Quantuminformation processing with circuit quantum electrodynamics
Abstract
We theoretically study single and twoqubit dynamics in the circuit QED architecture. We focus on the current experimental design [Wallraff et al., Nature (London) 431, 162 (2004); Schuster et al., ibid. 445, 515 (2007)] in which superconducting charge qubits are capacitively coupled to a single highQ superconducting coplanar resonator. In this system, logical gates are realized by driving the resonator with microwave fields. Advantages of this architecture are that it allows for multiqubit gates between nonnearest qubits and for the realization of gates in parallel, opening the possibility of faulttolerant quantum computation with superconducting circuits. In this paper, we focus on one and twoqubit gates that do not require moving away from the chargedegeneracy sweet spot'. This is advantageous as it helps to increase the qubit dephasing time and does not require modification of the original circuit QED. However, these gates can, in some cases, be slower than those that do not use this constraint. Five types of twoqubit gates are discussed, these include gates based on virtual photons, real excitation of the resonator, and a gate based on the geometric phase. We also point out the importance of selection rules when working at the charge degeneracy point.
 Authors:
 Departments of Applied Physics and Physics, Yale University, New Haven, Connecticut 06520 (United States)
 (Canada)
 (Switzerland)
 Publication Date:
 OSTI Identifier:
 20982275
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevA.75.032329; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; INFORMATION THEORY; JOSEPHSON EFFECT; MICROWAVE RADIATION; MODIFICATIONS; PHOTONS; QUANTUM COMPUTERS; QUANTUM ELECTRODYNAMICS; QUANTUM MECHANICS; QUBITS; RESONATORS; SELECTION RULES
Citation Formats
Blais, Alexandre, Departement de Physique et Regroupement Quebecois sur les Materiaux de Pointe, Universite de Sherbrooke, Sherbrooke, Quebec J1K 2R1, Gambetta, Jay, Schuster, D. I., Girvin, S. M., Devoret, M. H., Schoelkopf, R. J., Wallraff, A., and Department of Physics, ETH Zurich, CH8093 Zuerich. Quantuminformation processing with circuit quantum electrodynamics. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVA.75.032329.
Blais, Alexandre, Departement de Physique et Regroupement Quebecois sur les Materiaux de Pointe, Universite de Sherbrooke, Sherbrooke, Quebec J1K 2R1, Gambetta, Jay, Schuster, D. I., Girvin, S. M., Devoret, M. H., Schoelkopf, R. J., Wallraff, A., & Department of Physics, ETH Zurich, CH8093 Zuerich. Quantuminformation processing with circuit quantum electrodynamics. United States. doi:10.1103/PHYSREVA.75.032329.
Blais, Alexandre, Departement de Physique et Regroupement Quebecois sur les Materiaux de Pointe, Universite de Sherbrooke, Sherbrooke, Quebec J1K 2R1, Gambetta, Jay, Schuster, D. I., Girvin, S. M., Devoret, M. H., Schoelkopf, R. J., Wallraff, A., and Department of Physics, ETH Zurich, CH8093 Zuerich. Thu .
"Quantuminformation processing with circuit quantum electrodynamics". United States.
doi:10.1103/PHYSREVA.75.032329.
