Selective coupling of superconducting charge qubits mediated by a tunable stripline cavity

Abstract

We theoretically investigate selective coupling of superconducting charge qubits mediated by a superconducting stripline cavity with a tunable resonance frequency. The frequency control is provided by a flux biased dc-SQUID attached to the cavity. Selective entanglement of the qubit states is achieved by sweeping the cavity frequency through the qubit-cavity resonances. The circuit is able to accommodate several qubits and allows to keep the qubits at their optimal points with respect to decoherence during the whole operation. We derive an effective quantum Hamiltonian for the basic, two-qubit-cavity system, and analyze appropriate circuit parameters. We present a protocol for performing Bell inequality measurements, and discuss a composite pulse sequence generating a universal control-phase gate.Coherent coupling of superconducting qubits has been experimentally demonstrated for all major qubit types (charge 1,2 , flux 3,4,5 , and phase 6,7 qubits) using permanent direct qubit-qubit coupling, capacitive or inductive. A major challenge is to implement a tunable coupling of qubits required for any useful gate operation. Numerous suggestions in this direction have been discussed in recent literature together with related quantum gate protocols (for a review see, e.g. Ref. 8).There are two conceptually different approaches to the tunable coupling. The first approach is to employ direct coupling schemes using Josephson junctions in the non-resonant regime as passive controllable elements, either capacitive, 9 or inductive. 10,11,12,13,14 The second approach, which we adopt in this paper, suggests qubit coupling via a dynamic intermediate element, e.g., LCoscillator or Josephson junction, which becomes entangled with a qubit during a two-qubit operation. In this scheme, the entanglement is achieved by tuning the qubit and the mediator in resonance, and then transferring the entanglement to another qubit by tuning the mediator and the second qubit in the resonance. Such coupling method has been first suggested 15 and experimentally tested 16 for the ion trap qubits. For superconducting qubits, qubit-oscillator entanglement has been demonstrated experimentally for a charge qubit coupled to a microwave stripline cavity, 17 and a flux qubit coupled to a SQUID oscillator;18,19 the gate protocols based on controllable qubit-oscillator coupling have been theoretically discussed in Refs. 20,21.The experimental setup with the qubit coupling to a distributed oscillator -stripline cavity 17,22 possesses potential for scalability -several qubits can be coupled to the cavity. In this paper we investigate the possibility to use this setup for implementation of tunable qubit-qubit coupling and simple gate operations. Tunable qubitcavity coupling is achieved by varying the cavity frequency by controlling magnetic flux through a dc-SQUID attached to the cavity (see Fig. 1). An advantage of this method is the possibility to keep the qubits at the optimal points with respect to decoherence during the whole two-qubit operation. The qubi...

Microwave quantum optics and electron transport through a metallic dot strongly coupled to a transmission line cavity

“…(7) and (8)], the renormalization factor depends on the the distance a and the parameter α = CC g /(C Σ C C ). Since the dot can be placed at any position a, or effectively be moved by tuning the boundary conditions of the cavity, 19,70 it is interesting to study the position dependence of Θ, plotted in Fig. 2 for different values of α.…”

Generating stationary entangled states in superconducting qubits

“…Many strategies have been proposed to obtain a controllable coupling between qubits (see, e.g., [15,16,17,18,19,20,21,22,23,24]). Let us first study the superconducting circuit shown in Fig.…”

“…Examples of qubit-qubit direct coupling include, e.g., capacitivelycoupled charge qubits [5,6] or inductively-coupled flux qubits [8,9,12]. Examples of indirect coupling include, e.g., qubit-qubit coupling via a quantum LC oscillator or an inductance [15,16], a Josephson junction or an extra superconducting qubit acting as a coupler [18,19], a nanomechanical oscillator [20], or a one or three-dimensional transmission line resonator [21,22,23]. The main merit of indirect coupling is that any two qubits can be selectively coupled in a controllable way (see, e.g., [24]).…”

“…One-qubit and two-qubit quantum circuits (see, e.g., [5,6,7,8,9,10,11]) have been realized experimentally in superconducting systems. One of the most important issues in quantum information processing is how to couple two qubits, which has been widely studied theoretically and experimentally in superconducting quantum circuits (see, e.g., [5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25]). To couple two qubits, there are two types of approaches: (1) direct coupling and (2) indirect coupling.…”

Nondegenerate parametric oscillations in a tunable superconducting resonator

“…A typical cQED parametric device consists of a high-quality superconducting resonator integrated with Josephson elements that induce a Kerr nonlinearity in the resonator and also allow for rapid modulation of the resonator frequency [8][9][10][11].…”