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Physica Scripta

Use of discrete Wigner functions in the study of decoherence of a system of superconducting flux-qubits

M. Reboiro, Osvaldo Civitarese, Diego Tielas

Published Jun 1, 2015• 11 citations
Publisher

Abstract

The persistence of coherence of a system of superconducting flux-qubits, in the presence of an ensemble of electrons, is analysed. The time evolution of the system is solved exactly. We study the time evolution of the Wigner function of the reduced density matrix of the qubits, in order to determine the rate of decoherence induced by the coupling with the electrons. We found that the rate of induced decoherence may be reduced, depending on the interactions with the electrons. Also, we discuss the squeezing properties of the system.

DOI
10.1088/0031-8949/90/7/074028

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The persistence of coherence of a system of superconducting flux-qubits, in the presence of an ensemble of electrons, is analysed. The time evolution of the system is solved exactly. We study the time evolution of the Wigner function of the reduced density matrix of the qubits, in order to determine the rate of decoherence induced by the coupling with the electrons. We found that the rate of induced decoherence may be reduced, depending on the interactions with the electrons. Also, we discuss the squeezing properties of the system.
Abstract The persistence of coherence in a hybrid dissipative system, which is composed of superconducting flux-qubits (SFQs) and an electron ensemble, is analyzed. Both the interactions between the electrons and the SFQs are taken into account. The time evolution of the hybrid system is discussed in terms of the discrete Wigner function of each subsystem and in terms of the entropic uncertainty relations. The inclusion of a linewidth, both for the electrons and the SFQs, influences the coherence of each subsystem and the pattern of spin squeezing of the corresponding steady state.
We study theoretically how decoherence affects superposition states composed of entangled states in inductively coupled two superconducting flux-qubits. We discover that the quantum fluctuation of an observable in a coupled flux-qubit system plays a crucial role in decoherence when the expectation value of the observable is zero. This examplifies that decoherence can be also induced through a quantum mechanically higher-order effect. We also find that there exists a decoherence free subspace for the environment coupled via a charge degree of freedom of the qubit system.
The research work discussed in this thesis deals with the study of superconducting Josephson qubits. Superconducting qubits are solid-state artificial atoms which are based on lithographically defined Josephson tunnel junctions properties. When sufficiently cooled, these superconducting devices exhibit quantized states of charge, flux or junction phase depending on their design parameters. This allows to observe coherent evolutions of their states. The results presented can be divided into two parts. In a first part we investigate operations of superconducting qubits based on the quantum coherence in superconducting quantum interference devices (SQUID). We explain experimental data which has been observed in a SQUID subjected to fast, large-amplitude modifications of its effective potential shape. The motivations for this work come from the fact that in the past few years there have been attempts to interpret the supposed quantum behavior of physical systems, such as Josephson devices, within a classical framework. Moreover, we analyze the possibility of generating GHZ states, namely maximally entangled states, in a quantum system made out of three Josephson qubits. In particular, we investigate the possible limitations of the GHZ state generation due to coupling to bosonic baths. In the second part of the thesis we address a particular cause of decoherence of flux qubits which has been disregarded until now: thermal gradients, which can arise due to accidental non equilibrium quasiparticle distributions. The reason for these detrimental effects is that heat currents flowing through Josephson tunnel junctions in response to a temperature gradient are periodic functions of the phase difference between the electrodes. The phase dependence of the heat current comes from Andreev reflection, namely an interplay between the quasiparticles which carry heat and the superconducting condensate which is sensitive to the superconducting phase difference. Generally speaking, the flux qubit states are characterized by different values of the phase difference through their Josephson junctions. Consequently, the phase-dependent thermal current through a device subject a temperature gradient is related to the phase-dependent qubit states. We study how the thermal currents change according to the state of the qubits hence yielding a measurement of the qubit state. This in turn leads to an impact of temperature gradient on the dynamics of the system. We show that flux qubits in the Delft qubit design can have limitations of the decoherence time to the order of microseconds as a result of this newly discovered source of decoherence. In contrast, the fluxonium qubit is found to be well protected due to its superinductance.
We study decoherence in superconducting qubits due to quasiparticle tunneling which is enhanced by two known deviations from the equilibrium BCS theory. The first process corresponds to tunneling of an already existing quasiparticle across the junction. The quasiparticle density is increased, e.g., because of an effective quasiparticle doping of the system. The second process is quasiparticle tunneling by breaking of a Cooper pair. This can happen at typical energies of superconducting qubits if there is an extended quasiparticle density inside the gap. We calculate the induced energy decay and pure dephasing rates in typical qubit designs. Assuming the lowest reported value of the nonequilibrium quasiparticle density in Aluminum, we find for the persistent-current flux qubit decay times of the order of recent measurements. Using the typical subgap density of states in Niobium we also reproduce observed decay times in the corresponding Niobium flux qubits.
The superconducting qubits are nowadays considered as good candidates both for building a quantum computer and for the study of the quantum erects in macroscopic systems. The system of two coupled qubits can be described by the Liouville equation. We convert the Liouville equation in the system of real equations by making use of the convenient parametrization of the reduced density matrix. Phenomenological inclusion of the relaxation is presented. The time evolution of the levels population in coupled flux qubits is calculated by solving the Bloch-Redfield equations.
We perform a theoretical study of composed superconducting qubit systems for the case of a coupled qubit configuration based on a hybrid qubit circuit made of both charge and phase qubits, which are coupled via a σ x ⊗ σ z interaction. We compute the system's eigen-energies in terms of the qubit transition frequencies and the strength of the inter-qubit coupling, and describe the sensitivity of the energy crossing/anti-crossing features to such coupling. We compute the hybrid system's dissipative dynamics for the cases of i) collective and ii) independent decoherence, whereby the system interacts with one common and two different baths of harmonic oscillators, respectively. The calculations have been performed within the Bloch-Redfield formalism and we report the solutions for the populations and the coherences of the system's reduced density matrix. The dephasing and relaxation rates are explicitly calculated as a function of the heat bath temperature.