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Decoherence and a simple quantum computer

Isaac L. Chuang, Y. Yamamoto, Raymond Laflamme

Published Oct 1, 1995• 5 citations
OpenAlex

Abstract

The authors analyze the effect of decoherence on the operation of part of a simple quantum computer. The results indicate that quantum bit coding techniques may be used to mitigate the effects of two sources of decoherence - amplitude damping and phase randomization.

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Communications in Theoretical Physics•Aug 1, 2011•8 citations
We investigate the impact of loss (amplitude damping) and decoherence (phase damping) on the performance of a simple quantum computer which solves the one-bit Deutsch problem. The components of this machine are beamsplitters and nonlinear optical Kerr cells, but errors primarily originate from the latter. We develop models to describe the effect of these errors on a quantum optical Fredkin gate. The results are used to analyze possible error correction strategies in a complete quantum computer. We find that errors due to loss can be avoided perfectly by appropriate design techniques, while decoherence can be partially dealt with using projective error correction.
In the process of developing and operating quantum computing systems, quantum decoherence is a fundamental difficulty that poses a significant obstacle. The purpose of this study is to present a full understanding of quantum decoherence, which includes an examination of its impacts on quantum information processing as well as its origins and causes. Through our investigation of the dynamic relationship between decoherence and quantum error correction, we bring to light the significance of preserving coherence in order to ensure the reliability of quantum computation. In this study, we analyze a variety of sources of decoherence by means of theoretical models and practical research. These sources include environmental interactions, temperature fluctuations, and operational defects. Additionally, we address advanced strategies for minimizing decoherence, including as dynamical decoupling, error-correcting codes, and fault-tolerant quantum computing architectures. These techniques are discussed in this article. The results of our research highlight the significance of comprehending and effectively regulating quantum decoherence in order to develop quantum computing systems that are both scalable and attainable. By laying the groundwork for future research and development in the field of improving the robustness and performance of quantum computers, the purpose of this effort is being accomplished.
A scheme for protecting quantum states from both independent and cooperative decoherence is proposed. The scheme operates by pairing each qubit (two-state quantum system) with an ancilla qubit and by encoding the states of the qubits into corresponding coherence-preserving states of qubit pairs. In this scheme, amplitude damping (loss of energy) as well as phase damping (dephasing) is prevented by a strategy called ``free-Hamiltonian elimination.'' We further extend the scheme to include quantum gate operations and show that loss and decoherence during such operations can also be prevented.
This article presents a comprehensive study of the impact of decoherence on the average correlation for pure quantum states. We explore two primary mechanisms of decoherence: phase damping and amplitude damping, each having distinct effects on quantum systems. Phase damping, which describes the loss of quantum coherence without energy loss, primarily affects the phase relationships between the components of a quantum system while amplitude damping involves energy dissipation and also affects the state's occupation probabilities. We show that the average correlation follows a predictable decaying pattern in both scenarios. Our analysis can be understood in the context of quantum computing, by focusing on how phase damping influences the entanglement and correlation between qubits, key factors in quantum computational efficiency and error correction protocols.
To suppress the decoherence, in addition to error-correcting codes and the error-avoiding codes, bang-bang control has also been introduced. Here in this work, we discuss how to suppress decoherence in quantum systems using bang-bang control, two cases have been discussed, adiabatic decoherence alone, and decoherence with both phase and amplitude damping. We also discussed the different cases when the system is made up of one atom or multi-atom and when such atom with two level or multi-level. It is found that in all the above cases, bang-bang control can suppress decoherence effectively.
We study the behavior of cooperative multiplayer quantum games [Q. Chen, Y. Wang, J.T. Liu, and K.L. Wang, Phys. Lett. A 327 (2004) 98; A.P. Flitney and L.C.L. Hollenberg, Quantum Inf. Comput. 7 (2007) 111] in the presence of decoherence using different quantum channels such as amplitude damping, depolarizing and phase damping. It is seen that the outcomes of the games for the two damping channels with maximum values of decoherence reduce to same value. However, in comparison to phase damping channel, the payoffs of cooperators are strongly damped under the influence amplitude damping channel for the lower values of decoherence parameter. In the case of depolarizing channel, the game is a no-payoff game irrespective of the degree of entanglement in the initial state for the larger values of decoherence parameter. The decoherence gets the cooperators worse off.