Dephasing of Josephson qubits close to optimal points

Decoherence of Josephson qubits can be substantially reduced by tuning their parameters to optimal operation points with only quadratic coupling to fluctuations. We analyze dephasing due to 1/f noise for a two-level system detuned from an optimal point, i.e., the crossover to the linear-coupling regime, both for free induction decay and for spin-echo experiments. Influence of several noise sources is also discussed. The text was submitted by the authors in English.     

Dephasing of qubits by transverse low-frequency noise

We analyze the dissipative dynamics of a two-level quantum system subject to low-frequency, e.g., 1/f noise, motivated by recent experiments with superconducting quantum circuits. We show that the effect of transverse linear coupling of the system to low-frequency noise is equivalent to that of quadratic longitudinal coupling. We further find the decay law of quantum coherent oscillations under the influence of both low-and high-frequency fluctuations, in particular, for the case of comparable rates of relaxation and pure dephasing.     

Decoherence in solid-state qubits

The interaction of solid-state qubits with environmental degrees of freedom strongly affects the qubit dynamics, and leads to decoherence. In quantum information processing with solid-state qubits, decoherence significantly limits the performances of such devices. Therefore, it is necessary to fully understand the mechanisms that lead to decoherence. In this review, we discuss how decoherence affects two of the most successful realizations of solid-state qubits, namely, spin qubits and superconducting qubits. In the former, the qubit is encoded in the spin 1/2 of the electron, and it is implemented by confining the electron spin in a semiconductor quantum dot. Superconducting devices show quantum behaviour at low temperatures, and the qubit is encoded in the two lowest energy levels of a superconducting circuit. The electron spin in a quantum dot has two main decoherence channels, a (Markovian) phonon-assisted relaxation channel, due to the presence of a spin–orbit interaction, and a (non-Markovian) spin bath constituted by the spins of the nuclei in the quantum dot that interact with the electron spin via the hyperfine interaction. In a superconducting qubit, decoherence takes place as a result of fluctuations in the control parameters, such as bias currents, applied flux and bias voltages, and via losses in the dissipative circuit elements.     

Interfacing quantum-optical and solid-state qubits

We present a generic model of coupling quantum-optical and solid-state qubits, and the corresponding transfer protocols. The example discussed is a trapped ion coupled to a charge qubit (e.g., Cooper pair box). To enhance the coupling and to achieve compatibility between the different experimental setups we introduce a superconducting cavity as the connecting element.     

Current fluctuation spectrum in dissipative solid-state qubits

We present a formalism to calculate frequency dependent electron current noise for transport through two-level systems (such as coupled quantum dots or Cooper-pair boxes) in presence of dissipation. Perturbation theories in various regimes are formulated within a matrix scheme in Laplace scheme which we evaluate in detail both for weak and strong coupling to a bosonic environment.Received: 12 December 2003, Published online: 10 August 2004PACS: 72.70. + m Noise processes and phenomena - 73.23.Hk Coulomb blockade; single-electron tunneling     

Indirect interaction of solid-state qubits via two-dimensional electron gas

We propose a mechanism of long-range coherent coupling between nuclear spin qubits in semiconductor-heterojunction quantum information processing devices. The coupling is via localized donor electrons which interact with the two-dimensional electron gas. An effective interaction Hamiltonian is derived and the coupling strength is evaluated. We also discuss mechanisms of decoherence and consider gate control of the interaction between qubits. The resulting quantum computing scheme retains all the control and measurement aspects of earlier approaches, but allows qubit spacing at distances of the order of 100 nm, attainable with the present-day semiconductor device technologies.     

Weak values and the Leggett-Garg inequality in solid-state qubits

An implementation of weak values is investigated in solid-state qubits. We demonstrate that a weak value can be nonclassical if and only if a Leggett-Garg inequality can also be violated. Generalized weak values are described in which post-selection occurs on a range of weak measurement results. Imposing classical weak values permits the derivation of Leggett-Garg inequalities for bounded operators. Our analysis is presented in terms of kicked quantum nondemolition measurements on a quantum double-dot charge qubit.     

Robust optimal quantum gates for Josephson charge qubits

Quantum optimal control theory allows us to design accurate quantum gates. We employ it to design high-fidelity two-bit gates for Josephson charge qubits in the presence of both leakage and noise. Our protocol considerably increases the fidelity of the gate and, more important, it is quite robust in the disruptive presence of 1/f noise. The improvement in the gate performances discussed in this work (errors approximately 10(-3)-10(-4) in realistic cases) allows us to cross the fault tolerance threshold.     

Dephasing in the presence of a two-dimensional electron gas at high magnetic fields

By means of degenerate four-wave mixing (FWM), we investigate the quantum coherence of electron–hole pairs in the presence of a two-dimensional electron gas in modulation-doped GaAs–AlGaAs quantum wells in the regime of the integer quantum-Hall effect. We observe large jumps in the decay time of the FWM signal at even Landau level filling factors. The main features of the experimental observations can be qualitatively reproduced by a model which takes into account the number of unoccupied states within the highest partially occupied Landau level. Furthermore, we observe quantum beats between up to three different Landau level transitions.     

Robustness of optimal working points for nonadiabatic holonomic quantum computation

Geometric phases are an interesting resource for quantum computation in view of their robustness against decoherence effects. We study the effects of the environment on a class of one-qubit holonomic gates that have recently been shown to be characterized by “optimal” working times. We numerically analyze the behavior of these optimal points and focus on their robustness against noise.     

