Reduced dynamics with renormalization in solid-state charge qubit measurement

Quantum measurement will inevitably cause backaction on the measured system, resulting in the well-known dephasing and relaxation. In this paper, in the context of solid-state qubit measurement by a mesoscopic detector, we show that an alternative backaction known as renormalization is important under some circumstances. This effect is largely overlooked in the theory of quantum measurement.

Spontaneous relaxation of a charge qubit under electrical measurement

In this work we first derive a generalized conditional master equation for quantum measurement by a mesoscopic detector, then study the readout characteristics of qubit measurement where a number of remarkable new features are found. The work would, in particular, highlight the qubit spontaneous relaxation effect induced by the measurement itself rather than an external thermal bath.

Continuous weak measurement and feedback control of a solid-state charge qubit: A physical unravelling of non-Lindblad master equation

Conventional quantum trajectory theory developed in quantum optics is largely based on the physical unravelling of a Lindblad-type master equation, which constitutes the theoretical basis of continuous quantum measurement and feedback control. In this work, in the context of continuous quantum measurement and feedback control of a solid-state charge qubit, we present a physical unravelling scheme of a non-Lindblad-type master equation. Self-consistency and numerical efficiency are well demonstrated. In particular, the control effect is manifested in the detector noise spectrum, and the effect of measurement voltage is discussed.

Quantum coherence control of solid-state charge qubit by means of a suboptimal feedback algorithm

The quantum coherence control of a solid-state charge qubit is studied by using a suboptimal continuous feedback algorithm within the Bayesian feedback scheme. For the coherent Rabi oscillation, the present algorithm suggests a simple bang-bang control protocol, in which the control parameter is modulated between two values. For the coherence protection of the idle state, the present approach is applicable to arbitrary states, including those lying on the equator of the Bloch sphere which are out of control in the previous Markovian feedback scheme.

Quantum trajectories for the realistic measurement of a solid-state charge qubit

We present a new model for the continuous measurement of a coupled quantum dot charge qubit. We model the effects of a realistic measurement, namely adding noise to, and filtering, the current through the detector. This is achieved by embedding the detector in an equivalent circuit for measurement. Our aim is to describe the evolution of the qubit state conditioned on the macroscopic output of the external circuit. We achieve this by generalizing a recently developed quantum trajectory theory for realistic photodetectors [P. Warszawski, H. M. Wiseman, and H. Mabuchi, Phys. Rev. A 65, 023802 (2002)] to treat solid-state detectors. This yields stochastic equations whose (numerical) solutions are the realistic quantum trajectories of the conditioned qubit state. We derive our general theory in the context of a low transparency quantum point contact. Areas of application for our theory and its relation to previous work are discussed.

Decoherence of charge qubit coupled to interacting background charges

The major contribution to decoherence of a double quantum dot or a Josephson-junction charge qubit comes from the electrostatic coupling to fluctuating background charges hybridized with the conduction electrons in the reservoir. However, estimations according to previously developed theories show that finding a sufficient number of effective fluctuators in a realistic experimental layout is quite improbable. We show that this paradox is resolved by allowing for a short-range Coulomb interaction of the fluctuators with the electrons in the reservoir. This dramatically enhances both the number of effective fluctuators and their contribution to decoherence, resulting in the most dangerous decoherence mechanism for charge qubits.

Non-Markovian qubit dynamics in a circuit-QED setup

We consider a circuit-QED setup that allows the induction and control of non-Markovian dynamics of a qubit. Non-Markovianity is enforced over the qubit by means of its direct coupling to a bosonic mode which is controllably coupled to another qubit-mode system. We show that this configuration can be achieved in a circuit-QED setup consisting of two initially independent superconducting circuits, each formed by one charge qubit and one transmission-line resonator, which are put in interaction by coupling the resonators to a current-biased Josephson junction. We solve this problem exactly and then proceed with a thorough investigation of the emergent non-Markovianity in the dynamics of the qubits. Our study might serve the context for the first experimental assessment of non-Markovianity in a multielement solid-state device.

Charge-based quantum computing using single donors in semiconductors

Solid-state quantum computer architectures with qubits encoded using single atoms are now feasible given recent advances in the atomic doping of semiconductors. Here we present a charge qubit consisting of two dopant atoms in a semiconductor crystal, one of which is singly ionized. Surface electrodes control the qubit and a radio-frequency single-electron transistor provides fast readout. The calculated single gate times, of order 50 ps or less, are much shorter than the expected decoherence time. We propose universal one- and two-qubit gate operations for this system and discuss prospects for fabrication and scale up.

