Cluster state
Encyclopedia
In quantum information
and quantum computing, a cluster state is a type of highly entangled state of multiple qubit
s. Cluster states are generated in lattices of qubits with Ising
type interactions. A cluster C is a connected subset of a d-dimensional lattice, and a cluster state is a pure state of the qubits located on C. They are different from other types of entangled states such as GHZ states or W state
s because it is more difficult to eliminate quantum entanglement
(via projective measurements) in the case of cluster states. Another way of thinking of cluster states is as a particular instance of graph states, where the underlying graph is a connected subset of a d-dimensional lattice
.Cluster states are especially useful in the context of the one-way quantum computer
.
Formally a cluster state is a state which obeys the set eigenvalue equations:
where
Quantum information
In quantum mechanics, quantum information is physical information that is held in the "state" of a quantum system. The most popular unit of quantum information is the qubit, a two-level quantum system...
and quantum computing, a cluster state is a type of highly entangled state of multiple qubit
Qubit
In quantum computing, a qubit or quantum bit is a unit of quantum information—the quantum analogue of the classical bit—with additional dimensions associated to the quantum properties of a physical atom....
s. Cluster states are generated in lattices of qubits with Ising
Ising
Ising may refer to:* The Ising model* Ernst Ising, inventor of the above model* Jane Ising, wife of the late Ernst Ising* Rudolf “Rudy” Ising, animator by MGM, together with Hugh Harman often credited as: Harman-Ising...
type interactions. A cluster C is a connected subset of a d-dimensional lattice, and a cluster state is a pure state of the qubits located on C. They are different from other types of entangled states such as GHZ states or W state
W state
The W state is an entangled quantum state of three qubits which has the following shapeand which is remarkable for representing a specific type of multipartite entanglement and for occurring in several applications in quantum information theory.-Properties:...
s because it is more difficult to eliminate quantum entanglement
Quantum entanglement
Quantum entanglement occurs when electrons, molecules even as large as "buckyballs", photons, etc., interact physically and then become separated; the type of interaction is such that each resulting member of a pair is properly described by the same quantum mechanical description , which is...
(via projective measurements) in the case of cluster states. Another way of thinking of cluster states is as a particular instance of graph states, where the underlying graph is a connected subset of a d-dimensional lattice
Lattice (group)
In mathematics, especially in geometry and group theory, a lattice in Rn is a discrete subgroup of Rn which spans the real vector space Rn. Every lattice in Rn can be generated from a basis for the vector space by forming all linear combinations with integer coefficients...
.Cluster states are especially useful in the context of the one-way quantum computer
One-way quantum computer
The one-way or measurement based quantum computer is a method of quantum computing that first prepares an entangled resource state, usually a cluster state or graph state, then performs single qubit measurements on it...
.
Formally a cluster state is a state which obeys the set eigenvalue equations:
where
