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Attention to quantum complexity. [PDF]

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Quantum Error Correction

2013
We look at the problem of communication of states of a finite level quantum system through a channel disturbed by noise. Such a quantum system is described by a finite dimensional complex Hilbert space \( \mathcal{H} \) and its states are density operators, in other words, positive hermitian operators of unit trace.
Daniel A. Lidar, Todd A. Brun
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Quantum Error Correction

2021
DiVincenzo criterion #5 from Chap. 18 states that the qubit lifetimes should be long compared to the duration of the algorithm. However, quantum systems are fragile. Unwanted external perturbations from the environment (e.g., electromagnetic waves, thermal excitations, charge, etc.) can interact with the quantum system, such that the system becomes ...
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Quantum Error Correction

2011
In this chapter, we discuss the basic theory of quantum error-correcting codes, fault-tolerant quantum computation, and the threshold theorem.
Igor Volovich, Masanori Ohya
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Quantum Error Correction

2015
A quantum system can never be seen as being completely isolated from its environment, thereby permanently causing disturbance to the state of the system. The resulting noise problem threatens quantum computers and their great promise, namely, to provide a computational advantage over classical computers for certain problems (see also the cross ...
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