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arXiv:quant-ph/0303115 · Physical Review A

Method for modeling decoherence on a quantum-information processor

Grum Teklemariam, Evan M. Fortunato, Cecilia C. López, Joseph Emerson, Juan Pablo Paz, Timothy F. Havel, David G. Cory

Published Jun 30, 2003• 31 citations
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Abstract

We develop and implement a method for modeling decoherence processes on an N-dimensional quantum system that requires only an ${N}^{2}$-dimensional quantum environment and random classical fields. This model offers the advantage that it may be implemented on small quantum-information processors in order to explore the intermediate regime between semiclassical and fully quantum models. We consider in particular ${\ensuremath{\sigma}}_{z}{\ensuremath{\sigma}}_{z}$ system-environment couplings which induce coherence (phase) damping, although the model is directly extendable to other coupling Hamiltonians. Effective, irreversible phase damping of the system is obtained by applying an additional stochastic Hamiltonian on the environment alone, periodically redressing it and thereby irreversibliy randomizing the system phase information that has leaked into the environment as a result of the coupling. This model is exactly solvable in the case of phase damping, and we use this solution to describe the model's behavior in some limiting cases. In the limit of small stochastic phase kicks the system's coherence decays exponentially at a rate that increases linearly with the kick frequency. In the case of strong kicks we observe an effective decoupling of the system from the environment. We present a detailed implementation of the method on a nuclear magnetic resonance quantum-information processor.

DOI
10.1103/physreva.67.062316

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In this work, two experimentally feasible methods of decoherence engineering-one based on the application of stochastic classical kicks and the other based on temporally randomized pulse sequences are combined. A different coupling interaction is proposed, which leads to amplitude damping as compared to existing methods which model phase damping, utilizing the zzzzzz coupling interaction. The decoherence process on combining the stochastic kick method and the randomized pulse sequence method and the effectiveness of dynamical decoupling under these coupling interactions are analyzed. Finally, a counter-intuitive result where decoherence is suppressed in the presence of two noise sources under certain resonant conditions is presented.
We consider a model of environment-induced dissipationless decoherence of a quantum system where the system is coupled to the bath degrees of freedom via the system Hamiltonian itself. We solve exactly for the reduced density operator of the system for an arbitrary spectral density of the thermal bath and also write down an exact master equation in the Lindblad form. We compare and contrast the above results with those obtained by considering the system frequencies to be randomly modulated as in stochastic models. We observe that a coupling to the bath as above necessarily induces a Kerr-like coherent contribution in the reduced dynamics of the system. This Kerr-like term is a reflection of the quantum nature of the bath and cannot be obtained from stochastic models. For the special case of a harmonic oscillator we consider the influence of decoherence and its relation with phase diffusion. Our numerical results exhibit oscillations in the evolution of system variables which overall is a signature of the quantum nature of the environment.
Due to omnipresent environmental interferences, quantum coherences inevitably undergo irreversible transformations over certain time scales, thus leading to the loss of encoded information. This process, known as decoherence, has been a major obstacle in realizing efficient quantum information processors. Understanding the mechanism of decoherence is crucial in developing tools to inhibit it. Here we utilize a method proposed by Teklemariam et al. [Phys. Rev. A 67, 062316 (2003)] to engineer artificial decoherence in the system qubits by randomly perturbing their surrounding ancilla qubits. Using a two-qubit nuclear magnetic resonance quantum register, we characterize the artificial decoherence by noise spectroscopy and quantum process tomography. Further, we study the efficacy of dynamical decoupling sequences in suppressing the artificial decoherence. Here we describe the experimental results and their comparisons with theoretical simulations.
A phase damping reservoir composed by NNN-bosons coupled to a system of interest through a cross-Kerr interaction is proposed and its effects on quantum superpositions are investigated. By means of analytical calculations we show that: (i) the reservoir induces a Gaussian decay of quantum coherences, and (ii) the inherent incommensurate character of the spectral distribution yields irreversibility. A state-independent decoherence time and a master equation are both derived analytically. These results, which have been extended for the thermodynamic limit, show that nondissipative decoherence can be suitably contemplated within the environment-induced decoherence (EID) approach. Finally, it is shown that the same mechanism yielding decoherence are also responsible for inducing dynamical disentanglement.
We study the dynamics of the entanglement between two qubits coupled to a common chaotic environment, described by the quantum kicked rotator model. We show that the kicked rotator, which is a single-particle deterministic dynamical system, can reproduce the effects of a pure dephasing many-body bath. Indeed, in the semiclassical limit the interaction with the kicked rotator can be described as a random phase kick, so that decoherence is induced in the two-qubit system. We also show that our model can efficiently simulate non-Markovian environments.
The article examines the problem of physical interpretation of quantum decoherence, which is traditionally described within phenomenological models of interaction between a quantum system and its environment. It is shown that standard approaches effectively reproduce the dynamics of phase damping but do not provide an explanation of the physical origin of coherence loss. A temporal interpretation of decoherence is proposed, in which phase damping is considered as a consequence of disruption of time synchronization in an inhomogeneous temporal environment. The paper demonstrates that the proposed approach is formally consistent with the density matrix formalism and Lindblad-type equations, reproducing standard exponential decoherence laws. It is substantiated that stochastic and non-Markovian effects can be interpreted as manifestations of temporal correlations and slow temporal drift. The practical value of the research lies in the possibility of applying the proposed interpretation to analyze noise, memory effects, and phase dynamics stability in complex information and quantum systems.