# Bulletin of the American Physical Society

## APS March Meeting 2010  Volume 55, Number 2

Monday–Friday, March 15–19, 2010; Portland, Oregon

### Session W26: Quantum Control and Resources for Quantum Computing

Sponsoring Units: GQI
Chair: Frank Wilhelm, University of Waterloo
Room: D136

Thursday, March 18, 2010 			  11:15AM - 11:27AM  W26.00001: Quantum Eraser and Phase-Matching for Exponential Spin-Squeezing via Coherent Optical Feedback 			 			 	   Collin Trail 	   	  , Ivan Deutsch 	   	  , Poul Jessen 	   	  , Leigh Norris 	  A scheme for squeezing collective atomic spin states via coherent optical feedback was proposed by M. Takeuchi et. al., Phys. Rev. Lett. 94, 023003, 2005.  In the first pass, the Faraday effect acts to entangle the light with the atoms.  In a coherent second pass, this information is imprinted back onto the atoms, creating an effective nonlinear interaction and entanglement between atoms. However, the light is still entangled to the atoms when it escapes, leading to substantial decoherence, and moreover, the interaction slowly rotates the system out of sync with the squeezing axis, both of which result in suboptimal squeezing. We show how the addition of a quantum eraser and phase matching can lead to radically improved exponential scaling. We analyze this system in the presence of realistic imperfections such as photon scattering, optical pumping, losses in transmission and reflection, finite detector efficiency, and nonprojective measurements, and show that spin squeezing near 10 dB should be possible.
Thursday, March 18, 2010 			  11:27AM - 11:39AM  W26.00002: High fidelity gates with simple pulses 			 			 	   Felix Motzoi 	   	  , Jay Gambetta 	   	  , Frank Wilhelm 	  Fast oscillating terms in the Hamiltonian such as off-resonant excitation and counter- rotating terms can be a significant source of error in quantum information  implementations.  We expand on techniques first developed for controlling 3-level  systems, Derivative Removal by Adiabatic Gate (DRAG) published in PRL 103 110501,  which was experimentally tested in arXiv:0908.1955v1.  Here we show how this  technique can be applied specifically to 2-level systems, selective qubit addressing,  and in general to multi-channel leakage systems to vastly improve fidelities.   In all  these cases, the error corresponds to a dragging of the adiabatic frame used for the  coherent rotation, which is proportional to the derivative and can easily be corrected  using a second quadrature control. The pulse shapes obtained are smooth and very  short in duration, corresponding to very few cycles of the unwanted fast oscillation.
Thursday, March 18, 2010 			  11:39AM - 11:51AM  W26.00003: Generation of ion-photon entangled state with trapped barium ions 			 			 	   Nathan Kurz 	   	  , Gang Shu 	   	  , Matthew Dietrich 	   	  , Katherine Mitchell 	   	  , Boris Blinov 	  Trapped ions are an attractive qubit candidate, particularly for their long coherence  times and natural coupling to photons.  We trap single Barium-138 ions in a linear  Paul trap and excite these ions with mode-locked pulses to generate a single photon  per excitation.  The Zeeman sublevels of the ground state can then be entangled with  orthogonal polarization modes of the photons emitted upon decay from either the  $6P_{3/2}$ or $6P_{1/2}$ state at 455 and 493 nm, respectively.  Preliminary results  have been obtained using weak continuous wave excitation to generate single photons  at 493 nm, as confirmed by anti-coincidence measurements.  Such work represents a  crucial step toward the generation of multi-ion entangled states.
Thursday, March 18, 2010 			  11:51AM - 12:03PM  W26.00004: Qubit decoherence due to detector switching 			 			 	   Frank Wilhelm 	   	  , Ioana Serban 	  We provide insight into the  qubit measurement process involving a switching type of detector. We study the switching-induced decoherence during escape events. We present a simple method to obtain analytical results for the qubit dephasing and bit-flip errors, which can be easily adapted to various systems. Within this frame we investigate potential of switching detectors for a fast but only weakly invasive type of detection. We show that the mechanism that leads to strong dephasing, and thus fast measurement, inverts potential bit flip errors due to an intrinsic approximate time reversal symmetry.  Based on arXiv:0905.3045
Thursday, March 18, 2010 			  12:03PM - 12:15PM  W26.00005: CNOT gates with weakly coupled qubits: Dependence of fidelity on form of  interaction 			 			 	   Joydip Ghosh 	   	  , Michael Geller 	  An approach to the construction of a CNOT quantum logic gate for a  4-dimensional coupled-qubit model with weak but otherwise arbitrary coupling has been given recently (e-print arXiv0906.5209). How does the resulting fidelity depend on the form of qubit-qubit coupling? We calculate intrinsic fidelity curves (fidelity vs. total gate time) for a variety of qubit-qubit  interactions, including the commonly occurring isotropic Heisenberg and XY models, as well as randomly generated ones. For interactions not too close to that of the Ising model, we find that the fidelity curves do not significantly depend on the form of the interaction, and we provide the fidelity curve for the non-Ising-like cases and a criterion for determining its applicability.