Low-temperature decoherence of qubit coupled to background charges

We have found an exact expression for the decoherence rate of a Josephson charge qubit coupled to fluctuating background charges. At low temperatures T the decoherence rate Γ is linear in T while at high temperatures it saturates in agreement with a known classical solution which, however, reached at surprisingly high T. In contrast to the classical picture, impurity states spread in a wide interval of energies (> T) may essentially contribute to Γ.

Quantum measurement of an electron in a disordered potential: Delocalization versus measurement voltages

Quantum point contact (QPC), one of the typical mesoscopic transport devices, has been suggested to be an efficient detector for quantum measurement. In the context of two-state charge qubit, our previous studies showed that the QPC's measurement back-action cannot be described by the conventional Lindblad quantum master equation. In this work, we study the measurement problem of a multistate system, say, an electron in disordered potential, subject to the quantum measurement of the mesoscopic detector QPC. The effect of measurement back-action and the detector's readout current are analyzed, where particular attention is focused on some new features and the underlying physics associated with the measurement-induced delocalization versus the measurement voltages.

Progress in silicon-based quantum computation

We review progress at the Australian Centre for Quantum Computer Technology towards the fabrication and demonstration of spin qubits and charge qubits based on phosphorus donor atoms embedded in intrinsic silicon. Fabrication is being pursued via two complementary pathways: a 'top-down' approach for near-term production of few-qubit demonstration devices and a 'bottom-up' approach for large-scale qubit arrays with sub-nanometre precision. The 'top-down' approach employs a low-energy (keV) ion beam to implant the phosphorus atoms. Single-atom control during implantation is achieved by monitoring on-chip detector electrodes, integrated within the device structure. In contrast, the 'bottom-up' approach uses scanning tunnelling microscope lithography and epitaxial silicon overgrowth to construct devices at an atomic scale. In both cases, surface electrodes control the qubit using voltage pulses, and dual single-electron transistors operating near the quantum limit provide fast read-out with spurious-signal rejection.

Weak measurement of qubit oscillations with strong response detectors: Violation of the fundamental bound imposed on linear detectors

Qubit measurement by mesoscopic charge detectors has received great interest in the community of mesoscopic transport and solid-state quantum computation, and some controversial issues still remain unresolved. In this work, we revisit the continuous weak measurement of a solid-state qubit by single electron transistors (SETs) in nonlinear-response regime. For two SET models typically used in the literature, we find that the signal-to-noise ratio can violate the universal upper bound "4," which is imposed quantum mechanically on linear-response detectors. This different result can be understood by means of the cross correlation of the detector currents by viewing the two junctions of the single SET as two detectors. Possible limitation of the potential-scattering approach to this result is also discussed.

Decoherence of two Josephson charge qubits coupled via sigma(x)sigma(x)-type coupling and exposed to sigma(x) noise

Decoherence properties of two Josephson charge qubits coupled via the sigma(x)sigma(x) type are investigated. Considering the special structure of this new design, the dissipative effects arising from the circuit impedance providing the fluxes for the qubits' superconducting quantum interference device loops coupled to the sigma(x) qubit variables are considered. The results show that the overall decoherence effects are significantly strong in this qubit design. It is found that the dissipative effects are stronger in the case of coupling to two uncorrelated baths than are found in the case of one common bath.

Superconducting charge qubits: The roles of self and mutual inductances

We study the essential roles of self and mutual inductances in superconducting charge qubits and propose a scheme to couple charge qubits by means of mutual inductance. We also show that the Hamiltonians can be exactly formulated in compact forms in the spin-1/2 representation for both single- and double-qubit structures.

Comparing charge transport predictions for a ternary electrolyte using the Maxwell–Stefan and Nernst–Planck equations

In this work, we investigate and compare the Maxwell–Stefan and Nernst–Planck equations for modeling multicomponent charge transport in liquid electrolytes. Specifically, we consider charge transport in the Li+/I−/I3−/ACN ternary electrolyte originally found in dye-sensitized solar cells. We employ molecular dynamics simulations to obtain the Maxwell–Stefan diffusivities for this electrolyte. These simulated diffusion coefficients are used in a multicomponent charge transport model based on the Maxwell– Stefan equations, and this is compared to a Nernst–Planck based model which employs binary diffusion coefficients sourced from the literature. We show that significant differences between the electrolyte concentrations at electrode interfaces, as predicted by the Maxwell–Stefan and Nernst–Planck models, can occur. We find that these differences are driven by a pressure term that appears in the Maxwell–Stefan equations. We also investigate what effects the Maxwell–Stefan diffusivities have on the simulated charge transport. By incorporating binary diffusivities found in the literature into the Maxwell–Stefan framework, we show that the simulated transient concentration profiles depend on the diffusivities; however, the simulated equilibrium profiles remain unaffected.