@article{osti_20982275,
title = {Quantuminformation processing with circuit quantum electrodynamics},
author = {Blais, Alexandre and Departement de Physique et Regroupement Quebecois sur les Materiaux de Pointe, Universite de Sherbrooke, Sherbrooke, Quebec J1K 2R1 and Gambetta, Jay and Schuster, D. I. and Girvin, S. M. and Devoret, M. H. and Schoelkopf, R. J. and Wallraff, A. and Department of Physics, ETH Zurich, CH8093 Zuerich},
abstractNote = {We theoretically study single and twoqubit dynamics in the circuit QED architecture. We focus on the current experimental design [Wallraff et al., Nature (London) 431, 162 (2004); Schuster et al., ibid. 445, 515 (2007)] in which superconducting charge qubits are capacitively coupled to a single highQ superconducting coplanar resonator. In this system, logical gates are realized by driving the resonator with microwave fields. Advantages of this architecture are that it allows for multiqubit gates between nonnearest qubits and for the realization of gates in parallel, opening the possibility of faulttolerant quantum computation with superconducting circuits. In this paper, we focus on one and twoqubit gates that do not require moving away from the chargedegeneracy sweet spot'. This is advantageous as it helps to increase the qubit dephasing time and does not require modification of the original circuit QED. However, these gates can, in some cases, be slower than those that do not use this constraint. Five types of twoqubit gates are discussed, these include gates based on virtual photons, real excitation of the resonator, and a gate based on the geometric phase. We also point out the importance of selection rules when working at the charge degeneracy point.},
doi = {10.1103/PHYSREVA.75.032329},
journal = {Physical Review. A},
number = 3,
volume = 75,
place = {United States},
year = {Thu Mar 15 00:00:00 EDT 2007},
month = {Thu Mar 15 00:00:00 EDT 2007}
}

In this Brief Report, we propose a potential scheme to implement oneway quantum computation with circuit quantum electrodynamics (QED). Large cluster states of charge qubits can be generated in just one step with a superconducting transmission line resonator (TLR) playing the role of a dispersive coupler. A singlequbit measurement in the arbitrary basis can be implemented using a single electron transistor with the help of onequbit gates. By examining the main decoherence sources, we show that circuit QED is a promising architecture for oneway quantum computation.

Evaluating charge noise acting on semiconductor quantum dots in the circuit quantum electrodynamics architecture
We evaluate the charge noise acting on a GaAs/GaAlAs based semiconductor double quantum dot dipolecoupled to the voltage oscillations of a superconducting transmission line resonator. The inphase (I) and the quadrature (Q) components of the microwave tone transmitted through the resonator are sensitive to charging events in the surrounding environment of the double dot with an optimum sensitivity of 8.5×10{sup −5} e/√(Hz). A low frequency 1/f type noise spectrum combined with a white noise level of 6.6×10{sup −6} e{sup 2}/Hz above 1 Hz is extracted, consistent with previous results obtained with quantum point contact charge detectors on similar heterostructures. The slope ofmore » 
Stopping single photons in onedimensional circuit quantum electrodynamics systems
We propose a mechanism to stop and time reverse single photons in onedimensional circuit quantum electrodynamics systems. As a concrete example, we exploit the large tunability of the superconducting charge quantum bit (charge qubit) to predict onephoton transport properties in multiplequbit systems with dynamically controlled transition frequencies. In particular, two qubits coupled to a waveguide give rise to a singlephoton transmission line shape that is analogous to electromagnetically induced transparency in atomic systems. Furthermore, by cascading doublequbit structures to form an array and dynamically controlling the qubit transition frequencies, a single photon can be stopped, stored, and time reversed. Withmore » 
Dynamics of dispersive singlequbit readout in circuit quantum electrodynamics
The quantum state of a superconducting qubit nonresonantly coupled to a transmission line resonator can be determined by measuring the quadrature amplitudes of an electromagnetic field transmitted through the resonator. We present experiments in which we analyze in detail the dynamics of the transmitted field as a function of the measurement frequency for both weak continuous and pulsed measurements. We find excellent agreement between our data and calculations based on a set of Blochtype differential equations for the cavity field derived from the dispersive JaynesCummings Hamiltonian including dissipation. We show that the measured system response can be used to constructmore » 
Engineering squeezed states of microwave radiation with circuit quantum electrodynamics
We introduce a squeezed state source for microwave radiation with tunable parameters in circuit quantum electrodynamics. We show that when a superconducting artificial multilevel atom interacting with a transmission line resonator is suitably driven by external classical fields, twomode squeezed states of the cavity modes can be engineered in a controllable fashion from the vacuum state via adiabatic following of the ground state of the system. This scheme appears to be robust against decoherence and is realizable with present techniques in circuit quantum electrodynamics.