The time evolution of a qubit, consisting of two single-level quantum dots, is studied in the presence of telegraph noise. The dots are connected by two tunneling paths with an Aharonov-Bohm flux enclosed between them. Under special symmetry conditions, which can be achieved by tuning gate voltages, there develops partial decoherence: at long times, the off-diagonal element of the reduced density matrix (in the basis of the two dot states) approaches a nonzero value, generating a circulating current around the loop. The flux dependence of this current contains full information on the initial quantum state of the qubit, even at infinite time. Small deviations from this symmetry yield a very slow exponential decay toward the fully decoherent limit. However, the amplitudes of this decay also contain the full information on the initial qubit state, measurable either via the current or via the occupations of the qubit dots.
The time evolution of a qubit, consisting of two single-level quantum dots, is studied in the presence of telegraph noise. The dots are connected by two tunneling paths with an Aharonov-Bohm flux enclosed between them. Under special symmetry conditions, which can be achieved by tuning gate voltages, there develops partial decoherence: at long times, the off-diagonal element of the reduced density matrix (in the basis of the two dot states) approaches a nonzero value, generating a circulating current around the loop. The flux dependence of this current contains full information on the initial quantum state of the qubit, even at infinite time. Small deviations from this symmetry yield a very slow exponential decay toward the fully decoherent limit. However, the amplitudes of this decay also contain the full information on the initial qubit state, measurable either via the current or via the occupations of the qubit dots.
A qubit (containing two quantum states, 1 and 2), is coupled to a control register (state 3), which is subject to telegraph noise. We study the time evolution of the density matrix ρ of an electron which starts in some coherent state on the qubit. At infinite time, ρ usually approaches the fully decoherent state, with ρnm=δnm/3. However, when the Hamiltonian is symmetric under 1↔2, the element ρ12 approaches a non-zero real value, implying a partial coherence of the asymptotic state. The asymptotic density matrix depends only on Re[ρ12(t=0)]. In several cases, the information stored on the qubit is protected from the noise.
In this thesis, we study the evolution of qubits evolving according to the Schrödinger equation with a Hamiltonian containing noise terms, modeled by random diagonal and off-diagonal matrix elements. For a single qubit exposed to such noise, we show that the noise-averaged qubit density matrix converges to a specific final state, in the limit of large time t. We find that the convergence speed is polynomial in 1=t, with a power that depends on the regularity and the low frequency behaviour of the noise probability density. We evaluate the final state explicitly in the regimes of weak and strong off-diagonal noise. We show that the process implements the well-known dephasing channel in the localized and delocalized basis, respectively. Furthermore, we consider the evolution of the entanglement of two (or more) qubits subject to Gaussian noises with varying means and variances. We consider two different cases: individual noise where each qubit feels an independent noise, and common noise where all qubits are subjected to the same noise. We find the following characteristics of entanglement, measured by the concurrence of qubits. Initially entangled states lose their amount of entanglement in time due to the presence of the noise. The decay of entanglement happens more quickly for common noise than for individual noise. We also detect creation of entanglement due to the common noise: for some initially disentangled states, entanglement is created for intermediate times and then decays to zero in the long time again.
The coupling of a mesoscopic system with its environment usually causes total decoherence: at long times the reduced density matrix of the system evolves in time to a limit which is independent of its initial value, losing all the quantum information stored in its initial state. Under special circumstances, a subspace of the system's Hilbert space remains coherent, or "decoherence free", and the reduced density matrix approaches a non-trivial limit which contains information on its initial quantum state, despite the coupling to the environment. This situation is called "partial decoherence". Here we find the conditions for partial decoherence for a mesoscopic system (with N quantum states) which is coupled to an environment. When the Hamiltonian of the system commutes with the total Hamiltonian, one has "adiabatic decoherence", which yields N-1 time-independent combinations of the reduced density matrix elements. In the presence of a magnetic flux, one can measure circulating currents around loops in the system even at long times, and use them to retrieve information on the initial state. For N=2, we demonstrate that partial decoherence can happen only under adiabatic decoherence conditions. However, for N>2 we find partial decoherence even when the Hamiltonian of the system does not commute with the total Hamiltonian, and we obtain the general conditions for such non-adiabatic partial decoherence. For an electron moving on a ring, with N>2 single-level quantum dots, non-adiabatic partial decoherence can arise only when the total flux through the ring vanishes (or equals an integer number of flux quanta), and therefore there is no asymptotic circulating current.
