One-way quantum computer
Encyclopedia
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. It is "one-way" because the resource state is destroyed by the measurements.
The outcome of each individual measurement is random, but they are related in such a way that the computation always succeeds. In general the choices of basis
for later measurements need to depend on the results of earlier measurements, and hence the measurements cannot all be performed at the same time.
by using quantum gate
s to prepare the resource state. For cluster and graph resource states, this requires only one two-qubit gate per bond, so is efficient.
Conversely, any quantum circuit can be simulated by a one-way computer using a two-dimensional cluster state as the resource state, by laying out the circuit diagram on the cluster; Z measurements (
basis) remove physical qubits from the cluster, while measurements in the X-Y plane (
basis) teleport
the logical qubits along the "wires" and perform the required quantum gates. This is also polynomially efficient, as the required size of cluster scales as the size of the circuit (qubits x timesteps), while the number of measurement timesteps scales as the number of circuit timesteps.
on a 2x2 cluster state of photons. A linear optics quantum computer based on one-way computation has been proposed.
Cluster states have also been created in optical lattice
s, but were not used for computation as the atom qubits were too close together to measure individually.
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...
resource state, usually a cluster state
Cluster state
In quantum information and quantum computing, a cluster state is a type of highly entangled state of multiple qubits. 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...
or graph state, then performs single 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....
measurements on it. It is "one-way" because the resource state is destroyed by the measurements.
The outcome of each individual measurement is random, but they are related in such a way that the computation always succeeds. In general the choices of basis
Basis (linear algebra)
In linear algebra, a basis is a set of linearly independent vectors that, in a linear combination, can represent every vector in a given vector space or free module, or, more simply put, which define a "coordinate system"...
for later measurements need to depend on the results of earlier measurements, and hence the measurements cannot all be performed at the same time.
Equivalence to quantum circuit model
Any one-way computation can be made into a quantum circuitQuantum circuit
In quantum information theory, a quantum circuit is a model for quantum computation in which a computation is a sequence of quantum gates, which are reversible transformations on a quantum mechanical analog of an n-bit register...
by using quantum gate
Quantum gate
In quantum computing and specifically the quantum circuit model of computation, a quantum gate is a basic quantum circuit operating on a small number of qubits. They are the building blocks of quantum circuits, like classical logic gates are for conventional digital circuits.Unlike many classical...
s to prepare the resource state. For cluster and graph resource states, this requires only one two-qubit gate per bond, so is efficient.
Conversely, any quantum circuit can be simulated by a one-way computer using a two-dimensional cluster state as the resource state, by laying out the circuit diagram on the cluster; Z measurements (
basis) remove physical qubits from the cluster, while measurements in the X-Y plane ( basis) teleportQuantum teleportation
Quantum teleportation, or entanglement-assisted teleportation, is a process by which a qubit can be transmitted exactly from one location to another, without the qubit being transmitted through the intervening space...
the logical qubits along the "wires" and perform the required quantum gates. This is also polynomially efficient, as the required size of cluster scales as the size of the circuit (qubits x timesteps), while the number of measurement timesteps scales as the number of circuit timesteps.
Implementations
One-way quantum computation has been demonstrated by running the 2 qubit Grover's algorithmGrover's algorithm
Grover's algorithm is a quantum algorithm for searching an unsorted database with N entries in O time and using O storage space . It was invented by Lov Grover in 1996....
on a 2x2 cluster state of photons. A linear optics quantum computer based on one-way computation has been proposed.
Cluster states have also been created in optical lattice
Optical lattice
An optical lattice is formed by the interference of counter-propagating laser beams, creating a spatially periodic polarization pattern. The resulting periodic potential may trap neutral atoms via the Stark shift. Atoms are cooled and congregate in the locations of potential minima...
s, but were not used for computation as the atom qubits were too close together to measure individually.