Tensor Product Approach to Quantum Control

Diego Quiñones-Valles; Sergey Dolgov; Dmitry Savostyanov

doi:10.1007/978-3-030-16077-7_29

Tensor Product Approach to Quantum Control

Diego Quiñones-Valles, Sergey Dolgov, Dmitry Savostyanov

University of Brighton

Research output: Chapter or section in a book/report/conference proceeding › Chapter or section

6 Citations (SciVal)

60 Downloads (Pure)

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
Title of host publication	Integral Methods in Science and Engineering
Subtitle of host publication	Analytic Treatment and Numerical Approximations
Editors	Christian Constanda, Paul Harris
Publisher	Springer International Publishing
Pages	367-379
Number of pages	13
ISBN (Electronic)	978-3-030-16077-7
ISBN (Print)	978-3-030-16076-0
DOIs	https://doi.org/10.1007/978-3-030-16077-7_29
Publication status	E-pub ahead of print - 19 Jul 2019

Access to Document

10.1007/978-3-030-16077-7_29

grape-arxiv.PDF
This is a post-peer-review, pre-copyedit version of a chapter published in Integral Methods in Science and Engineering. The final authenticated version is available online at: https://doi.org/10.1007/978-3-030-16077-7_29
Accepted author manuscript, 349 KB

Sergey Dolgov Fellowship - Tensor Product Numerical Methods for High-Dimensional Problems in Probablility and Quantum Calculations
Scheichl, R. (PI)
Engineering and Physical Sciences Research Council
1/01/16 → 31/12/18
Project: Research council

Cite this

Quiñones-Valles, D., Dolgov, S., & Savostyanov, D. (2019). Tensor Product Approach to Quantum Control. In C. Constanda, & P. Harris (Eds.), Integral Methods in Science and Engineering: Analytic Treatment and Numerical Approximations (pp. 367-379). Article Chapter 29 Springer International Publishing. Advance online publication. https://doi.org/10.1007/978-3-030-16077-7_29

Tensor Product Approach to Quantum Control. / Quiñones-Valles, Diego; Dolgov, Sergey; Savostyanov, Dmitry.
Integral Methods in Science and Engineering: Analytic Treatment and Numerical Approximations. ed. / Christian Constanda; Paul Harris. Springer International Publishing, 2019. p. 367-379 Chapter 29.

Research output: Chapter or section in a book/report/conference proceeding › Chapter or section

@inbook{bc79732790de44649addd1ea0acf49ca,

title = "Tensor Product Approach to Quantum Control",

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.",

author = "Diego Qui{\~n}ones-Valles and Sergey Dolgov and Dmitry Savostyanov",

year = "2019",

month = jul,

day = "19",

doi = "10.1007/978-3-030-16077-7_29",

language = "English",

isbn = "978-3-030-16076-0",

pages = "367--379",

editor = "Christian Constanda and Paul Harris",

booktitle = "Integral Methods in Science and Engineering",

publisher = "Springer International Publishing",

address = "Switzerland",

}

TY - CHAP

T1 - Tensor Product Approach to Quantum Control

AU - Quiñones-Valles, Diego

AU - Dolgov, Sergey

AU - Savostyanov, Dmitry

PY - 2019/7/19

Y1 - 2019/7/19

N2 - 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.

AB - 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.

U2 - 10.1007/978-3-030-16077-7_29

DO - 10.1007/978-3-030-16077-7_29

M3 - Chapter or section

SN - 978-3-030-16076-0

SP - 367

EP - 379

BT - Integral Methods in Science and Engineering

A2 - Constanda, Christian

A2 - Harris, Paul

PB - Springer International Publishing

ER -

Tensor Product Approach to Quantum Control

Abstract

Access to Document

Fingerprint

Projects

Sergey Dolgov Fellowship - Tensor Product Numerical Methods for High-Dimensional Problems in Probablility and Quantum Calculations

Cite this