# Feed-forward and its role in conditional linear optical quantum dynamics

## Abstract

Nonlinear optical quantum gates can be created probabilistically using only single-photon sources, linear optical elements, and photon-number-resolving detectors. These gates are heralded but operate with probabilities much less than 1. There is currently a large gap between the performance of the known circuits and the established upper bounds on their success probabilities. One possibility for increasing the probability of success of such gates is feed-forward, where one attempts to correct certain failure events that occurred in the gate's operation. In this Brief Report we examine the role of feed-forward in improving the success probability. In particular, for the nonlinear sign-shift gate, we find that in a three-mode implementation with a single round of feed-forward the optimal average probability of success is approximately given by p{sub success}=0.272. This value is only slightly larger than the general optimal success probability without feed-forward, p{sub success}=0.25.

- Authors:

- QOLS, Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2BW (United Kingdom)
- Hewlett-Packard Laboratories, Filton Road, Stoke Gifford, Bristol BS34 8QZ (United Kingdom)
- (United Kingdom)
- National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430 (Japan)

- Publication Date:

- OSTI Identifier:
- 20787006

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 73; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevA.73.034301; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; GATING CIRCUITS; IMPLEMENTATION; NONLINEAR OPTICS; NONLINEAR PROBLEMS; PERFORMANCE; PHOTONS; PROBABILITY; QUANTUM MECHANICS

### Citation Formats

```
Scheel, S., Munro, W. J., Kok, P., Eisert, J., Institute for Mathematical Sciences, Imperial College London, Prince's Gardens, London SW7 2PE, and Nemoto, K.
```*Feed-forward and its role in conditional linear optical quantum dynamics*. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVA.73.0.

```
Scheel, S., Munro, W. J., Kok, P., Eisert, J., Institute for Mathematical Sciences, Imperial College London, Prince's Gardens, London SW7 2PE, & Nemoto, K.
```*Feed-forward and its role in conditional linear optical quantum dynamics*. United States. doi:10.1103/PHYSREVA.73.0.

```
Scheel, S., Munro, W. J., Kok, P., Eisert, J., Institute for Mathematical Sciences, Imperial College London, Prince's Gardens, London SW7 2PE, and Nemoto, K. Wed .
"Feed-forward and its role in conditional linear optical quantum dynamics". United States.
doi:10.1103/PHYSREVA.73.0.
```

```
@article{osti_20787006,
```

title = {Feed-forward and its role in conditional linear optical quantum dynamics},

author = {Scheel, S. and Munro, W. J. and Kok, P. and Eisert, J. and Institute for Mathematical Sciences, Imperial College London, Prince's Gardens, London SW7 2PE and Nemoto, K.},

abstractNote = {Nonlinear optical quantum gates can be created probabilistically using only single-photon sources, linear optical elements, and photon-number-resolving detectors. These gates are heralded but operate with probabilities much less than 1. There is currently a large gap between the performance of the known circuits and the established upper bounds on their success probabilities. One possibility for increasing the probability of success of such gates is feed-forward, where one attempts to correct certain failure events that occurred in the gate's operation. In this Brief Report we examine the role of feed-forward in improving the success probability. In particular, for the nonlinear sign-shift gate, we find that in a three-mode implementation with a single round of feed-forward the optimal average probability of success is approximately given by p{sub success}=0.272. This value is only slightly larger than the general optimal success probability without feed-forward, p{sub success}=0.25.},

doi = {10.1103/PHYSREVA.73.0},

journal = {Physical Review. A},

number = 3,

volume = 73,

place = {United States},

year = {Wed Mar 15 00:00:00 EST 2006},

month = {Wed Mar 15 00:00:00 EST 2006}

}