Thursday, March 18, 2010 			  12:15PM - 12:27PM  W26.00006: Optical generation of Fock states in a weakly nonlinear oscillator 			 			 	   Botan Khani 	   	  , Jay Gambetta 	   	  , Felix Motzoi 	   	  , Frank Wilhelm 	  We apply optimal control theory to determine the shortest time in which an energy eigenstate of a weakly anharmonic oscillator can be created under the practical constraint of linear driving. We show that the optimal pulses are beatings of mostly the transition frequencies for the transitions up to the desired state and the next leakage level. The time of a shortest possible pulse for a given nonlinearity scale with the nonlinearity parameter as a  power law. This power law is weaker than the one expected by a simple spectroscopic argument, emphasizing the benefits of quantum interference. Furthermore we confirm that even with realistic models for decoherence high fidelity energy eigenstates can be achieved.
Thursday, March 18, 2010 			  12:27PM - 12:39PM  W26.00007: Free-time and Fixed End-point Multi-target Optimal Control Theory:  Application to Quantum Computing 			 			 	   Kenji Mishima 	   	  , Koichi Yamashita 	  An extension of monotonically convergent free-time and fixed end-point  optimal control theory (FRFP-OCT) to monotonically convergent free-time and  fixed end-point \textit{multi-target} optimal control theory (FRFP-MTOCT) is presented. The  features of our theory include optimization of the laser pulses with high  transition probabilities, that of the temporal duration, the monotonic  convergence, and the ability to optimize multiple-laser pulses  simultaneously. The advantage of the theory and a comparison with  conventional fixed-time and fixed end-point multi-target optimal control  theory (FIFP-MTOCT) are presented by comparing data calculated using the  present theory with those published previously [K. Mishima and K. Yamashita,  Chem. Phys. \textbf{361}, 106 (2009)], where qubit system of interest  consists of two polar NaCl molecules coupled by dipole-dipole interaction.
Thursday, March 18, 2010 			  12:39PM - 12:51PM  W26.00008: Feedback Control of the Two Components of a Schroedinger-Cat 			 			 	   Justin Finn 	   	  , Kurt Jacobs 	  While quantum resonators can exist in mesoscopic superpositions of different locations in phase space (so called Schroedinger-cat states), to date feedback control protocols have been restricted to stabilizing such systems about a single point in phase space. This is due to the fact that measurements usually destroy phase-space superpositions.   Here we show how it is possible to realize the feedback control of a Schroedinger-cat state of a mesoscopic resonator, by using a combination of linear and quadratic measurements of position. We show how these measurements can be realized experimentally, and present an explicit protocol for tracking and controlling the components of a cat-state in real-time.
Thursday, March 18, 2010 			  12:51PM -  1:03PM  W26.00009: Manipulation of the dynamics of many-body systems via quantum control methods 			 			 	   Julie Dinerman 	   	  , Lea Santos 	  We investigate how dynamical decoupling methods may be used to  manipulate the transport behavior of quantum many-body systems.  These methods consist of sequences of unitary transformations  designed to induce a desired dynamics. The systems considered  for the analysis are one-dimensional spin-1/2 models, which,  according to the parameters of the Hamiltonian, may be in the  integrable or non-integrable limits, and in the gapped or  gapless phases. Given a system in a certain regime, we develop  control sequences that lead to an effective evolution typical  of a system in the opposite regime, that is, a chaotic chain  evolves as an integrable one and a system in the gapless phase  behaves as a gapped one.
Thursday, March 18, 2010 			   1:03PM -  1:15PM  W26.00010: Magic recovery of spin coherence in an interacting quantum bath 			 			 	   Nan Zhao 	   	  , Jian-Liang Hu 	   	  , Ren-Bao Liu 	  The magic recovery of the spin coherence is a distinguished feature  due to the quantum nature of the spin bath, which was first  proposed from a pseudo-spin model. Here we proved without resorting  to a specific bath model that this magic coherence recovery is  general. Based on this proof and numerical simulations, we proposed  the conditions under which the $\sqrt{2}\tau$  recovery would be  experimentally observed. In particular, we explored the possibility  of observing the phenomenon by measuring central nuclear spin  coherence in solid state NMR experiments, where the coherence time  $T_{2}$ and the inhomogeneous broadening time $T^{*}_{2}$  are of  the same order.
