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Register a new userHybrid quantum circuit with implanted erbium ions
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We report on hybrid circuit QED experiments with focused ion beam implanted Er$^{3+}$ ions in Y$_2$SiO$_5$ coupled to an array of superconducting lumped element microwave resonators. The Y$_2$SiO$_5$ crystal is divided into several areas with distinct erbium doping concentrations, each coupled to a separate resonator. The coupling strength is varied from 5 MHz to 18.7 MHz, while the linewidth ranges between 50 MHz and 130 MHz. We confirm the paramagnetic properties of the implanted spin ensemble by evaluating the temperature dependence of the coupling. The efficiency of the implantation process is analyzed and the results are compared to a bulk doped Er:Y$_2$SiO$_5$ sample. We demonstrate the successful integration of these engineered erbium spin ensembles with superconducting circuits.
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We theoretically study single and two-qubit dynamics in the circuit QED architecture. We focus on the current experimental design [Wallraff et al., Nature 431, 162 (2004); Schuster et al., Nature 445, 515 (2007)] in which superconducting charge qubits are capacitively coupled to a single high-Q 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 multi-qubit gates between non-nearest qubits and for the realization of gates in parallel, opening the possibility of fault-tolerant quantum computation with superconduting circuits. In this paper, we focus on one and two-qubit gates that do not require moving away from the charge-degeneracy `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 two-qubit 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.
Cavity quantum electrodynamics allows one to study the interaction between light and matter at the most elementary level. The methods developed in this field have taught us how to probe and manipulate individual quantum systems like atoms and superconducting quantum bits with an exquisite accuracy. There is now a strong effort to extend further these methods to other quantum systems, and in particular hybrid quantum dot circuits. This could turn out to be instrumental for a noninvasive study of quantum dot circuits and a realization of scalable spin quantum bit architectures. It could also provide an interesting platform for quantum simulation of simple fermion-boson condensed matter systems. In this short review, we discuss the experimental state of the art for hybrid circuit quantum electrodynamics with quantum dots, and we present a simple theoretical modeling of experiments.
We present measurements of superconducting flux qubits embedded in a three dimensional copper cavity. The qubits are fabricated on a sapphire substrate and are measured by coupling them inductively to an on-chip superconducting resonator located in the middle of the cavity. At their flux-insensitive point, all measured qubits reach an intrinsic energy relaxation time in the 6-20 microseconds range and a pure dephasing time comprised between 3 and 10 microseconds. This significant improvement over previous works opens the way to the coherent coupling of a flux-qubit to individual spins.
We propose the implementation of fast resonant gates in circuit quantum electrodynamics for quantum information processing. We show how a suitable utilization of three-level superconducting qubits inside a resonator constitutes a key tool to perform diverse two-qubit resonant gates, improving the operation speed when compared to slower dispersive techniques. To illustrate the benefit of resonant two-qubit gates in circuit QED, we consider the implementation of a two-dimensional cluster state in an array of N x N superconducting qubits by using resonant controlled-phase (CPHASE) and one-qubit gates, where the generation time grows linearly with N. For N=3, and taking into account decoherence mechanisms, a fidelity over 60% for the generation of this cluster state is obtained.
We introduce a systematic formalism for two-resonator circuit QED, where two on-chip microwave resonators are simultaneously coupled to one superconducting qubit. Within this framework, we demonstrate that the qubit can function as a quantum switch between the two resonators, which are assumed to be originally independent. In this three-circuit network, the qubit mediates a geometric second-order circuit interaction between the otherwise decoupled resonators. In the dispersive regime, it also gives rise to a dynamic second-order perturbative interaction. The geometric and dynamic coupling strengths can be tuned to be equal, thus permitting to switch on and off the interaction between the two resonators via a qubit population inversion or a shifting of the qubit operation point. We also show that our quantum switch represents a flexible architecture for the manipulation and generation of nonclassical microwave field states as well as the creation of controlled multipartite entanglement in circuit QED. In addition, we clarify the role played by the geometric interaction, which constitutes a fundamental property characteristic of superconducting quantum circuits without counterpart in quantum-optical systems. We develop a detailed theory of the geometric second-order coupling by means of circuit transformations for superconducting charge and flux qubits. Furthermore, we show the robustness of the quantum switch operation with respect to decoherence mechanisms. Finally, we propose a realistic design for a two-resonator circuit QED setup based on a flux qubit and estimate all the related parameters. In this manner, we show that this setup can be used to implement a superconducting quantum switch with available technology.
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