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The toric code, and surface codes more generally, [1] are types of stabilizer codes considered very important for the practical realization of quantum information processing. Conceptual background [ edit ]
For example, to measure the first stabilizer (), a parity measurement of of the first qubit, on the second, on the third, on the fourth , and on the fifth is performed. Since there are four stabilizers, 4 ancillas will be used to measure them.
For the toric code, this space is four-dimensional, and so can be used to store two qubits of quantum information. This can be proven by considering the number of independent stabilizer operators. The occurrence of errors will move the state out of the stabilizer space, resulting in vertices and plaquettes for which the above condition does not ...
In an -qubit stabilizer code, we can describe this subspace by its Pauli stabilizing group, the set of all -qubit Pauli operators which stabilize every logical state. The stabilizer formalism allows us to define the codespace of a stabilizer code by specifying its Pauli stabilizing group.
Given the stabilizer generators of Shor's code: ... Contact Wikipedia; Code of Conduct; Developers; Statistics; Cookie statement; Mobile view ...
Quantum capacity. In the theory of quantum communication, the quantum capacity is the highest rate at which quantum information can be communicated over many independent uses of a noisy quantum channel from a sender to a receiver. It is also equal to the highest rate at which entanglement can be generated over the channel, and forward classical ...
Entanglement-assisted stabilizer formalism. In the theory of quantum communication, the entanglement-assisted stabilizer formalism is a method for protecting quantum information with the help of entanglement shared between a sender and receiver before they transmit quantum data over a quantum communication channel.
A more general class of codes (encompassing the former) are the stabilizer codes discovered by Daniel Gottesman, and by Robert Calderbank, Eric Rains, Peter Shor, and N. J. A. Sloane; these are also called additive codes. Two dimensional Bacon–Shor codes are a family of codes parameterized by integers m and n.