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

A Abliz, Li Ss, Sun Ll, Feng Sl, Zheng Hz

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

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.

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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.
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.
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.
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.
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.
Based on a network graph analysis of the underlying circuit, a quantum theory of arbitrary superconducting charge qubits is derived. Describing the dissipative elements of the circuit with a Caldeira-Leggett model, we calculate the decoherence and leakage rates of a charge qubit. The analysis includes decoherence due to a dissipative circuit element such as a voltage source or the quasiparticle resistances of the Josephson junctions in the circuit. The theory presented here is dual to the quantum circuit theory for superconducting flux qubits. In contrast to spin-boson models, the full Hilbert space structure of the qubit and its coupling to the dissipative environment are taken into account. Moreover, both self- and mutual inductances of the circuit are fully included.