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OSA Workshop on Entanglement and Quantum Decoherence

Dynamical Localization and Environmental Noise: a Quantum Trajectory

Jin Woo Jun

Published Jan 1, 2008• 0 citations
Publisher

Abstract

Using the quantum trajectory approach, we study the effects of environmental noise on dynamical localization in a quantum algorithm simulating the kicked rotator. We apply two models that generalize single qubit noisy channels, like phase flip and amplitude damping, to the many-qubit situation. Our numerical results show that the quantum trajectory approach is suitable for simulating the quantum kicked rotator in realistic environments.

DOI
10.1364/weqd.2008.p3

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Using the quantum trajectory approach, we study the effects of environmental noise on dynamical localization in a quantum algorithm simulating the kicked rotator. We apply two models that generalize single qubit noisy channels, like phase flip and amplitude damping, to the many-qubit situation. Our numerical results show that the quantum trajectory approach is suitable for simulating the quantum kicked rotator in realistic environments.
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The theory of quantum trajectories is applied to simulate the effects of quantum noise sources induced by the environment on quantum information protocols. We study two models that generalize single qubit noise channels like amplitude damping and phase flip to the many-qubit situation. We calculate the fidelity of quantum information transmission through a chaotic channel using the teleportation scheme with different environments. In this example, we analyze the role played by the kind of collective noise suffered by the quantum processor during its operation. We also investigate the stability of a quantum algorithm simulating the quantum dynamics of a paradigmatic model of chaos, the baker's map. Our results demonstrate that, using the quantum trajectories approach, we are able to simulate quantum protocols in the presence of noise and with large system sizes of more than 20 qubits.
We study the fidelity of quantum teleportation for the situation in which quantum logic gates are used to provide the long distance entanglement required in the protocol, and where the effect of a noisy environment is modeled by means of a generalized amplitude damping channel. Our results demonstrate the effectiveness of the quantum trajectories approach, which allows the simulation of open systems with a large number of qubits (up to 24). This shows that the method is suitable for modeling quantum information protocols in realistic environments.
We analyze the modification of entanglement dynamics in the Grover algorithm when the qubits are subjected to single-qubit amplitude-damping or phase-flip noise. We compare quantum trajectories with full density-matrix simulations, analyzing the dynamics of averaged trajectory entanglement (TE) and operator entanglement (OE), in the respective state representation. Although not a genuine entanglement measure, both TE and OE are connected to the efficiency of matrix product state simulations and thus of fundamental interest. As in many quantum algorithms, at the end of the Grover circuit entanglement decreases as the system converges towards the target product state. While we find that this is well captured in the OE dynamics, quantum trajectories rarely follow paths of reducing entanglement. Optimized unraveling schemes can lower TE slightly, however we show that deep in the circuit OE is generally smaller than TE. This implies that matrix product density operator (MPDO) simulations of quantum circuits can in general be more efficient than quantum trajectories. In addition, we investigate the noise-rate scaling of success probabilities for both amplitude-damping and phase-flip noise in Grover's algorithm.