Session B17: Focus Session: Progress towards Scalable Quantum Information Processing

Electrons on Helium using circuit quantum electrodynamics[1]

It is possible to form a two dimensional electron gas at the interface between superfluid helium and vacuum.~ This unique heterostructure has exceptional bulk properties including electron mobilities exceeding 10$^{7}$ cm$^{2}$/Vs and electron spin coherence times estimated to exceed 100s.~ One of the first proposals [2] for quantum computation employed the \textit{vertical} motional states of electrons on helium but coherent interactions have yet to be realized.~ I will describe a new proposal [3] which uses a high finesse superconducting transmission line cavity to detect and manipulate the \textit{lateral} motional and spin states of a single trapped electron on helium. We estimate that it is possible to attain vacuum Rabi frequencies of g=10 MHz and T$_{1}\sim $T$_{2}\sim $1 ms for the motional state and perhaps even longer coherence times if spin encoding is used. \newline \newline [1] Wallraff, et. al. Nature, 2004, 431, 162 \newline [2] Plattzman and Dykman, Science, 1999, 284, 1967 \newline [3] In preparation   

Simulating electron transport and devices on liquid helium

Manipulation of the spin of electrons in surface states on superfluid helium is a promising method for the implementation of a quantum computer. The electrons can be transported around a substrate along channels in a manner analogous to charge-coupled devices. These devices operate on one or a few electrons, which are sufficiently isolated to be treated as classical point charges. The model must therefore incorporate the discreteness of the charges and their interactions, as well as their response to external potentials. These constraints lead towards considering a ``molecular'' dynamics, multi-electron simulation. The calculation of the electron-electron interactions are complicated by the presence of nearby metallic gates and insulating layers. The concepts necessary for a fast, accurate dynamic simulation of a large collection of individual electrons are elaborated. A computationally cheap approximation of the electrostatic potential due to substrate polarisation for an electron above a channel is proposed. The approximation is compared to an analytic solution. Other substrate geometries which might be used in a quantum computer are also discussed, concentrating on approximations of the potential.   

Quantum logic with weakly coupled qubits

Effective protocols for performing CNOT quantum logic with qubits coupled by particular high-symmetry (Ising or Heisenberg) interactions are well established. However, many architectures being considered for quantum computation involve qubits or qubits and resonators coupled by more complicated and less symmetric interactions. Here we consider a widely applicable model of weakly but otherwise arbitrarily coupled two-level systems, and use quantum gate design techniques to derive a simple and intuitive CNOT construction. Useful variations and extensions of the solution are given for common special cases.   

Quantum gates that correct their own (quantum) errors

Scalable quantum computation in realistic devices requires that precise control can be implemented efficiently in the presence of decoherence and operational errors. I will describe a general constructive procedure for designing robust unitary gates on an open quantum system without encoding or measurement overhead. These results allow for a low-level error correction strategy solely based on Hamiltonian engineering using realistic bounded-strength controls, and may prove instrumental to substantially reduce implementation requirements for fault-tolerant quantum computing architectures.   

A few-electron triple quantum dot incorporating two fast charge sensors

A triple quantum dot is defined in a GaAs heterostructure. The occupation of all three dots is monitored using two nearby charge sensing point contacts. Radio frequency multiplexing in a reflectometry setup allows MHz-bandwidth measurements of both charge sensors independently. Configuring the device in the few-electron regime, we achieve coherent spin manipulation using the exchange interaction.   

Interqubit coupling mediated by a high-excitation-energy quantum object

We consider a system composed of two qubits and a high-excitation-energy quantum object used to mediate coupling between the qubits. After reproducing well-known results concerning the leading term in the mediated coupling, we obtain an expression for the residual coupling between the qubits in the off state. We also analyze the entanglement between the three objects, i.e. the two qubits and the coupler, in the eigenstates of the total Hamiltonian. Although we focus on the application of our results to the recently realized parametric-coupling scheme with two qubits, we also discuss extensions of our results to harmonic-oscillator couplers, couplers that are near resonance with the qubits and multi-qubit systems. In particular, we find that certain errors that are absent for a two-qubit system arise when dealing with multi-qubit systems.   

