Pauli spectrum and nonstabilizerness of typical quantum many-body states

Xhek Turkeshi; Anatoly Dymarsky; Piotr Sierant

doi:10.1103/PhysRevB.111.054301

Pauli spectrum and nonstabilizerness of typical quantum many-body states

Xhek Turkeshi
, Anatoly Dymarsky
, Piotr Sierant

Research output: Contribution to journal › Article › peer-review

41 Scopus citations

Abstract

An important question of quantum information is to characterize genuinely quantum (beyond-Clifford) resources necessary for universal quantum computing. Here, we use the Pauli spectrum to quantify how "magic,"beyond Clifford, typical many-qubit states are. We first present a phenomenological picture of the Pauli spectrum based on quantum typicality, and then we confirm it for Haar random states. We then introduce filtered stabilizer entropy, a magic measure that can resolve the difference between typical and atypical states. We proceed with the numerical study of the Pauli spectrum of states created by random circuits as well as for eigenstates of chaotic Hamiltonians. We find that in both cases, the Pauli spectrum approaches the one of Haar random states, up to exponentially suppressed tails. We discuss how the Pauli spectrum changes when ergodicity is broken due to disorder. Our results underscore the difference between typical and atypical states from the point of view of quantum information.

Original language	English
Article number	054301
Journal	Physical Review B
Volume	111
Issue number	5
DOIs	https://doi.org/10.1103/PhysRevB.111.054301
State	Published - Feb 1 2025

Bibliographical note

Publisher Copyright:
© 2025 American Physical Society.

Funding

We thank M. Dalmonte, R. Fazio, G. Fux, M. Lewenstein, L. Piroli, S. Pappalardi, P. S. Tarabunga, E. Tirrito, and L. Vidmar for insightful discussions. X.T. acknowledges DFG under Germany's Excellence Strategy– Cluster of Excellence Matter and Light for Quantum Computing (ML4Q) EXC 2004/1–390534769, and DFG Collaborative Research Center (CRC) 183 Project No. 277101999-project B01. A.D. is supported by the National Science Foundation under Grant No. PHY 2310426. P.S. acknowledges support from ERC AdG NOQIA; MICIN/AEI [PGC2018-0910.13039/501100011033, CEX2019-000910-S/10.13039/501100011033, Plan National FIDEUA PID2019-106901GB-I00, FPI; MICIIN with funding from European Union NextGenerationEU (PRTR-C17.I1): QUANTERA MAQS PCI2019-111828-2]; MCIN/AEI/10.13039/501100011033 and by the “European Union NextGeneration EU/PRTR” QUANTERA DYNAMITE PCI2022-132919 within the QuantERA II Programme that has received funding from the European Union's Horizon 2020 research and innovation programme under Grant Agreement No. 101017733Proyectos de “Retos Colaboración” QUSPIN RTC2019-007196-7; Fundació Cellex; Fundació Mir-Puig; Generalitat de Catalunya (European Social Fund FEDER and CERCA program, AGAUR Grant No. 2021 SGR 01452, QuantumCAT U16-011424, cofunded by ERDF Operational Program of Catalonia 2014-2020); Barcelona Supercomputing Center MareNostrum (FI-2023-1-0013); EU (PASQuanS2.1, 101113690); EU Horizon 2020 FET-OPEN OPTOlogic (Grant No 899794); EU Horizon Europe Program (Grant Agreement 101080086—NeQST), National Science Centre, Poland (Symfonia Grant No. 2016/20/W/ST4/00314); ICFO Internal “QuantumGaudi” project; European Union's Horizon 2020 research and innovation program under the Marie-Skłodowska-Curie Grant Agreement No. 101029393 (STREDCH) and No. 847648 (“La Caixa” Junior Leaders fellowships ID100010434: LCF/BQ/PI19/11690013, LCF/BQ/PI20/11760031, LCF/BQ/PR20/11770012, LCF/BQ/PR21/11840013). Views and opinions expressed are, however, those of the author(s) only and do not necessarily reflect those of the European Union, European Commission, European Climate, Infrastructure and Environment Executive Agency (CINEA), nor any other granting authority. Neither the European Union nor any granting authority can be held responsible for them.

