Entanglement of random hypergraph states

Random quantum states and operations are of fundamental and practical interests. In this work, we investigate the entanglement properties of random hypergraph states, which generalize the notion of graph states by applying generalized controlled-phase gates on an initial reference product state....

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Main Authors: Zhou, You, Hamma, Alioscia
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2023
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Online Access:https://hdl.handle.net/10356/164310
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-1643102023-02-28T20:09:38Z Entanglement of random hypergraph states Zhou, You Hamma, Alioscia School of Physical and Mathematical Sciences Nanyang Quantum Hub Science::Physics Controlled Phase Gate Entanglement Entropy Random quantum states and operations are of fundamental and practical interests. In this work, we investigate the entanglement properties of random hypergraph states, which generalize the notion of graph states by applying generalized controlled-phase gates on an initial reference product state. In particular, we study the two ensembles generated by random Controlled-Z(CZ) and Controlled-Controlled-Z(CCZ) gates, respectively. By applying tensor network representation and combinational counting, we analytically show that the average subsystem purity and entanglement entropy for the two ensembles feature the same volume law, but greatly differ in typicality, namely the purity fluctuation is small and universal for the CCZ ensemble while it is large for the CZ ensemble. We discuss the implications of these results for the onset of entanglement complexity and quantum chaos. Ministry of Education (MOE) National Research Foundation (NRF) Published version Y.Z. is supported by the startup funding of Fudan Univ., the Quantum Engineering Program No. QEP-SF3, National Research Foundation of Singapore under its NRF-ANR joint program (No. NRF2017-NRFANR004 VanQuTe), the Singapore Ministry of Education Tier 1 Grant No. RG162/19, FQXi-RFP-IPW-1903 from the foundational Questions Institute and Fetzer Franklin Fund, a donor-advised fund of the Silicon Valley Community Foundation. A.H. acknowledges support from NSF Award No. 2014000. 2023-01-16T02:20:39Z 2023-01-16T02:20:39Z 2022 Journal Article Zhou, Y. & Hamma, A. (2022). Entanglement of random hypergraph states. Physical Review A, 106(1), 012410-1-012410-17. https://dx.doi.org/10.1103/PhysRevA.106.012410 2469-9926 https://hdl.handle.net/10356/164310 10.1103/PhysRevA.106.012410 2-s2.0-85134213882 1 106 012410-1 012410-17 en NRF2017-NRFANR004 VanQuTe RG162/19 Physical Review A © 2022 American Physical Society. All rights reserved. This paper was published in Physical Review A and is made available with permission of American Physical Society. application/pdf
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic Science::Physics
Controlled Phase Gate
Entanglement Entropy
spellingShingle Science::Physics
Controlled Phase Gate
Entanglement Entropy
Zhou, You
Hamma, Alioscia
Entanglement of random hypergraph states
description Random quantum states and operations are of fundamental and practical interests. In this work, we investigate the entanglement properties of random hypergraph states, which generalize the notion of graph states by applying generalized controlled-phase gates on an initial reference product state. In particular, we study the two ensembles generated by random Controlled-Z(CZ) and Controlled-Controlled-Z(CCZ) gates, respectively. By applying tensor network representation and combinational counting, we analytically show that the average subsystem purity and entanglement entropy for the two ensembles feature the same volume law, but greatly differ in typicality, namely the purity fluctuation is small and universal for the CCZ ensemble while it is large for the CZ ensemble. We discuss the implications of these results for the onset of entanglement complexity and quantum chaos.
author2 School of Physical and Mathematical Sciences
author_facet School of Physical and Mathematical Sciences
Zhou, You
Hamma, Alioscia
format Article
author Zhou, You
Hamma, Alioscia
author_sort Zhou, You
title Entanglement of random hypergraph states
title_short Entanglement of random hypergraph states
title_full Entanglement of random hypergraph states
title_fullStr Entanglement of random hypergraph states
title_full_unstemmed Entanglement of random hypergraph states
title_sort entanglement of random hypergraph states
publishDate 2023
url https://hdl.handle.net/10356/164310
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