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### Abstract

In this proof-of-concept paper we show that tensor product approach is efficient for control of large quantum systems, such as Heisenberg spin wires, which are essential for emerging quantum computing technologies. We compute optimal control sequences using GRAPE method, applying the recently developed tAMEn algorithm to calculate evolution of quantum states represented in the tensor train format to reduce storage. Using tensor product algorithms we can overcome the curse of dimensionality and compute the optimal control pulse for a 41 spin system on a single workstation with fully controlled accuracy and huge savings of computational time and memory. The use of tensor product algorithms opens new approaches for development of quantum computers with 50–100 qubits.

Original language | English |
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Title of host publication | Integral Methods in Science and Engineering |

Editors | Cristian Constanda, Paul J Harris |

Publisher | Birkhäuser |

Chapter | 29 |

Pages | 367-379 |

ISBN (Electronic) | 9783030160777 |

ISBN (Print) | 9783030160760 |

DOIs | |

Publication status | Published - 19 Jul 2019 |

### Keywords

- quantum control
- high-dimensional problems
- optimisation
- tensor product approximations
- algorithmic synthesis of quantum circuits

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## Activities

- 1 Oral presentation

## Tensor product approach to quantum control

Dmitry Savostyanov (Presenter)

26 Sep 2019 → 27 Sep 2019

Activity: External talk or presentation › Oral presentation

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## Cite this

Quinones Valles, D. A., Dolgov, S., & Savostyanov, D. (2019). Tensor Product Approach to Quantum Control. In C. Constanda, & P. J. Harris (Eds.),

*Integral Methods in Science and Engineering*(pp. 367-379). Birkhäuser. https://doi.org/10.1007/978-3-030-16077-7_29