Quantum information and quantum computation implementation in terms of electron charges and spin has attracted tremendous attention for the development of large-scale quantum information processing [1-5]. Artificial and tunable charge qubits fabricated in a semiconductor nanostructure are suitable for the purpose, since various parameters can be controlled by external gate voltages [6,7]. The rapid control of external gate voltage in two-electron double quantum dots has been demonstrated [8,9].Entanglement has recently emerged as a significant resource in quantum information and other applications. However an important problem is to ensure the robustness of this resource; that is, the ability to maintain it against decay. Decoherence is one of the fundamental limitation in quantum information science, and the understanding and the control of its dynamics appears as a crucial issue for the development of quantum information devices.For charge qubits in quantum dots, the effects of phonons and electromagnetic and background charge fluctuations are important in the decoherence process. The effect of phonons on the dynamics of two charge qubits has been examined [10,11].In this work, we analyze the effect of telegraph noise on the dynamical of two electrons in laterally coupled quantum dots. The resulting qubit is supposed to evolve in the basis spanned by the states |0〉 and |1〉 which describe the electron localized in the left and right dot respectively. We investigate theoretically the quantum dynamics of two interacting electrons driven by an oscillatory electric field. In order to study the effect of the telegraph noise on the entanglement we adopt the concurrence.
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.
We study Landau-Zener-like dynamics of a qubit influenced by transverse random telegraph noise. The telegraph noise is characterized by its coupling strength $\ensuremath{\upsilon}$ and switching rate $\ensuremath{\gamma}$. The qubit energy levels are driven nonlinearly in time, $\ensuremath{\propto}\mathrm{sgn}(t){\ensuremath{\mid}t\ensuremath{\mid}}^{\ensuremath{\nu}}$, and we derive the transition probability in the limit of sufficiently fast noise, for arbitrary exponent $\ensuremath{\nu}$. The level occupation after the transition depends strongly on $\ensuremath{\nu}$, and there exists a critical ${\ensuremath{\nu}}_{c}$ with qualitative difference between $\ensuremath{\nu}<{\ensuremath{\nu}}_{c}$ and $\ensuremath{\nu}>{\ensuremath{\nu}}_{c}$. When $\ensuremath{\nu}<{\ensuremath{\nu}}_{c}$, the final state is always fully incoherent with equal population of both quantum levels, even for arbitrarily weak noise. For $\ensuremath{\nu}>{\ensuremath{\nu}}_{c}$, the system keeps some coherence depending on the strength of the noise, and in the limit of weak noise, no transition takes place. For fast noise ${\ensuremath{\nu}}_{c}=1∕2$, while for slow noise ${\ensuremath{\nu}}_{c}<1∕2$ and it depends on $\ensuremath{\gamma}$. We also discuss phase coherence, which is relevant when the qubit has a nonzero minimum energy gap. The qualitative dependency on $\ensuremath{\nu}$ is the same for the phase coherence and level occupation. The state after the transition does, in general, depend on $\ensuremath{\gamma}$. For fixed $\ensuremath{\upsilon}$, increasing $\ensuremath{\gamma}$ decreases the final state coherence when $\ensuremath{\nu}<1$ and increases the final state coherence when $\ensuremath{\nu}>1$. Only the conventional linear driving is independent of $\ensuremath{\gamma}$.