# Resource-efficient generation of linear cluster states by linear optics with postselection

## Abstract

Here we report on theoretical research in photonic cluster-state computing. Finding optimal schemes of generating non-classical photonic states is of critical importance for this field as physically implementable photon-photon entangling operations are currently limited to measurement-assisted stochastic transformations. A critical parameter for assessing the efficiency of such transformations is the success probability of a desired measurement outcome. At present there are several experimental groups that are capable of generating multi-photon cluster states carrying more than eight qubits. Separate photonic qubits or small clusters can be fused into a single cluster state by a probabilistic optical CZ gate conditioned on simultaneous detection of all photons with 1/9 success probability for each gate. This design mechanically follows the original theoretical scheme of cluster state generation proposed more than a decade ago by Raussendorf, Browne, and Briegel. The optimality of the destructive CZ gate in application to linear optical cluster state generation has not been analyzed previously. Our results reveal that this method is far from the optimal one. Employing numerical optimization we have identified that the maximal success probability of fusing n unentangled dual-rail optical qubits into a linear cluster state is equal to 1/2 ^{n-1}; an m-tuple of photonic Bell pairmore »

- Authors:

- Brescia Univ., Owensboro, KY (United States); Tulane Univ., New Orleans, LA (United States)
- Air Force Research Lab., Rome, NY (United States). Information Directorate
- Tulane Univ., New Orleans, LA (United States)
- Univ. of Dayton Research Inst., Dayton, OH (United States)
- Air Force Research Lab., Rome, NY (United States). Information Directorate; Wright-Patterson Air Force Base, Dayton, OH (United States)
- Air Force Research Lab., Rome, NY (United States). Information Directorate; ; Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Publication Date:

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

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1185631

- Grant/Contract Number:
- AC05-00OR22725; PHY- 1005709; FA 8750-11-2-0218

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Journal of Physics. B, Atomic, Molecular and Optical Physics

- Additional Journal Information:
- Journal Volume: 48; Journal Issue: 4; Journal ID: ISSN 0953-4075

- Publisher:
- IOP Publishing

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; quantum computer; cluster states; photonic Bell states

### Citation Formats

```
Uskov, D. B., Alsing, P. M., Fanto, M. L., Kaplan, L., Kim, R., Szep, A., and Smith, A. M..
```*Resource-efficient generation of linear cluster states by linear optics with postselection*. United States: N. p., 2015.
Web. doi:10.1088/0953-4075/48/4/045502.

```
Uskov, D. B., Alsing, P. M., Fanto, M. L., Kaplan, L., Kim, R., Szep, A., & Smith, A. M..
```*Resource-efficient generation of linear cluster states by linear optics with postselection*. United States. doi:10.1088/0953-4075/48/4/045502.

```
Uskov, D. B., Alsing, P. M., Fanto, M. L., Kaplan, L., Kim, R., Szep, A., and Smith, A. M.. Fri .
"Resource-efficient generation of linear cluster states by linear optics with postselection". United States.
doi:10.1088/0953-4075/48/4/045502. https://www.osti.gov/servlets/purl/1185631.
```

```
@article{osti_1185631,
```

title = {Resource-efficient generation of linear cluster states by linear optics with postselection},

author = {Uskov, D. B. and Alsing, P. M. and Fanto, M. L. and Kaplan, L. and Kim, R. and Szep, A. and Smith, A. M.},

abstractNote = {Here we report on theoretical research in photonic cluster-state computing. Finding optimal schemes of generating non-classical photonic states is of critical importance for this field as physically implementable photon-photon entangling operations are currently limited to measurement-assisted stochastic transformations. A critical parameter for assessing the efficiency of such transformations is the success probability of a desired measurement outcome. At present there are several experimental groups that are capable of generating multi-photon cluster states carrying more than eight qubits. Separate photonic qubits or small clusters can be fused into a single cluster state by a probabilistic optical CZ gate conditioned on simultaneous detection of all photons with 1/9 success probability for each gate. This design mechanically follows the original theoretical scheme of cluster state generation proposed more than a decade ago by Raussendorf, Browne, and Briegel. The optimality of the destructive CZ gate in application to linear optical cluster state generation has not been analyzed previously. Our results reveal that this method is far from the optimal one. Employing numerical optimization we have identified that the maximal success probability of fusing n unentangled dual-rail optical qubits into a linear cluster state is equal to 1/2n-1; an m-tuple of photonic Bell pair states, commonly generated via spontaneous parametric down-conversion, can be fused into a single cluster with the maximal success probability of 1/4m-1.},

doi = {10.1088/0953-4075/48/4/045502},

journal = {Journal of Physics. B, Atomic, Molecular and Optical Physics},

number = 4,

volume = 48,

place = {United States},

year = {Fri Jan 30 00:00:00 EST 2015},

month = {Fri Jan 30 00:00:00 EST 2015}

}

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