# Fast simulation of stabilizer circuits using a graph-state representation

## Abstract

According to the Gottesman-Knill theorem, a class of quantum circuits--namely, the so-called stabilizer circuits--can be simulated efficiently on a classical computer. We introduce an algorithm for this task, which is based on the graph-state formalism. It shows significant improvement in comparison to an existing algorithm, given by Gottesman and Aaronson, in terms of speed and of the number of qubits the simulator can handle. We also present an implementation.

- Authors:

- Institut fuer Theoretische Physik, Universitaet Innsbruck, Innsbruck (Austria)
- (Austria)

- Publication Date:

- OSTI Identifier:
- 20974550

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 73; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevA.73.022334; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; INFORMATION THEORY; QUANTUM COMPUTERS; QUANTUM ENTANGLEMENT; QUBITS; SIMULATION

### Citation Formats

```
Anders, Simon, Briegel, Hans J., and Institut fuer Quantenoptik und Quanteninformation der Oesterreichischen Akademie der Wissenschaften, Innsbruck.
```*Fast simulation of stabilizer circuits using a graph-state representation*. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVA.73.022334.

```
Anders, Simon, Briegel, Hans J., & Institut fuer Quantenoptik und Quanteninformation der Oesterreichischen Akademie der Wissenschaften, Innsbruck.
```*Fast simulation of stabilizer circuits using a graph-state representation*. United States. doi:10.1103/PHYSREVA.73.022334.

```
Anders, Simon, Briegel, Hans J., and Institut fuer Quantenoptik und Quanteninformation der Oesterreichischen Akademie der Wissenschaften, Innsbruck. Wed .
"Fast simulation of stabilizer circuits using a graph-state representation". United States.
doi:10.1103/PHYSREVA.73.022334.
```

```
@article{osti_20974550,
```

title = {Fast simulation of stabilizer circuits using a graph-state representation},

author = {Anders, Simon and Briegel, Hans J. and Institut fuer Quantenoptik und Quanteninformation der Oesterreichischen Akademie der Wissenschaften, Innsbruck},

abstractNote = {According to the Gottesman-Knill theorem, a class of quantum circuits--namely, the so-called stabilizer circuits--can be simulated efficiently on a classical computer. We introduce an algorithm for this task, which is based on the graph-state formalism. It shows significant improvement in comparison to an existing algorithm, given by Gottesman and Aaronson, in terms of speed and of the number of qubits the simulator can handle. We also present an implementation.},

doi = {10.1103/PHYSREVA.73.022334},

journal = {Physical Review. A},

number = 2,

volume = 73,

place = {United States},

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

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

}

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