Thursday, March 18, 2010 			   1:15PM -  1:27PM  W26.00011: Path integral representation of a two qubit system 			 			 	   Justin Wilson 	   	  , Victor Galitski 	  In the path integral representation of a one qubit system, extra degrees of freedom are needed to pass from the Hamiltonian formulation to the path integral (Lagrangian) formulation. This leads to a topological term in the Lagrangian much like a Wess-Zumino term. Such a term is topological and is related to the Hopf fibration of $S^3$ by $S^1$ over $S^2$ (and indeed this term appears even when the Hamiltonian is zero). There is an analogous Hopf fibration for the two qubit state from $S^7$ by $S^3$ over $S^4$. We explore how this is related to the topological term in the path integral formulation for two qubit systems.
Thursday, March 18, 2010 			   1:27PM -  1:39PM  W26.00012: Fermionic Resources for Quantum Teleportation 			 			 	   Adam D'Souza 	   	  , David Feder 	  The measurement-based quantum computing (MBQC) model requires the creation of a massively entangled resource state,'' on which computation proceeds via single-qubit measurements. Although 2D resource states are believed necessary for universal MBQC, 1D states can serve as resources for certain tasks as well, such as quantum teleportation. One possible route to a resource state is to cool a gapped, two-body system whose ground state encodes the resource. I will discuss our recent work in this area, in which we investigate candidate fermionic systems using the Density Matrix Renormalization Group method and the Matrix Product States description of highly entangled 1D states.
Thursday, March 18, 2010 			   1:39PM -  1:51PM  W26.00013: Quantum computation in the ground state of interacting fermions 			 			 	   David Feder 	   	  , Gora Shlyapnikov 	  In measurement-based quantum computation (MBQC), an algorithm proceeds entirely by making projective measurements on successive qubits comprising some highly entangled `resource state.' While two-dimensional cluster states are known to be universal resources for MBQC, it has been proven that they cannot be the unique ground states of any two-body spin Hamiltonian. We show that a particular ground state of non-interacting fermions (equivalent to a many-body spin system) is formally equivalent to a cluster state, though only capable of simulating a limited set of quantum operations. In the presence of two-particle interactions, however, the ground state becomes a universal resource for MBQC. This result suggests that arbitrary quantum algorithms could be simulated fault-tolerantly simply by measuring a cold gas of interacting fermions, such as ultracold atoms in optical lattices.
Thursday, March 18, 2010 			   1:51PM -  2:03PM  W26.00014: How to implement a quantum algorithm on a large number of qubits by controlling one central qubit 			 			 	   Alexander Zagoskin 	   	  , Sahel Ashhab 	   	  , J.R. Johansson 	   	  , Franco Nori 	  It is desirable to minimize the number of control parameters needed to perform a quantum algorithm. We show that, under certain conditions, an entire quantum algorithm can be efficiently implemented by controlling a single central qubit in a quantum computer. We also show that the different system parameters do not need to be designed accurately during fabrication. They can be determined through the response of the central qubit to external driving. Our proposal is well suited for hybrid architectures that combine microscopic and macroscopic qubits.  More details can be found in: A.M. Zagoskin, S. Ashhab, J.R. Johansson, F. Nori, Quantum two-level systems in Josephson junctions as naturally formed qubits, Phys. Rev. Lett. 97, 077001 (2006); and S. Ashhab, J.R. Johansson, F. Nori, Rabi oscillations in a qubit coupled to a quantum two-level system, New J. Phys. 8, 103 (2006).
Thursday, March 18, 2010 			   2:03PM -  2:15PM  W26.00015: Self-organization in optical lattices studied within the positive-P  representation 			 			 	   Ray Ng 	   	  , Erik S. Sorensen 	  The positive-P representation is a commonly used quantum phase space method  in quantum optics. It allows for the conversion of the master equation of a  quantum mechanical system to a Fokker-Planck Equation, which can then be  mapped on to a set of Stochastic Differential Equations. This makes it an  ideal method when dealing with open systems and for studying real time  dynamics. We use the positive-P representation to simulate ultra cold atoms  trapped in an optical lattice within a cavity in the presence of a coupling  to a resonant mode. It has been proposed that in this system the trapped  atoms self-organize from a uniform starting configuration of equally  occupied lattice sites to one where either only even or odd lattice sites  are occupied.
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