acting on pairing neutral atoms with cavity-assisted interaction in decoherence-free subspace which from the beginning immunizes our logical qubits against the dominant source of decoherence-----collective dephasing due to fluctuations of the potential and external electromagnetic (stray) fields in both optical lattice and cavity. The efficiency of this scheme is characterized through exact numerical simulations with experimental parameters that incorporate various sources of experiment noise such as phone losses, shape mismatching between the input and output optical pulses and the fluctuations in atomic position, and these results demonstrate the practicality by way of current experimental technology. Some processes proposed here such as full Bell-state measurement and unitary operations based on teleportation may also find applications in quantum communication and metrology.
