Josephson charge qubits: a brief review

Abstract

The field of solid-state quantum computation is expanding rapidly initiated by our original charge qubit demonstrations. Various types of solid-state qubits are being studied, and their coherent properties are improving. The goal of this review is to summarize achievements on Josephson charge qubits. We cover the results obtained in our joint group of NEC Nano Electronics Research Laboratories and RIKEN Advanced Science Institute, also referring to the works done by other groups. Starting from a short introduction, we describe the principle of the Josephson charge qubit, its manipulation and readout. We proceed with coupling of two charge qubits and implementation of a logic gate. We also discuss decoherence issues. Finally, we show how a charge qubit can be used as an artificial atom coupled to a resonator to demonstrate lasing action.

Generating the Schrödinger cat state in a nanomechanical resonator coupled to a charge qubit

“…Note that the thermal phonons of the NAMR have been ignored in Eq. (18), due to the assumption that the thermal phonons can be neglected since the high-frequency NAMR can be remained in its ground state at the work temperature (T = 20 mK) of the charge qubit [15,33]. We define the fidelity of the entangled cat state…”

“…Using the realistic parameter values from Refs. [15,28,30,[33][34][35][36], we show in Figure 3 the numerical results for the fidelities of the generated state and the corresponding average phonon number T r(ρ(t)a † a) versus the decays of the charge qubit and the NAMR with respect to different Rabi frequencies, where we consider ±10% change of the Rabi frequency by parameter fluctuations.…”

“…Moreover, the last condition ensures that the terms proportional to |g| 2 are negligible. Therefore, we obtain the following effective Hamiltonian Figure 2, the effective Hamiltonian (5) presents the main feature of the interaction Hamiltonian (4), particularly within the decoherence times of the transmon-type charge qubit and the NAMR (i.e., t < 50 µs [15,25,28,33]). …”

“…By a single qubit operation, i.e., |e → (|g − |e )/ √ 2 and |g → (|g + |e )/ √ 2 [33], on the charge qubit, Eq. (16) changes as…”

Persistent Rabi oscillations probed via low-frequency noise correlation

“…These experiments (as well as the experiment proposed in the present paper) touch upon the most intriguing property of quantum measurement: the presence of a "spooky" quantum back-action [4], which changes the system to agree with the observation, and cannot be explained in a realistic way, i.e. by using the Schrödinger equation.The quantum coherent (Rabi) oscillations in solid-state qubits are usually measured in an ensemble-averaged way [5,6] and decay within a short timescale, even though it can be much longer than the oscillation period. However, for a continuous weak measurement of a single qubit, the Rabi oscillations are non-decaying and can in principle be monitored in real time, as follows, e.g., from the quantum Bayesian formalism [7], which is generally similar to the formalism of quantum trajectories [8].…”