Efficient preparation of the AKLT State with Measurement-based Imaginary Time Evolution

Quantum state preparation plays a crucial role in several areas of quantum information science, in applications such as quantum simulation, quantum metrology and quantum computing. However, typically state preparation requires resources that scale exponentially with the problem size, due to their pr...

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Main Authors: Tianqi Chen, Tim Byrnes
Format: Article
Language:English
Published: Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften 2024-12-01
Series:Quantum
Online Access:https://quantum-journal.org/papers/q-2024-12-10-1557/pdf/
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author Tianqi Chen
Tim Byrnes
author_facet Tianqi Chen
Tim Byrnes
author_sort Tianqi Chen
collection DOAJ
description Quantum state preparation plays a crucial role in several areas of quantum information science, in applications such as quantum simulation, quantum metrology and quantum computing. However, typically state preparation requires resources that scale exponentially with the problem size, due to their probabilistic nature or otherwise, making studying such models challenging. In this article, we propose a method to prepare the ground state of the Affleck-Lieb-Kennedy-Tasaki (AKLT) model deterministically using a measurement-based imaginary time evolution (MITE) approach. By taking advantage of the special properties of the AKLT state, we show that it can be prepared efficiently using the MITE approach. Estimates based on the convergence of a sequence of local projections, as well as direct evolution of the MITE algorithm suggest a constant scaling with respect to the number of AKLT sites, which is an exponential improvement over the naive estimate for convergence. We show that the procedure is compatible with qubit-based simulators, and show that using a variational quantum algorithm for circuit recompilation, the measurement operator required for MITE can be well approximated by a circuit with a much shallower circuit depth compared with the one obtained using the default Qiskit method.
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issn 2521-327X
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publisher Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
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spelling doaj-art-8b2e822ebc144650971db0e9b5acf8ae2024-12-10T16:32:33ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2024-12-018155710.22331/q-2024-12-10-155710.22331/q-2024-12-10-1557Efficient preparation of the AKLT State with Measurement-based Imaginary Time EvolutionTianqi ChenTim ByrnesQuantum state preparation plays a crucial role in several areas of quantum information science, in applications such as quantum simulation, quantum metrology and quantum computing. However, typically state preparation requires resources that scale exponentially with the problem size, due to their probabilistic nature or otherwise, making studying such models challenging. In this article, we propose a method to prepare the ground state of the Affleck-Lieb-Kennedy-Tasaki (AKLT) model deterministically using a measurement-based imaginary time evolution (MITE) approach. By taking advantage of the special properties of the AKLT state, we show that it can be prepared efficiently using the MITE approach. Estimates based on the convergence of a sequence of local projections, as well as direct evolution of the MITE algorithm suggest a constant scaling with respect to the number of AKLT sites, which is an exponential improvement over the naive estimate for convergence. We show that the procedure is compatible with qubit-based simulators, and show that using a variational quantum algorithm for circuit recompilation, the measurement operator required for MITE can be well approximated by a circuit with a much shallower circuit depth compared with the one obtained using the default Qiskit method.https://quantum-journal.org/papers/q-2024-12-10-1557/pdf/
spellingShingle Tianqi Chen
Tim Byrnes
Efficient preparation of the AKLT State with Measurement-based Imaginary Time Evolution
Quantum
title Efficient preparation of the AKLT State with Measurement-based Imaginary Time Evolution
title_full Efficient preparation of the AKLT State with Measurement-based Imaginary Time Evolution
title_fullStr Efficient preparation of the AKLT State with Measurement-based Imaginary Time Evolution
title_full_unstemmed Efficient preparation of the AKLT State with Measurement-based Imaginary Time Evolution
title_short Efficient preparation of the AKLT State with Measurement-based Imaginary Time Evolution
title_sort efficient preparation of the aklt state with measurement based imaginary time evolution
url https://quantum-journal.org/papers/q-2024-12-10-1557/pdf/
work_keys_str_mv AT tianqichen efficientpreparationoftheakltstatewithmeasurementbasedimaginarytimeevolution
AT timbyrnes efficientpreparationoftheakltstatewithmeasurementbasedimaginarytimeevolution