Dissipative quantum dynamics and optimal control using iterative time ordering: an application to superconducting qubits

We combine a quantum dynamical propagator that explicitly accounts for quantum mechanical time ordering with optimal control theory. After analyzing its performance with a simple model, we apply it to a superconducting circuit under so-called Pythagorean control. Breakdown of the rotating-wave approximation is the main source of the very strong time-dependence in this example. While the propagator that accounts for the time ordering in an iterative fashion proves its numerical efficiency for the dynamics of the superconducting circuit, its performance when combined with optimal control turns out to be rather sensitive to the strength of the time-dependence. We discuss the kind of quantum gate operations that the superconducting circuit can implement including their performance bounds in terms of fidelity and speed.     

Disentanglement of Qubit in Dephasing Model

We investigate the entanglement evolution of two qubits that are initially in Werner state under the classical phase noise. We discuss the influence of mixture degree on disentanglement. It is showed that the more mixed the state, the shorter is the time of disentanglement.     

Typicality at quantum-critical points

We discuss the concept of typicality of quantum states at quantum-critical points, using projector Monte Carlo simulations of an S = 1/2 bilayer Heisenberg antiferromagnet as an illustration. With the projection(imaginary) time τ scaled as τ = a Lz, L being the system length and z the dynamic critical exponent(which takes the value z = 1 in the bilayer model studied here), a critical point can be identified which asymptotically flows to the correct location and universality class with increasing L, independently of the prefactor a and the initial state. Varying the proportionality factor a and the initial state only changes the cross-over behavior into the asymptotic large-L behavior. In some cases, choosing an optimal factor a may also lead to the vanishing of the leading finite-size corrections. The observation of typicality can be used to speed up simulations of quantum criticality, not only within the Monte Carlo approach but also with other numerical methods where imaginary-time evolution is employed, e.g., tensor network states, as it is not necessary to evolve fully to the ground state but only for sufficiently long times to reach the typicality regime.     

Dephasing of a superconducting flux qubit

In order to gain a better understanding of the origin of decoherence in superconducting flux qubits, we have measured the magnetic field dependence of the characteristic energy relaxation time (T(1)) and echo phase relaxation time (T(2)(echo)) near the optimal operating point of a flux qubit. We have measured T(2)(echo) by means of the phase cycling method. At the optimal point, we found the relation T(2)(echo) approximately 2T(1). This means that the echo decay time is limited by the energy relaxation (T(1) process). Moving away from the optimal point, we observe a linear increase of the phase relaxation rate (1/T(2)(echo)) with the applied external magnetic flux. This behavior can be well explained by the influence of magnetic flux noise with a 1/f spectrum on the qubit.     

Entanglement of three qubits

For the formulation of Bell inequalities, it is important to include not just N-site correlation functions, but also (N-n)-site correlation functions. In this article, we focus on a three-qubit Bell inequality, which has been shown to be a good candidate for generalizing Gisin’s theorem to three qubits. The three-qubit Bell inequality can be used to detect the W-type entanglement in a proposed experiment.     

Dephasing of quantum tunnelling in molecular nanomagnets

Dephasing mechanism of quantum tunnelling in molecular magnets has been studied by means of the spin-coherentstate path integral in a mean field approximation. It is found that the fluctuating uncompensated transverse field from the dipolar-dipolar interaction between molecular magnets contributes a random phase to the quantum interference phase. The resulting transition rate is determined by the average tunnel splitting over the random phase. Such a dephasing process leads to the suppression of quenching due to the quantum phase interference, and to the steps due to odd resonances in hysteresis loop survived, which is in good agreement with experimental observations in molecular nanomagnets Fes and Mn12.     

Dephasing of atomic tunneling by nuclear quadrupoles

Recent experiments revealed a most surprising magnetic-field dependence of coherent echoes in amorphous solids. We show that a novel dephasing mechanism involving nuclear quadrupole moments is the origin of the observed phenomena.     

Transfer of quantum entangled states between superconducting qubits and microwave field qubits

Transferring entangled states between matter qubits and microwave-field (or optical-field) qubits is of fundamental interest in quantum mechanics and necessary in hybrid quantum information processing and quantum communication. We here propose a way for transferring entangled states between superconducting qubits (matter qubits) and microwave-field qubits. This proposal is realized by a system consisting of multiple superconducting qutrits and microwave cavities. Here, „qutrit” refers to a three-level quantum system with the two lowest levels encoding a qubit while the third level acting as an auxiliary state. In contrast, the microwave-field qubits are encoded with coherent states of microwave cavities. Because the third energy level of each qutrit is not populated during the operation, decoherence from the higher energy levels is greatly suppressed. The entangled states can be deterministically transferred because measurement on the states is not needed. The operation time is independent of the number of superconducting qubits or microwave-field qubits. In addition, the architecture of the circuit system is quite simple because only a coupler qutrit and an auxiliary cavity are required. As an example, our numerical simulations show that high-fidelity transfer of entangled states from two superconducting qubits to two microwave-field qubits is feasible with present circuit QED technology. This proposal is quite general and can be extended to transfer entangled states between other matter qubits (e.g., atoms, quantum dots, and NV centers) and microwave- or optical-field qubits encoded with coherent states.     

Topological states at exceptional points

We consider an N-level non-Hermitian Hamiltonian with an exceptional point of order N. We define adiabatic equivalence in such systems and explore topological phase. We show that the topological exceptional states appear at the interface of topologically distinct systems. We discuss that topological states appear even in closed systems. We explore dynamical robustness of exceptional edge states.