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Physical Review A

Decoherence of two Josephson charge qubits coupled via σxσx -type coupling and exposed to σx noise

Ahmad Abliz, Shu‐Shen Li, Lian-Liang Sun, Songlin Feng, Houzhi Zheng

Published May 12, 2004• 3 citations
Publisher

Abstract

Decoherence properties of two Josephson charge qubits coupled via the ${\ensuremath{\sigma}}_{x}{\ensuremath{\sigma}}_{x}$ 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 ${\ensuremath{\sigma}}_{x}$ 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.

DOI
10.1103/physreva.69.052309

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Decoherence properties of two Josephson charge qubits coupled via the \ensuremathσx\ensuremathσx{\ensuremath{\sigma}}_{x}{\ensuremath{\sigma}}_{x}\ensuremathσx​\ensuremathσx​ 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 \ensuremathσx{\ensuremath{\sigma}}_{x}\ensuremathσx​ 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.
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.
Solid-state quantum bits are promising candidates for the realization of a scalable quantum computer. However, they are usually strongly limited by decoherence due to the many extra degrees of freedom of a solid-state system. We investigate a system of two solid-state qubits that are coupled via ${\ensuremath{\sigma}}_{z}^{(i)}\ensuremath{\bigotimes}{\ensuremath{\sigma}}_{z}^{(j)}$ type of coupling. This kind of setup is typical for pseudospin solid-state quantum bits such as charge or flux systems. We evaluate decoherence properties and gate quality factors in the presence of a common and two uncorrelated baths coupling to ${\ensuremath{\sigma}}_{z},$ respectively. We show that at low temperatures, uncorrelated baths do degrade the gate quality more severely. In particular, we show that in the case of a common bath, optimum gate performance of a controlled-PHASE gate can be reached at very low temperatures, because our type of coupling commutes with the coupling to the decoherence, which makes this type of coupling interesting as compared to previously studied proposals with ${\ensuremath{\sigma}}_{y}^{(i)}\ensuremath{\bigotimes}{\ensuremath{\sigma}}_{y}^{(j)}$ coupling. Although less pronounced, this advantage also applies to the controlled-NOT gate.
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.
A complete analysis of the decoherence properties of a Josephson junction qubit is presented. The qubit is of the flux type and consists of two large loops forming a gradiometer, one small loop, and three Josephson junctions. We develop a complete, quantitative description of the inductances and capacitances of the circuit. Including two stray capacitances makes the quantum mechanical modeling of the system five dimensional. To make the required calculation tractable, we devise a general Born-Oppenheimer approximation which reduces the effective dimensionality in the calculation to one. Contributions to relaxation (T1)({T}_{1})(T1​) and dephasing $({T}_{\ensuremath{\phi}})$ arising from two different control circuits, one coupled to the small loop and one coupled to a large loop, is computed. We explore T1{T}_{1}T1​ and ${T}_{\ensuremath{\phi}}$ along an optimal line in the space of applied fluxes; along this ``S line'' we see significant and rapidly varying contributions to the decoherence parameters, primarily from the circuit coupling to the large loop.
By virtue of the canonical quantization method, we present a quantization scheme for a charge qubit based on the superconducting quantum interference device (SQUID), taking the self-inductance of the loop into account. Under reasonable short-time approximation, we study the effect of decoherence in the ohmic case by employing the response function and the norm. It is confirmed that the decoherence time, which depends on the parameters of the circuit components, the coupling strength, and the temperature, can be as low as several picoseconds, so there is enough time to record the information.
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.