Funders	Funder number
Institut de Ciències Fotòniques
European Social Fund FEDER
ICREA Foundation-Generalitat de Catalunya
European Union NextGeneration EU
Fundació Mir-Puig
Fundación Cellex
European Regional Development Fund
Narodowe Centrum Nauki	2016/20/W/ST4/00314
PRTR	PCI2022-132919
Deutsche Forschungsgemeinschaft	ML4Q) EXC 2004/1–390534769, 277101999-project B01
National Science Foundation Arctic Social Science Program	PHY 2310426
Horizon 2020	LCF/BQ/PI20/11760031, LCF/BQ/PR20/11770012, 101017733Proyectos, 899794, 847648, LCF/BQ/PR21/11840013, 101029393, LCF/BQ/PI19/11690013
European Union NextGenerationEU	PCI2019-111828-2, PRTR-C17, MCIN/AEI/10.13039/501100011033
Agència de Gestió d'Ajuts Universitaris i de Recerca	2021 SGR 01452, U16-011424
H2020 European Research Council	CEX2019-000910-S/10.13039/501100011033, PGC2018-0910.13039/501100011033, FIDEUA PID2019-106901GB-I00
European Commission	PASQuanS2.1, 101113690
Barcelona Supercomputing Center MareNostrum	FI-2023-1-0013
EU Horizon Europe Program	101080086—NeQST

ASJC Scopus subject areas

Electronic, Optical and Magnetic Materials
Condensed Matter Physics

Access to Document

10.1103/PhysRevB.111.054301

Cite this

@article{5cc7789888954cb09762a2df6030ebf6,

title = "Pauli spectrum and nonstabilizerness of typical quantum many-body states",

abstract = "An important question of quantum information is to characterize genuinely quantum (beyond-Clifford) resources necessary for universal quantum computing. Here, we use the Pauli spectrum to quantify how {"}magic,{"}beyond Clifford, typical many-qubit states are. We first present a phenomenological picture of the Pauli spectrum based on quantum typicality, and then we confirm it for Haar random states. We then introduce filtered stabilizer entropy, a magic measure that can resolve the difference between typical and atypical states. We proceed with the numerical study of the Pauli spectrum of states created by random circuits as well as for eigenstates of chaotic Hamiltonians. We find that in both cases, the Pauli spectrum approaches the one of Haar random states, up to exponentially suppressed tails. We discuss how the Pauli spectrum changes when ergodicity is broken due to disorder. Our results underscore the difference between typical and atypical states from the point of view of quantum information.",

author = "Xhek Turkeshi and Anatoly Dymarsky and Piotr Sierant",

note = "Publisher Copyright: {\textcopyright} 2025 American Physical Society. ",

year = "2025",

month = feb,

day = "1",

doi = "10.1103/PhysRevB.111.054301",

language = "English",

volume = "111",

number = "5",

}

TY - JOUR

T1 - Pauli spectrum and nonstabilizerness of typical quantum many-body states

AU - Turkeshi, Xhek

AU - Dymarsky, Anatoly

AU - Sierant, Piotr

PY - 2025/2/1

Y1 - 2025/2/1

N2 - An important question of quantum information is to characterize genuinely quantum (beyond-Clifford) resources necessary for universal quantum computing. Here, we use the Pauli spectrum to quantify how "magic,"beyond Clifford, typical many-qubit states are. We first present a phenomenological picture of the Pauli spectrum based on quantum typicality, and then we confirm it for Haar random states. We then introduce filtered stabilizer entropy, a magic measure that can resolve the difference between typical and atypical states. We proceed with the numerical study of the Pauli spectrum of states created by random circuits as well as for eigenstates of chaotic Hamiltonians. We find that in both cases, the Pauli spectrum approaches the one of Haar random states, up to exponentially suppressed tails. We discuss how the Pauli spectrum changes when ergodicity is broken due to disorder. Our results underscore the difference between typical and atypical states from the point of view of quantum information.

AB - An important question of quantum information is to characterize genuinely quantum (beyond-Clifford) resources necessary for universal quantum computing. Here, we use the Pauli spectrum to quantify how "magic,"beyond Clifford, typical many-qubit states are. We first present a phenomenological picture of the Pauli spectrum based on quantum typicality, and then we confirm it for Haar random states. We then introduce filtered stabilizer entropy, a magic measure that can resolve the difference between typical and atypical states. We proceed with the numerical study of the Pauli spectrum of states created by random circuits as well as for eigenstates of chaotic Hamiltonians. We find that in both cases, the Pauli spectrum approaches the one of Haar random states, up to exponentially suppressed tails. We discuss how the Pauli spectrum changes when ergodicity is broken due to disorder. Our results underscore the difference between typical and atypical states from the point of view of quantum information.

UR - https://www.scopus.com/pages/publications/85217471338

UR - https://www.scopus.com/pages/publications/85217471338#tab=citedBy

U2 - 10.1103/PhysRevB.111.054301

DO - 10.1103/PhysRevB.111.054301

M3 - Article

AN - SCOPUS:85217471338

SN - 2469-9950

VL - 111

JO - Physical Review B

JF - Physical Review B

IS - 5

M1 - 054301

ER -

Pauli spectrum and nonstabilizerness of typical quantum many-body states

Abstract

Bibliographical note

Funding

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this