Decoherence-free subspaces | Wikipedia audio article
Channel: wikipedia tts
Date: 31/12/2018

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Decoherence-free_subspaces


00:01:35 1 Background
00:01:44 1.1 Origins
00:02:59 1.2 Further development
00:05:48 1.3 Recent research
00:06:53 2 Conditions for the existence of decoherence-free subspaces
00:07:06 2.1 Hamiltonian formulation
00:15:42 2.1.1 Operator-sum representation formulation
00:27:48 2.1.2 Semigroup formulation
00:31:43 3 DFSs as a special class of information-preserving structures (IPS) and quantum error-correcting codes (QECCs)
00:32:02 3.1 Information-preserving structures (IPS)
00:38:21 3.2 Quantum error-correcting codes (QECCs)
00:42:57 4 Example of a decoherence-free subspace
00:43:09 4.1 Collective dephasing
00:51:12 5 Alternative: decoherence-free subsystems
00:56:11 6 See also



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SUMMARY
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A decoherence-free subspace (DFS) is a subspace of a system's Hilbert space that is invariant to non-unitary dynamics. Alternatively stated, they are a small section of the system Hilbert space where the system is decoupled from the environment and thus its evolution is completely unitary. DFSs can also be characterized as a special class of quantum error correcting codes. In this representation they are passive error-preventing codes since these subspaces are encoded with information that (possibly) won't require any active stabilization methods. These subspaces prevent destructive environmental interactions by isolating quantum information. As such, they are an important subject in quantum computing, where (coherent) control of quantum systems is the desired goal. Decoherence creates problems in this regard by causing loss of coherence between the quantum states of a system and therefore the decay of their interference terms, thus leading to loss of information from the (open) quantum system to the surrounding environment. Since quantum computers cannot be isolated from their environment (i.e. we cannot have a truly isolated quantum system in the real world) and information can be lost, the study of DFSs is important for the implementation of quantum computers into the real world.