# Translating Non-Trivial Algorithms from the Circuit Model to the Measurement

## Abstract

We provide a set of prescriptions for implementing a circuit model algorithm as measurement based quantum computing via a large discrete cluster state constructed sequentially, from qubits implemented as single photons. We describe a large optical discrete graph state capable of searching logical 4 and 8 element lists as an example. To do so we have developed several prescriptions based on analytic evaluation of the evolution of discrete cluster states and graph state equations. We describe the cluster state as a sequence of repeated entanglement and measurement steps using a small number of single photons for each step. These prescriptions can be generalized to implement any logical circuit model operation with appropriate single photon measurements and feed forward error corrections. Such a cluster state is not guaranteed to be optimal (i.e. minimum number of photons, measurements, run time).

- Authors:

- ORNL
- Air Force Research Laboratory

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Sponsoring Org.:
- Work for Others (WFO)

- OSTI Identifier:
- 1185632

- DOE Contract Number:
- DE-AC05-00OR22725

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Modern Optics

- Country of Publication:
- United States

- Language:
- English

### Citation Formats

```
Smith IV, Amos M, Alsing, Paul, Lott, Capt. Gordon, and Fanto, Michael.
```*Translating Non-Trivial Algorithms from the Circuit Model to the Measurement*. United States: N. p., 2015.
Web.

```
Smith IV, Amos M, Alsing, Paul, Lott, Capt. Gordon, & Fanto, Michael.
```*Translating Non-Trivial Algorithms from the Circuit Model to the Measurement*. United States.

```
Smith IV, Amos M, Alsing, Paul, Lott, Capt. Gordon, and Fanto, Michael. Thu .
"Translating Non-Trivial Algorithms from the Circuit Model to the Measurement". United States.
doi:.
```

```
@article{osti_1185632,
```

title = {Translating Non-Trivial Algorithms from the Circuit Model to the Measurement},

author = {Smith IV, Amos M and Alsing, Paul and Lott, Capt. Gordon and Fanto, Michael},

abstractNote = {We provide a set of prescriptions for implementing a circuit model algorithm as measurement based quantum computing via a large discrete cluster state constructed sequentially, from qubits implemented as single photons. We describe a large optical discrete graph state capable of searching logical 4 and 8 element lists as an example. To do so we have developed several prescriptions based on analytic evaluation of the evolution of discrete cluster states and graph state equations. We describe the cluster state as a sequence of repeated entanglement and measurement steps using a small number of single photons for each step. These prescriptions can be generalized to implement any logical circuit model operation with appropriate single photon measurements and feed forward error corrections. Such a cluster state is not guaranteed to be optimal (i.e. minimum number of photons, measurements, run time).},

doi = {},

journal = {Journal of Modern Optics},

number = ,

volume = ,

place = {United States},

year = {Thu Jan 01 00:00:00 EST 2015},

month = {Thu Jan 01 00:00:00 EST 2015}

}