Bulletin of the American Physical Society
2005 APS March Meeting
Monday–Friday, March 21–25, 2005; Los Angeles, CA
Session H18: Modeling of Superconducting Systems for Quantum Computing 
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Sponsoring Units: DCMP Chair: Xuedong Hu University at Buffalo, SUNY Room: LACC 406A 
Tuesday, March 22, 2005 8:00AM  8:12AM 
H18.00001: Simple quantum feedback of a solidstate qubit Alexander Korotkov We propose an experiment on quantum feedback control of a solidstate qubit, which seems to be within the reach of the presentday technology. Similar to the earlier proposal, the feedback loop is used to maintain the coherent oscillations in a qubit for an arbitrary long time; however, this is done in a much simpler way, which eases significantly the bandwidth problem. The main idea is to use the quadrature components of the noisy detector current to monitor approximately the phase of qubit oscillations. The price for simplicity is a lessthanideal operation: the fidelity is limited by about 95\%. The feedback loop operation can be experimentally verified by appearance of a positive inphase component of the detector current relative to an external oscillating signal used for synchronization. [Preview Abstract] 
Tuesday, March 22, 2005 8:12AM  8:24AM 
H18.00002: Logic gates for superconducting qubits M. Steffen, R. McDermott, K.B. Cooper, M. Ansmann, J.M. Martinis, R. Simmonds, K. Cicak, K. Osborn, S. Oh, D.P. Pappas Owing to the recent impressive progress, superconducting qubits are closer than ever to demonstrating simple quantum algorithms. A wide variety of coupling and gate schemes has been previously proposed. However, as part of initial tests it is advantageous to consider the straightforward case of using fixed couplings between onresonance qubits. For many systems, including the current biased phase qubit, the natural interaction is the XYinteraction, which easily generates the iSWAP gate in a time of t = T/2 with T defined as the inverse coupling strength. Building on the iSWAP gate, I will describe a detailed sequence of operations to implement a CNOT (t $\sim $ T/2), a SWAP (t $\sim $ 3T/4), a combination CNOT/SWAP (t $\sim $ T/2), and a controlled Zrotation (t $\sim $ rotation angle). [Preview Abstract] 
Tuesday, March 22, 2005 8:24AM  8:36AM 
H18.00003: On a relation between the high and low frequency noise Alexander Shnirman, Gerd Sch\"on, Ivar Martin, Yuriy Makhlin Lowfrequency (1/f) noise dominates the decoherence in most superconducting qubits. Thus it is very important to understand its origin and properties. Recently, coherent twolevel systems have been observed in Josephson junctions [1]. These systems influence strongly qubits' dynamics at high ($\sim$ 10 GHz) frequencies. In addition, recent experiments [2] indicate a connection between the high and lowfrequency noise. In this work we note that an ensemble of coherent twolevel systems produces simultaneously high and lowfrequency noise. The relation between these two contributions depends on the statistical properties of the ensemble. We analyze several possible distribution functions and relate the results to the known experimental facts. We also note that a similar relation holds for ensembles of manylevel fluctuators with discrete spectrum. [1] R.W. Simmonds et al., Phys. Rev. Lett. 93, 035301 (2004) [2] O. Astafiev et al., condmat/0411216 (2004) [Preview Abstract] 
Tuesday, March 22, 2005 8:36AM  8:48AM 
H18.00004: Subgap states in dirty superconductors and their effect on dephasing in Josephson qubits Alessandro Silva, Lev Ioffe We present a theory of the subgap tails of the density of states in a diffusive superconductor containing magnetic impurities. We show that the subgap tails have two contributions: one arising from mesoscopic gap fluctuations, previously discussed by Lamacraft and Simons, and the other associated to the longwave fluctuations of the concentration of magnetic impurities. We study the latter both in small superconducting grains and in bulk systems [$d=1,2,3$], and establish the dimensionless parameter that controls which of the two contributions dominates the subgap tails. We observe that these contributions are related to each other by dimensional reduction. We apply the theory to estimate the effects of a weak concentration of magnetic impurities [$\approx 1 {\rm p.p.m}$] on the phase coherence of Josephson qubits. We find that at these typical concentrations, magnetic impurities are relevant for the dephasing in large qubits, designed around a $10\;{\rm \mu m}$ scale, where they limit the quality factor to be $Q<10^410^5$. [Preview Abstract] 
