Session U40: Focus Session: Pathways to Practical Quantum Computing III

Ion traps and cold atoms for quantum computers

Atoms can be used to store and manipulate quantum information. In particular, their internal state can be considered to form a register, and they can also be manipulated using laser light. In the case of trapped ions, the Coulomb force gives the required interaction to perform two-qubit gates. For neutral atoms, cold collisions can be used for that purpose. During the last years there has been an extraordinary experimental progress with those systems, and it is now possible to perform simple quantum information tasks with them. In this talk I will review several proposals for implementing quantum computers and quantum simulators using trapped ions and neutral atoms in optical lattices, and I will report on the latest experimental advances. Then, I will consider two particular aspects of those systems: (i) the possibility of simulating spin and bosonic systems with trapped ions; (ii) the possibility of performing quantum computations with neutral atoms without addressing them and in the presence of defects.   

Ion trap quantum computing with transverse phonon modes

We propose a scheme to use the transverse modes to implement conditional phase gates on two trapped ions immersed in a large linear crystal of ions, without the sideband addressing. Comparing with the conventional approach using the longitudinal modes, with the cost that the laser power is slightly stronger, the proposed gate operation can be well inside Lamb-Dicke region and the gate infidelity due to the fluctuation of the effective Rabi frequency as well as the fundamental limits of the cooling procedure are approximately two orders smaller.   

Robust quantum memory using magnetic-field-independent atomic qubits

Scalable quantum information processing requires physical systems capable of reliably storing coherent superpositions for times over which quantum error correction can be implemented. We experimentally demonstrate a robust quantum memory using a magnetic-field-independent hyperfine transition in $^{9}$Be$^{+} $ atomic ion qubits at a field B = 0.01194 T. Qubit superpositions are created and analyzed with two-photon stimulated-Raman transitions. We observe the single physical qubit memory coherence time to be greater than 10 seconds, an improvement of approximately five orders of magnitude from previous experiments. The probability of memory error for this qubit during the measurement period (the longest timescale in our system) is approximately 1.4~$\times$~$10^{-5}$ which is below fault-tolerance threshold for common quantum error correcting codes.   

Quantum logic in Group-II neutral atoms via nuclear-exchange interactions

The spin exchange-interaction generates an entangling quantum-logic gate, the square-root of SWAP, at the heart protocols employing single electron quantum dots. This is typically accompanied by strong Coulomb interactions and commensurate decoherence due to strong coupling of charge degrees of freedom to the noisy environment. We propose a protocol utilizing a \textit{nuclear-exchange} interaction that occurs through ultracold collisions of identical spin $\raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} $ Group-II \textit{neutral} atoms. A natural advantage is gained by storing the quantum information in nuclear spin states with long coherence times. Unlike NMR protocols based on weak magnetic dipole-dipole interaction, the nuclear exchange interaction stems from strong s-wave scattering of electrons. Nuclear exchange is ensured by the Fermi symmetry of the overall wave function. We have studied this protocol in the context of $^{171}$Yb atoms trapped in far-off resonance optical dipole traps. Using quantum control analysis, high-fidelity operation is possible through controlled collisions in dynamically varied double-well trapping potentials.   

Quantum state reconstruction via continuous measurement

We present a new protocol for quantum state reconstruction based on weak continuous measurement of an ensemble average. This procedure applies the techniques of quantum control theory and quantum measurement theory to achieve a more efficient reconstruction than those performed using standard projective measurement techniques. This efficiency allows reconstruction of a quantum state using an single emsemble with minimal quantum backaction, setting the stage for state-based feedback control. An experimental demonstration of the technique will be presented in the context of reconstruction of the spin state of the F=3 hyperfine ground-state manifold of Cs-133 using continuous polarization spectroscopy.   

Quantum state control of atoms in microscopic optical traps

We present recent progress in loading and manipulation of neutral atoms in microscopic optical traps. Single Rb atoms are loaded into far off resonant optical traps from a background vapor of cold atoms. Tightly focused optical beams are used to perform two-photon stimulated Raman rotations between hyperfine qubit states. We demonstrate qubit rotations at a rate of 1.4 MHz, 1 ms coherence time, and individual site addressing with crosstalk at the level of $10^{-3}$. These results are a significant step towards quantum computing using optically trapped neutral atoms. We discuss work in progress aimed at observing strong, angle independent dipole-dipole interactions for fast two-qubit gates using microwave dressing of Rydberg states. We demonstrate two-photon coherent excitation of Rydberg levels by a $5s_{1/2} - 5p_{3/2} - nd_ {5/2}$ sequence. The possibility of dipole-dipole interactions without angular zeroes will be important for gates, as well as for coupling to mesoscopic qubits to enable transmission of quantum states.   

Stochastic One-Way Quantum Computing with Ultracold Atoms in Optical Lattices

The one-way model of quantum computation has the advantage over conventional approaches of allowing all entanglement to be prepared in a single initial step prior to any logical operations, generating the so-called cluster state. One of the most promising experimental approaches to the formation of such a highly entangled resource employs a gas of ultracold atoms confined in an optical lattice. Starting with a Mott insulator state of pseudospin-1/2 bosons at unit filling, an Ising-type interaction can be induced by allowing weak nearest-neighbor tunneling, resulting in the formation of a cluster state. An alternate approach is to prepare each spin state in its own sublattice, and induce collisional phase shifts by varying the laser polarizations. In either case, however, there is a systematic phase error which is likely to arise, resulting in the formation of imperfect cluster states. We will present various approaches to one-way quantum computation using imperfect cluster states, and show that the algorithms are necessarily stochastic if the error syndrome is not known.   

