Abstract
In recent years, remarkable progress has been achieved in the development of quantum computers. For further development, it is important to clarify properties of errors by quantum noise and environment noise. However, when the system scale of quantum processors is expanded, it has been pointed out that a new type of quantum error, such as nonlinear error, appears. It is not clear how to handle such new effects in information theory. First of all, one should make the characteristics of the error probability of qubits clear as communication channel error models in information theory. The purpose of this paper is to survey the progress for modeling the quantum noise effects that information theorists are likely to face in the future, to cope with such nontrivial errors mentioned above. This paper explains a channel error model to represent strange properties of error probability due to new quantum noise. By this model, specific examples on the features of error probability caused by, for example, quantum recurrence effects, collective relaxation, and external force, are given. As a result, it is possible to understand the meaning of strange features of error probability that do not exist in classical information theory without going through complex physical phenomena.
Highlights
Introduction to SemiClassical Analysis for Digital Errors ofQubit in Quantum ProcessorOsamu Hirota 1,2,† †Reserch and Development Initiative, Chuo University, Tokyo 112-8551, JapanCurrent address: Quantum ICT Research Institute, Tamagawa University, 6-1-1 Tamagawa-gakuen, Machida, Tokyo 194-8610, Japan
A new type of error performance, the so called nonlinear error, where the error probability for a single qubit depends on the number of qubits in the system, has been discussed
It has been clarified that nonlinear errors give serious degradations of the capability of quantum computer, by the recurrence effect due to quantum correlation and by collective decoherence
Summary
When an ideal architecture of quantum processor is available, quantum computers are theoretically predicted to have significantly higher computing power than conventional computers [1]. I firstly present the most general classification of potential errors by quantum noise From such a classification, one can see a new kind of error that the error probability of a qubit depends on number of qubits in a quantum processor. I give the channel error model of error performance due to new quantum noise effects, and show several examples This means to clarify properties of error probability, and it does not mean to discuss the concrete error such as bit error, phase error, and so on. This provides a visualization of the strange error phenomena to researchers in information theory.
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