# Noise and Decoherence

In this article, we will discuss noise and the decoherence that it causes. Simply put, this is a degradation of quantum superposition. When this happens, the results of quantum calculations become unintended. To begin with, noise is always present in any system unless it is absolute zero. In a quantum computer, quantum computation is affected by internal noise from the structure of the bits and external noise caused by external manipulation. The former includes Josephson junction noise in superconducting systems and mean free path in Cooper pairs [1], and natural radiation in ion trap systems. The latter includes electromagnetic field noise and thermal gradients in the system used to manipulate the qubit.

As a result, decoherence occurs. For two qubits and above, there is also the destruction of entanglement. These effects can be interpreted as interactions with qubits corresponding to heat baths and information leakage to them. The von Neumann equation is used to describe this [2]. It is an equation that can describe the time evolution of a quantum state in a system of finite temperature. Even in a system of two qubits, the complexity is so high that only a simplified noisy system can be solved by hand. These include the quantum master equation and the Caldeira-Leggett model [3].

However, there is a limit to reproducing the noise with theory alone. Therefore, the best way is to build a real quantum computer and reproduce the noise with a simulator.

[1]Hikaru Wakaura and Hiroyasu Koizumi 2017 J. Phys. Commun. 1 055013

[2]Giuliano Benenti, Giuliano Casati, and Giuliano Strini. Principles of Quantum Computation and Information Volume I: Basic Concepts, Splinger, 2004

[3]A. Altrand and B. Simons, Condensed Matter Field Theory, First Edition(2006).