One-way quantum computer

Any one-way computation can be made into a quantum circuit by using quantum gates 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 (${\displaystyle \{|0\rangle ,|1\rangle \}}$ basis) remove physical qubits from the cluster, while measurements in the X-Y plane (${\displaystyle |0\rangle \pm e^{i\theta }|1\rangle }$ basis) teleport the logical qubits along the "wires" and perform the required quantum gates.[1] 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.

Measurement-based computation on a periodic 3D lattice cluster state can be used to implement topological quantum error correction.[2] Topological cluster state computation is closely related to Kitaev's toric code, as the 3D topological cluster state can be constructed and measured over time by a repeated sequence of gates on a 2D array.[3]

One-way quantum computation has been demonstrated by running the 2 qubit Grover's algorithm on a 2x2 cluster state of photons.[4][5] A linear optics quantum computer based on one-way computation has been proposed.[6]

Cluster states have also been created in optical lattices,[7] but were not used for computation as the atom qubits were too close together to measure individually.

It has been shown that the (spin ${\displaystyle {\tfrac {3}{2}}}$) AKLT state on a 2D honeycomb lattice can be used as a resource for MBQC.[8][9] More recently it has been shown that a spin-mixture AKLT state can be used as a resource.[10]

• Quantum gate teleportation

General