### Abstract

System identification is a key enabling component for the implementation of new quantum technologies, including quantum control. In this paper we consider a large class of input-output systems, namely linear passive quantum systems, and study the following identifiability question: if the system's Hamiltonian and coupling matrices are unknown, which of these dynamical parameters can be estimated by preparing appropriate input states and performing measurements on the output? The input-output mapping is explicitly given by the transfer function, which contains the maximum information about the system.We show that two minimal systems are indistinguishable (have the same transfer function) if and only if their Hamiltonians and the coupling to the input fields are related by a unitary transformation. Furthermore, we provide a canonical parametrization of the equivalence classes of indistinguishable systems. For models depending on (possibly lower dimensional) unknown parameters, we give a practical identifiability condition which is illustrated on several examples. In particular, we show that systems satisfying a certain Hamiltonian connectivity condition called "infecting", are completely identifiable.

Original language | English |
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Title of host publication | Proceedings of the IEEE Conference on Decision and Control |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 1930-1937 |

Number of pages | 8 |

ISBN (Print) | 9781467357173 |

DOIs | |

Publication status | Published - 2013 |

Event | 52nd IEEE Conference on Decision and Control, CDC 2013 - Florence, Italy Duration: 2013 Dec 10 → 2013 Dec 13 |

### Other

Other | 52nd IEEE Conference on Decision and Control, CDC 2013 |
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Country | Italy |

City | Florence |

Period | 13/12/10 → 13/12/13 |

### Fingerprint

### ASJC Scopus subject areas

- Control and Systems Engineering
- Modelling and Simulation
- Control and Optimization

### Cite this

*Proceedings of the IEEE Conference on Decision and Control*(pp. 1930-1937). [6760164] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2013.6760164

**Systems identification for passive linear quantum systems : The transfer function approach.** / Guta, Madalin; Yamamoto, Naoki.

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

*Proceedings of the IEEE Conference on Decision and Control.*, 6760164, Institute of Electrical and Electronics Engineers Inc., pp. 1930-1937, 52nd IEEE Conference on Decision and Control, CDC 2013, Florence, Italy, 13/12/10. https://doi.org/10.1109/CDC.2013.6760164

}

TY - GEN

T1 - Systems identification for passive linear quantum systems

T2 - The transfer function approach

AU - Guta, Madalin

AU - Yamamoto, Naoki

PY - 2013

Y1 - 2013

N2 - System identification is a key enabling component for the implementation of new quantum technologies, including quantum control. In this paper we consider a large class of input-output systems, namely linear passive quantum systems, and study the following identifiability question: if the system's Hamiltonian and coupling matrices are unknown, which of these dynamical parameters can be estimated by preparing appropriate input states and performing measurements on the output? The input-output mapping is explicitly given by the transfer function, which contains the maximum information about the system.We show that two minimal systems are indistinguishable (have the same transfer function) if and only if their Hamiltonians and the coupling to the input fields are related by a unitary transformation. Furthermore, we provide a canonical parametrization of the equivalence classes of indistinguishable systems. For models depending on (possibly lower dimensional) unknown parameters, we give a practical identifiability condition which is illustrated on several examples. In particular, we show that systems satisfying a certain Hamiltonian connectivity condition called "infecting", are completely identifiable.

AB - System identification is a key enabling component for the implementation of new quantum technologies, including quantum control. In this paper we consider a large class of input-output systems, namely linear passive quantum systems, and study the following identifiability question: if the system's Hamiltonian and coupling matrices are unknown, which of these dynamical parameters can be estimated by preparing appropriate input states and performing measurements on the output? The input-output mapping is explicitly given by the transfer function, which contains the maximum information about the system.We show that two minimal systems are indistinguishable (have the same transfer function) if and only if their Hamiltonians and the coupling to the input fields are related by a unitary transformation. Furthermore, we provide a canonical parametrization of the equivalence classes of indistinguishable systems. For models depending on (possibly lower dimensional) unknown parameters, we give a practical identifiability condition which is illustrated on several examples. In particular, we show that systems satisfying a certain Hamiltonian connectivity condition called "infecting", are completely identifiable.

UR - http://www.scopus.com/inward/record.url?scp=84902329776&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84902329776&partnerID=8YFLogxK

U2 - 10.1109/CDC.2013.6760164

DO - 10.1109/CDC.2013.6760164

M3 - Conference contribution

AN - SCOPUS:84902329776

SN - 9781467357173

SP - 1930

EP - 1937

BT - Proceedings of the IEEE Conference on Decision and Control

PB - Institute of Electrical and Electronics Engineers Inc.

ER -