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Journal of Physics A Mathematical and Theoretical

Decoherence recuperating fast environmental dynamics

Murat Çetinbaş

Published Jan 14, 2010• 0 citations
Publisher

Abstract

We examine the exact internal decoherence dynamics of a qubit in an isolated Josephson charge-qubit quantum computer in the presence of one- and two-body static internal imperfections. By help of open system dynamics quantifiers, i.e. purity, fidelity, covariance and Loschmidt echo, we distinguish between non-unitary and unitary components of internal decoherence dynamics and show that the non-unitary component consists of two processes: system-environment entanglement and incoherence. Our results indicate that the incoherence process is the major source of internal decoherence rather than system-environment entanglement. We find that strong one-body intra–environmental interactions, which generate fast environmental dynamics, result in a rapid suppression of decoherence induced by both system–environment entanglement and incoherence processes. We explain the mechanisms of suppression of decoherence for these two processes and discuss our results.

DOI
10.1088/1751-8113/43/5/055309

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We examine the exact internal decoherence dynamics of a qubit in an isolated Josephson charge-qubit quantum computer in the presence of one- and two-body static internal imperfections. By help of open system dynamics quantifiers, i.e. purity, fidelity, covariance and Loschmidt echo, we distinguish between non-unitary and unitary components of internal decoherence dynamics and show that the non-unitary component consists of two processes: system-environment entanglement and incoherence. Our results indicate that the incoherence process is the major source of internal decoherence rather than system-environment entanglement. We find that strong one-body intra–environmental interactions, which generate fast environmental dynamics, result in a rapid suppression of decoherence induced by both system–environment entanglement and incoherence processes. We explain the mechanisms of suppression of decoherence for these two processes and discuss our results.
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Condensed and solid phase environments offer a wide range of controllable interactions for new quantum technologies.Understanding the dynamics of open quantum systems interacting with such complex environments is important for correct modeling of many chemical and physical phenomena and for development of new quantum technologies.The central theme of this thesis is the open system dynamics of a small qua.ntum system coupled to self-interacting chaotic environments.This thesis consists of Lhree related parts.In the first part, a theory predicting open dynamics of a quantum system interacting with chaotic environments is reported.The theory is of a Kraus decomposition form, which is exact for chaotic environments of thermodynamic dimension.Extension of the theory to time-dependent system Hamiltonians is also presented so that it may have practical applications for studies of new quantum technologies.In tbe second part, extensive numerical calculations are performed to obtain the exact quantum dynamic::; for two realistic models of self-int(~ra.ctingenvironments.Both models represent a statistically Hawed isolated quantum computer (QC) core.In the first model, the open dynamics of a quantum-control NOT (CNOT) gate in the pre::;ence of static internal imperfections are invcstigated and internal error sources are identified for a large number of QC configurations.The results indicate that the strong two-body imperfections suppress the interna.! decohcrence and enhance the performancc of the CNOT gate.Moreover, the largest source of error is found to be unitary due to coherent shifting rather than III
Different approaches in quantifying environmentally-induced decoherence are considered. We identify a measure of decoherence, derived from the density matrix of the system of interest, that quantifies the environmentally induced error, i.e., deviation from the ideal isolated-system dynamics. This measure can be shown to have several useful features. Its behavior as a function of time has no dependence on the initial conditions, and is expected to be insensitive to the internal dynamical time scales of the system, thus only probing the decoherence-related time dependence. For a spin-boson model - a prototype of a qubit interacting with environment - we also demonstrate the property of additivity: in the regime of the onset of decoherence, the sum of the individual qubit error measures provides an estimate of the error for a several-qubit system, even if the qubits are entangled, as expected in quantum-computing applications. This makes it possible to estimate decoherence for several-qubits quantum computer gate designs for which explicit calculations are exceedingly difficult.
The thesis is contributed to the study of the decoherence dynamics of dissipative qubit systems. We reveal the profound impact of the formation of a bound state between the qubit and its local environment on the decoherence dynamics of qubit system in non-Markovian regime. We find that the decoherence can be suppressed greatly under the non-Markovian dynamics when the bound state is formed. Consequently, the entanglement can be partially preserved in the steady state. A criterion on this decoherence/disentanglement suppression is given explicitly. It can give a useful guideline on the decoherence control in experiment. We also find that the entanglement can be stably distributed among all components and particularly it always satisfies an identity. Our unified treatment includes the previous results in the literatures as special cases. The result reveals the profound nature of the entanglement and should have significant implications for quantum information processing.
Considering two non-interacting qubits in the context of open quantum systems, it is well known that their common environment may act as an entangling agent. In a perturbative regime the influence of the environment on the system dynamics can effectively be described by a unitary and a dissipative contribution. For the two-spin Boson model with (sub-) Ohmic spectral density considered here, the particular unitary contribution (Lamb shift) easily explains the buildup of entanglement between the two qubits. Furthermore it has been argued that in the adiabatic limit, adding the so-called counterterm to the microscopic model compensates the unitary influence of the environment and, thus, inhibits the generation of entanglement. Investigating this assertion is one of the main objectives of the work presented here. Using the hierarchy of pure states (HOPS) method to numerically calculate the exact reduced dynamics, we find and explain that the degree of inhibition crucially depends on the parameter s determining the low frequency power law behavior of the spectral density J(ω)∼ωse−ω/ωc . Remarkably, we find that for resonant qubits, even in the adiabatic regime (arbitrarily large ωc ), the entanglement dynamics is still influenced by an environmentally induced Hamiltonian interaction. Further, we study the model in detail and present the exact entanglement dynamics for a wide range of coupling strengths, distinguish between resonant and detuned qubits, as well as Ohmic and deep sub-Ohmic environments. Notably, we find that in all cases the asymptotic entanglement does not vanish and conjecture a linear relation between the coupling strength and the asymptotic entanglement measured by means of concurrence. Further we discuss the suitability of various perturbative master equations for obtaining approximate entanglement dynamics.