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arXiv:quant-ph/0402102 · Physical Review A

Simulating noisy quantum protocols with quantum trajectories

Gabriel G. Carlo, Giuliano Benenti, Giulio Casati, Carlos Mejía-Monasterio

Published Jun 18, 2004• 28 citations
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Abstract

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.

DOI
10.1103/physreva.69.062317

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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.
Noise is a major challenge in quantum computing, affecting the reliability of quantum protocols. In this work, we analytically study the impact of various noise processes, such as depolarization, bit flip, and phase flip, on the quantum state teleportation protocol. Each noise process is modeled as a quantum channel and is applied individually to all qubits after the corresponding unitary operations to simulate realistic conditions. We evaluate the fidelity between the ideal and noisy teleported states to quantify the effect of noise. Our analysis shows that the fidelity decreases polynomially, in general, as the noise strength increases for all noise types, highlighting the sensitivity of state teleportation to different noise mechanisms. However, in the low noise regime, the fidelity decreases only linearly, indicating the robustness of the teleportation protocol. These results provide insight into error characterization and can inform strategies for noise mitigation in practical quantum computing applications.
Using the theory of quantum trajectories, we study the classical capacity C\mathbf{C}C of noisy quantum channels in the superdense coding protocol. We apply the two models that generalize single-qubit noisy channels, such as amplitude damping and phase flip, to the many-qubit situation. Our numerical results show that the quantum trajectory approach is suitable for modeling the superdense coding protocol in realistic environments.
Abstract We propose a new protocol for quantum teleportation (QT) which adopts the Brown state as the quantum channel. This work focuses on the teleportation of a single unknown two-qubit state via a Brown state channel in an ideal environment. To validate the effectiveness of our proposed scheme, we conduct experiments by using the quantum circuit simulator Quirk. Furthermore, we investigate the effects of four noisy channels, namely, the phase damping noise, the bit-flip noise, the amplitude damping noise, and the phase-flip noise. Notably, we employ Monte Carlo simulation to elucidate the fidelity density under various noise parameters. Our analysis demonstrates that the fidelity of the protocol in a noisy environment is influenced significantly by the amplitude of the initial state and the noise factor.