Generalized Coherent States via Markovian Decoherence

Coherent states were introduced in the early days of quantum physics as 'quasiclassical' quantum states of an isolated quantum system. The decoherence program defines 'quasiclassical' (or 'pointer') states as states which are most stable in the presence of a coupling with the environment. Pointer states may be identified through the extremization of a 'predictability' functional on the Hilbert space. It has been known for some time that for the harmonic oscillator both concepts coincide under very generic conditions. Coherent states have been extended in the 70s to generalized coherent states. Recently, this approach has served as the basis to define generalized entanglement and conditions for quantum complexity. Here, we investigate the stability of generalized coherent states under Markovian open-system dynamics. In particular, we identify conditions under which generalized coherent states emerge as pointer states for systems described by algebras more general that the standard oscillator algebra. We present a streamlined method to find pointer states in the weak-coupling approximation, and discuss conditions for this approximation to be valid. We find that generalized coherent states and pointer states coincide under more restrictive conditions than the canonical, harmonic-oscillator coherent states. Finally, we address the connection of generalized coherent states to noiseless subspaces and subsystems.   

Generation of Werner states via collective decay of coherently driven atoms

We demonstrate deterministic generation of Werner states as a steady state of the collective decay dynamics of a pair of neutral atom coupled to a leaky cavity and strong coherent drive. We also show how the scheme can be extended to generate $2N$-particle analogue of the bipartite Werner states.   

Two-Qubit Quantum Computing using Pulsed ESR of N@C$_{60}$

N@C$_{60}$ is a fullerene molecule containing an atom of nitrogen. The low-temperature decoherence time, $T_{2}$, can be increased to 215 $\mu $s, which is attractive for quantum information processing applications. The electronic and nuclear spins of the nitrogen atom are good quantum numbers in a strong magnetic field, coupled by the hyperfine interaction. Pulsed ENDOR (electron nuclear double resonance) can be used to initialize, manipulate and measure this two-qubit system. We used dynamic nuclear polarization (DNP) to prepare an initial state in which the nuclear and electronic spins were aligned with the applied field.   

Optimal control of logical operations in the presence of decoherence: A two-spin model

We study the feasibility of optimal control of logical operations in a simple model system composed of two interacting spins. In our model, one spin serves as a qubit and its evolution is controlled by a time-dependent external field. The other (uncontrolled) spin serves as an effective environment, coupling to which is a source of decoherence. The aim of control is to generate a target unitary operation for the qubit in the presence of the environmentally-induced decoherence. Given a target unitary operation $G$ for the system, the fidelity of the actual transformation achieved is maximized with respect to the electric field $\epsilon(t)$ using two techniques, optimal control theory (OCT) and ``pre-design'' methods, which are well-developed in the field of nuclear magnetic resonance. The primary goal of this work is to illustrate the importance of OCT in designing logical operations, especially in the presence of environmental coupling, and the inadequacy of pre-designed gates in such situations.   

Rapid State-Reduction of Quantum Systems Using Feedback Control

Many potential applications of quantum devices, particularly in information processing, require quantum systems to be prepared in pure states. Due to environmental noise quantum systems often exist naturally in mixed states, and as a result a process of cooling or measurement must be used to purify them. In this work we consider the use of measurement for this purpose. The speed with which a measurement can purify, or reduce, the state of a quantum system is determined by the interaction between the system and measuring device, and places a limit on the speed of state-preparation. Here we consider using feedback control during the measurement to increase the rate of state-reduction. It was shown in [1] that for a single qubit this rate could be increased by a factor of 2. Here we show that for higher dimensional systems feedback control can provide a much larger speed-up. In particular, we show that for a measurement of an observable with $N$ equally spaced eigenvalues, there exists a feedback algorithm which will increase the rate of state-reduction by a factor proportional to $N$. References: 1. K. Jacobs, Phys. Rev. A \textbf{67}, 030301(R) (2003). 2. J. Combes and K. Jacobs, Phys. Rev. Lett. (in press).   

Quantum Zeno stabilization in weak continuous measurement of two qubits

We have studied quantum coherent oscillations of two qubits under continuous measurement by a symmetrically coupled mesoscopic detector. The analysis is based on a Bayesian formalism that is applicable to individual quantum systems. Measurement continuously collapses the two-qubit system to one of the sub-spaces of the Bell basis. For a detector with linear response this corresponds to measurement of the total spin of the qubits. In the other extreme of purely quadratic response the operator $\sigma_y^1 \sigma_y^2 +\sigma_z^1\sigma_z^2$ is measured. In both cases, collapse naturally leads to spontaneous entanglement which can be identified by measurement of the power spectrum and/or the average current of the detector. Asymmetry between the two qubits results in evolution between the different measurement subspaces. However, when the qubits are even weakly coupled to the detector, a kind of quantum Zeno effect cancels the gradual evolution and replaces it with rare, abrupt switching events. We obtain the asymptotic switching rates for these events and confirm them with numerical simulations. We show how such switching affects the observable power spectrum on different time scales.