Tuesday, March 22, 2005 8:48AM  9:00AM 
H18.00005: Asymmetry and decoherence in a doublelayer persistentcurrent qubit G. Burkard, D. P. DiVincenzo, P. Bertet, I. Chiorescu, J. E. Mooij Superconducting circuits fabricated using the widely used shadow evaporation technique can contain unintended junctions which change their quantum dynamics. We discuss a superconducting flux qubit design that exploits the symmetries of a circuit to protect the qubit from unwanted coupling to the noisy environment, in which the unintended junctions can spoil the quantum coherence. We present a theoretical model based on a recently developed circuit theory for superconducting qubits and calculate relaxation and decoherence times that can be compared with existing experiments. Furthermore, the coupling of the qubit to a circuit resonance (plasmon mode) is explained in terms of the asymmetry of the circuit. Finally, possibilities for prolonging the relaxation and decoherence times of the studied superconducting qubit are proposed on the basis of the obtained results. [Preview Abstract] 
Tuesday, March 22, 2005 9:00AM  9:12AM 
H18.00006: NonStationary Dephasing by a Classical Intermittent Noise Pascal Degiovanni, David Carpentier, Maxime Clusel, Josef Schriefl We investigate the influence of nonstationary intermittent 1/f noise on a quantum twolevel system. Adopting a simple phenomenological model for this (collective) noise, we describe exactly the corresponding dephasing in various regimes. The nonstationarity and pronounced nonGaussian features of this noise induce new anomalous dephasing scenarii. Beyond a historydependent crossover coupling strength, the dephasing time exhibits a strong dependence on the age of the noise and the decay of coherence is not exponential. [Preview Abstract] 
Tuesday, March 22, 2005 9:12AM  9:24AM 
H18.00007: Measurement induced dephasing of a superconducting qubit strongly coupled to a resonator Jay Gambetta, Alexandre Blais, David Schuster, Andreas Wallraff, RenShou Huang, Johannes Majer, Luigi Frunzio, Steven Girvin, Robert Schoelkopf Recently, the solid state equivalent of a cavity QED system has been experimentally observed using a Cooper pair box as the artificial atom (qubit) and a transmission line resonator as the cavity [1]. This system is a good candidate for quantum computation as, in the dispersive limit, quantum control and readout can be achieved by multiplexing RF pulses [2]. In this talk only the readout scheme will be considered, in particular experimental [3] and theoretical results for the measurement induced dephasing will be presented.\newline [1] A. Wallraff, D. Schuster, A. Blais, L. Frunzio, R.S. Huang, J. Majer, S. Kumar, S. M. Girvin and R. J. Schoelkopf, Nature {\bf 431}, 162 (2004).\newline [2] A. Blais, R.S. Huang, A. Wallraff, S. M. Girvin and R. J. Schoelkopf, Phys. Rev. A {\bf 69}, 062320 (2004).\newline [3] D. Schuster, A. Wallraff, A. Blais, L. Frunzio, R.S. Huang, J. Majer, S. M. Girvin and R. J. Schoelkopf, condmat/0408367. [Preview Abstract] 
Tuesday, March 22, 2005 9:24AM  9:36AM 
H18.00008: Nonadditivity of decoherence rates in superconducting qubits Guido Burkard, Frederico Brito We show that the relaxation and decoherence rates $T_1^{1}$ and $T_2^{1}$ of a qubit coupled to several noise sources are in general not additive, i.e., that the total rates are not the sums of the rates due to each individual noise source. To demonstrate this, we calculate the relaxation and pure dephasing rates $T_1^{1}$ and $T_\phi^{1}$ of a superconducting (SC) flux qubit in the BornMarkov approximation in the presence of several circuit impedances $Z_i$ using network graph theory and determine their deviation from additivity (the mixing term). We find that there is no mixing term in $T_\phi^{1}$ and that the mixing terms in $T_{1}^{1}$ and $T_2^{1}$ can be positive or negative, leading to reduced or enhanced relaxation and decoherence times $T_1$ and $T_2$. The mixing term due to the circuit inductance $L$ at the qubit transition frequency $\omega_{01}$ is generally of second order in $\omega_{01}L/Z_i$, but of third order if all impedances $Z_i$ are pure resistances. We calculate $T_{1,2}$ for an example of a SC flux qubit coupled to two impedances. [Preview Abstract] 
Tuesday, March 22, 2005 9:36AM  9:48AM 
