Method for modeling decoherence on a quantum-information processor

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 σzσz system-environment couplings which induce coherence (phase) damping, though 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 which 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 an nuclear magnetic resonance quantum information processor.

Phase-space approach to the study of decoherence in quantum walks

“…To describe such coupling we will use a model which was introduced and studied in detail in Ref. [19]. In that paper it was shown that one can mimic the coupling to an external environment by a sequence of random rotations applied to the quantum coin, which have the effect of scrambling the spin polarization.…”

“…[19] (see Ref. [6] for a similar approach): Assuming that these angles are randomly distributed in an interval (−α,+α), this density matrix is…”

NMR Quantum Information Processing

“…This has the effect of scrambling the system phase information stored in the environment during the coupling interaction and therefore emulates the loss of memory. When the kick angles are averaged over small angles, the decay induced by the kicks is exponential and the rate is linear in the number of the kicks [96]. As the kick angles are completely randomized over the interval from 0 to 2π, a Zeno type effect is observed.…”

“…This can be circumvented by using a second "classical" environment which interacts with a small size quantum environment (see Fig. 10 for an illustration of the model) [96].…”

Generation and Suppression of Decoherence in Artificial Environment for Qubit System

“…Here we would like to give a remark on the work by Teklemariam et al 17 They used a three-spin molecule as a composite of a one-qubit system and a two-qubit environment. Their initial state vector takes the form |χ s ⊗ |φ e ⊗ |ψ e .…”