Tensor Product Approach to Quantum Control

Diego A. Quinones Valles; Sergey Dolgov; Dmitry Savostyanov

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

Tensor Product Approach to Quantum Control

Diego A. Quinones Valles, Sergey Dolgov, Dmitry Savostyanov

Research output: Chapter in Book/Conference proceeding with ISSN or ISBN › Conference contribution with ISSN or ISBN › peer-review

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
Editors	Cristian Constanda, Paul J Harris
Publisher	Birkhäuser
Chapter	29
Pages	367-379
ISBN (Electronic)	9783030160777
ISBN (Print)	9783030160760
DOIs	https://doi.org/10.1007/978-3-030-16077-7_29
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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10.1007/978-3-030-16077-7_29

Tensor product approach to quantum controlAccepted author manuscript, 276 KB
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Tensor product approach to quantum control
Dmitry Savostyanov (Presenter)
26 Sept 2019 → 27 Sept 2019
Activity: External talk or presentation › Oral presentation

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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.",

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author = "{Quinones Valles}, {Diego A.} and Sergey Dolgov and Dmitry Savostyanov",

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AU - Quinones Valles, Diego A.

AU - Dolgov, Sergey

AU - Savostyanov, Dmitry

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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.

KW - quantum control

KW - high-dimensional problems

KW - optimisation

KW - tensor product approximations

KW - algorithmic synthesis of quantum circuits

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

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

M3 - Conference contribution with ISSN or ISBN

SN - 9783030160760

SP - 367

EP - 379

BT - Integral Methods in Science and Engineering

A2 - Constanda, Cristian

A2 - Harris, Paul J

PB - Birkhäuser

ER -

Tensor Product Approach to Quantum Control

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Tensor product approach to quantum control

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