Excitons in cavity-embedded quantum dot lattices

We investigate excitons and trions in a two-dimensional quantum dot lattice embedded in a planar optical cavity. The strong exciton (trion)-photon coupling is described in terms of polariton quasiparticles. First, we focus on Bragg polariton modes obtained by tuning the exciton and the cavity modes into resonance at high symmetry points of the Brillouin zone. The effective mass of these polaritons can be extremely small, of the order of $10^8\,m_0$ ($m_0$ is the bare electron mass) and makes them the lightest exciton-like quasiparticle in solids [1]. Second, we consider how disorder affects the properties of Bragg polariton modes. We focus on three kinds of disorder: (i) inhomogeneous exciton energy, (ii) inhomogeneous exciton-photon coupling, and (iii) deviations from an ideal lattice. It is found that in some cases weak disorder increases the light matter coupling and it leads to a larger polariton splitting [2]. Finally, each dot has one electron, and the electron spin determines the polarization of the cavity photon that couples to the dot. Such a ``spin lattice'' can be used for quantum information processing and we show that by using exciton detuning a conditional phase shift gate with high fidelity can be obtained [3]. [1] E. M. Kessler, et al., Phys. Rev. B ${\bf 77}$, 085306 (2008). [2] M. Grochol et al., Phys. Rev. B ${\bf 78}$, 035323 (2008). [3] M. Grochol et al., Phys. Rev. B ${\bf 78}$, 165324 (2008).   

Low Disorder Si MOSFET Dots for Quantum Computing

Silicon quantum dot based qubits have emerged as an appealing approach to extending the success of GaAs spin based double quantum dot qubits. Research in this field is motivated by the promise of long spin coherence times, and within a MOS system the potential for variable carrier density, very small dot sizes, and CMOS compatibility. In this work, we will present results on the fabrication and transport properties of quantum dots in novel double gated Si MOS structures. Coulomb blockade is observed from single quantum dots with extracted charging energies up to an including 5meV. Observed dots were formed both from disorder within a quantum point contact, and through disorder free electrostatic confinement. Extracted capacitances, verified with 3D finite element simulations confirm the location of the disorder free dot to be within the designed lithographic structure. Distinctions will be made regarding the effects of feature sizes and sample processing. 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.   

Steps toward donor based qubits in Si through integrating single ion Geiger mode avalanche diode detectors

Donor based qubits in Si for solid-state quantum information processing require precise dopant placement into the bulk Si. Placement precision donor is limited by straggle which is strongly dependant upon dopant selection and implantation energy, therefore detection of low energy ions ($<$10 keV) is desired. Great progress has been made using the combination of a $p-i-n$ diode and electron beam lithography patterned surface mask resulting in a signal to noise limited $\sim $10$^{3}$ electron-hole (e-h) pairs detection (D. N. Jamieson \textit{et al.,} Appl. Phys. Lett. \textbf{86}, 202101 (2005)). We present experimental results for a single ion Geiger mode avalanche diode (SIGMA) detector has been shown to be sensitive to a single 250 keV H+ ion with 100{\%} detection efficiency (J. A. Seamons \textit{et al.,} Appl. Phys. Lett. \textbf{93}, 403124 (2008)) as well as advances that have been made with the SIGMA detector in reducing dark (false) counts by three orders of magnitude and placing an upper bound on the e-h pair sensitivity of $\sim $10$^{3}$ produced outside the active region of the SIGMA detector. Future SIGMA designs will enable low energy single ion detection with reduced straggle single donor qubit integration. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under Contract No. DE-AC04-94AL85000.   

Zeno Quantum Gates in Semiconductor Quantum Dots

Quantum Zeno effect (QZE) is one of the most intriguing quantum phenomena. In the recent literature, there is a series of strongly linked ideas on entanglement generation or computation using the QZE, which have mainly been discussed and explored experimentally in pure quantum optics and superconductors. We propose a scheme for a two-qubit conditional phase gate by QZE with three parallel semiconductor quantum dots [1]. Two of them are charged dots with one additional electron. The spin of these electrons are the logical qubits on which the phase-gate acts. The other dot is an ancillary neutral dot that can perform Rabi oscillations under a resonant laser pulse. With our system setup, we can make use of QZE to gain a $\pi $ phase shift after a 2$\pi $ laser pulse depending on the spin configuration in the logical qubits. This phase shift can realize a conditional phase gate. We solve analytically and numerically the master equation with a realistic set of parameters. The result shows that, despite the widely-held belief that decoherence must always be minimized in quantum information processing, in our scheme decoherence can in principle be harnessed to generate high-fidelity gate operation using the QZE. [1] K.J. Xu, Y.P. Huang, M.G. Moore, and C. Piermarocchi, arXiv: 0810.4489 (2008).   

Large Scale Quantum Computation in a Linear Ion Trap

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.   

Quantifying and Tuning Entanglement for Spin Systems

The research carries out a benchmark exact calculation in the field of entanglement in a 19-site two-dimensional spin system. Of particular interest, we study one or more impurities embedded into such systems. We demonstrate that entanglement can be controlled and tuned by varying the ratio of the strength of the magnetic field to the exchange interaction h/J and by introducing impurities. We also discuss the relation of the amount of entanglement, between the impurity spins and the environment, and the decoherence time, which is a quantity measurable in experiments and of relevance in various proposals for traditional and quantum computer hardware.