### Abstract

For pure three-qubit states the classification ofentanglement is both non-trivial and well understood. In thiswork, we study the quantum algorithmic complexity introducedin [1] of three-qubit pure states belonging to the most generalclass of entanglement. Contrary to expectations we find out thatthe degree of entanglement of states in this class quantified bythe measure of 3-tangle, does not correlate with the quantumalgorithmic complexity, defined as the length of the shortestcircuit needed to prepare the state. For a given entangled statethe evaluation of its quantum complexity is done via a pseudorandomevolutionary algorithm. This algorithm allows us notonly to determine the complexity of a quantum circuit in termsof the number of required quantum gates, but also to estimateanother type of complexity related to the time required to obtainthe correct answer.

Original language | English |
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Title of host publication | Proceedings - 2016 IEEE 46th International Symposium on Multiple-Valued Logic, ISMVL 2016 |

Publisher | IEEE Computer Society |

Pages | 253-257 |

Number of pages | 5 |

Volume | 2016-July |

ISBN (Electronic) | 9781467394888 |

DOIs | |

Publication status | Published - Jul 18 2016 |

Event | 46th IEEE International Symposium on Multiple-Valued Logic, ISMVL 2016 - Sapporo, Hokkaido, Japan Duration: May 18 2016 → May 20 2016 |

### Other

Other | 46th IEEE International Symposium on Multiple-Valued Logic, ISMVL 2016 |
---|---|

Country | Japan |

City | Sapporo, Hokkaido |

Period | 5/18/16 → 5/20/16 |

### Fingerprint

### Keywords

- Algorithmic complexity
- Entanglement
- Pure States

### ASJC Scopus subject areas

- Computer Science(all)
- Mathematics(all)

### Cite this

*Proceedings - 2016 IEEE 46th International Symposium on Multiple-Valued Logic, ISMVL 2016*(Vol. 2016-July, pp. 253-257). [7515557] IEEE Computer Society. https://doi.org/10.1109/ISMVL.2016.37

**Quantum algorithmic complexity of three-qubit pure states.** / Lukac, Martin; Mandilara, Aikaterini.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings - 2016 IEEE 46th International Symposium on Multiple-Valued Logic, ISMVL 2016.*vol. 2016-July, 7515557, IEEE Computer Society, pp. 253-257, 46th IEEE International Symposium on Multiple-Valued Logic, ISMVL 2016, Sapporo, Hokkaido, Japan, 5/18/16. https://doi.org/10.1109/ISMVL.2016.37

}

TY - GEN

T1 - Quantum algorithmic complexity of three-qubit pure states

AU - Lukac, Martin

AU - Mandilara, Aikaterini

PY - 2016/7/18

Y1 - 2016/7/18

N2 - For pure three-qubit states the classification ofentanglement is both non-trivial and well understood. In thiswork, we study the quantum algorithmic complexity introducedin [1] of three-qubit pure states belonging to the most generalclass of entanglement. Contrary to expectations we find out thatthe degree of entanglement of states in this class quantified bythe measure of 3-tangle, does not correlate with the quantumalgorithmic complexity, defined as the length of the shortestcircuit needed to prepare the state. For a given entangled statethe evaluation of its quantum complexity is done via a pseudorandomevolutionary algorithm. This algorithm allows us notonly to determine the complexity of a quantum circuit in termsof the number of required quantum gates, but also to estimateanother type of complexity related to the time required to obtainthe correct answer.

AB - For pure three-qubit states the classification ofentanglement is both non-trivial and well understood. In thiswork, we study the quantum algorithmic complexity introducedin [1] of three-qubit pure states belonging to the most generalclass of entanglement. Contrary to expectations we find out thatthe degree of entanglement of states in this class quantified bythe measure of 3-tangle, does not correlate with the quantumalgorithmic complexity, defined as the length of the shortestcircuit needed to prepare the state. For a given entangled statethe evaluation of its quantum complexity is done via a pseudorandomevolutionary algorithm. This algorithm allows us notonly to determine the complexity of a quantum circuit in termsof the number of required quantum gates, but also to estimateanother type of complexity related to the time required to obtainthe correct answer.

KW - Algorithmic complexity

KW - Entanglement

KW - Pure States

UR - http://www.scopus.com/inward/record.url?scp=84981333213&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84981333213&partnerID=8YFLogxK

U2 - 10.1109/ISMVL.2016.37

DO - 10.1109/ISMVL.2016.37

M3 - Conference contribution

AN - SCOPUS:84981333213

VL - 2016-July

SP - 253

EP - 257

BT - Proceedings - 2016 IEEE 46th International Symposium on Multiple-Valued Logic, ISMVL 2016

PB - IEEE Computer Society

ER -