H18.00009: Phononinduced decoherence of Andreev level qubit Alexander Zazunov, Vitaly S. Shumeiko, Goran Wendin, Ekaterina N. Bratus' We use the kinetic equation for the density matrix to investigate the decoherence of the Andreev level qubit [1] due to coupling to soft acoustic modes in the quantum point contact (QPC) electrodes [2], in the light of recent results concering intrinsic sources of decoherence of superconducting qubits caused by microscopic modes and losses within the Josephson Phononinduced decoherence of Andreev level qubit junctions [3]. We find a result different from the conventional BlochRedfield equation describing decoherence of macroscopic superconducting qubits. Suppression of the interlevel transitions by the many body effects results nonexponential decay, and in dramatic reduction of the qubit decoherence rate at low temperature due to strong reduction of the relevant phonon phase space. Furthermore, the rate of phononinduced transitions between the Andreev levels is found to be significantly smaller than the bulk transition rate. $\backslash \vert $1] A. Zazunov, et al., Phys. Rev. Lett. 90, 087003 (2003).2] A. Zazunov, et al., condmat/0404656.3] R. W. Simmonds, et al., Phys. Rev. Lett. 93, 077003 (2004); L. B. Ioffe, et al., Phys. Rev. Lett. 93, 057001 (2004) [Preview Abstract] 
Tuesday, March 22, 2005 9:48AM  10:00AM 
H18.00010: Fidelity and quantum chaos in the nanocircuit for the Josephson flux qubit E. N. Pozzo, D. Dominguez We study the dynamics of the Josephson flux qubit of Mooij et al, which consists on a SQUID with 3 Josephson junctions. We find that the classical dynamics is chaotic and that the onset of chaos occurs at low energies. We perform numerical simulations of the timedependent Schrodinger equation of the flux qubit. We study the fidelity or Loschmidt echo (LE), corresponding to the sensibility of the quantum dynamics to a perturbation in the hamiltonian, for high energies. We analyze the effect of perturbations in the magnetic field, in the gate voltage and in the critical currents. We obtain the critical value of the perturbation where the chaotic Lyapunov regime starts in each case. We will show results as a function of the ratio between the Josephson energy and the charging energy. [Preview Abstract] 
Tuesday, March 22, 2005 10:00AM  10:12AM 
H18.00011: Correlationinduced suppression of decoherence in capacitively coupled Cooperpair boxes Xuedong Hu, J. Q. You, Franco Nori Charge fluctuations from gate bias and background traps severely limit the performance of a charge qubit in a Cooperpair box (CPB). Here we discuss an encoding approach\footnote{J.Q. You, X.Hu, and F. Nori, condmat/0407423.} to control the decoherence effects of these charge fluctuations using two strongly capacitively coupled CPBs. This coupledbox system has a lowdecoherence subspace of two states, for which we calculate the dephasing and relaxation rates using a master equation approach. Our results show that the interbox Coulomb correlation can significantly suppress decoherence of this twolevel system by reducing the strength of the systemenvironment interaction, making it a promising candidate as a logical qubit, encoded using two CPBs. [Preview Abstract] 

H18.00012: Microwave Parametric Down Conversion and Squeezing Using Circuit QED K. Moon, S.M. Girvin, A. Blais, J. Gambetta We study theoretically the parametric down conversion and squeezing of microwaves using cavity quantum electrodynamics of a superconducting Cooper pair box (CPB) qubit located inside a transmission line resonator. The nonlinear susceptibility $\chi_2$ can be tuned by dc gate voltage applied to the CPB and vanishes at the charge degeneracy point. We show that the coherent coupling of different cavity modes through the qubit can generate a squeezed state, whose quadrature angle changes by $\pi/2$ depending on the state of the qubit. We will present estimates of parametric down conversion rate and squeezing efficiency based on realistic parameters obtained in recent successful circuit QED experiments$^{1,2,3}$. \\\ $^1$ A. Wallraff et al., Nature (London) 431, 162167 (2004). \\ $^2$ A. Blais et al., Phys. Rev. A, 69, 062320 (2004). \\ $^3$ D.I. Schuster et al., Phys. Rev. Lett., in press. \\\\ $^*$This work was partially supported by ARDA through the Army Research Office, grant number DAAD190210045, NSF ITR0325580, NSF DMR 0342157, and the National Program for TeraLevel Nanodevices of the KMOST. [Preview Abstract] 
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