Pith Number

pith:HGRYLHRH

pith:2025:HGRYLHRHICTNPJWPK2DUI6WOJL

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Krylov Complexity

Adri\'an S\'anchez-Garrido, Eliezer Rabinovici, Julian Sonner, Ruth Shir

Krylov complexity measures operator growth in quantum systems without depending on arbitrary parameters.

arxiv:2507.06286 v1 · 2025-07-08 · hep-th · cond-mat.str-el · quant-ph

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Claims

C1strongest claim

Krylov complexity is a canonical measure of operator growth and spreading whose definition does not depend on arbitrary control parameters and whose phenomenology serves as a rich and sensitive probe of chaotic dynamics up to exponentially late times.

C2weakest assumption

That the Lanczos algorithm yields a unique, physically meaningful complexity measure whose growth reliably distinguishes chaotic from integrable dynamics across all regimes, including holographic duals, without hidden parameter dependence.

C3one line summary

Krylov complexity is a canonical, parameter-independent measure of operator spreading that probes chaotic dynamics to late times and admits a geometric interpretation in holographic duals.

References

297 extracted · 297 resolved · 44 Pith anchors

[1] author author Aaronson , Scott ( year 2013 ),\ @noop title Quantum computing since Democritus \ ( publisher Cambridge University Press ) NoStop 2013

[2] author author Adhikari , Kiran , author Adwait \ Rijal , author Ashok Kumar \ Aryal , author Mausam \ Ghimire , author Rajeev \ Singh , and\ author Christian \ Deppe ( year 2024 ),\ title title Krylov 2024 · doi:10.1002/prop.202400014

[3] author author Afrasiar , Mir , author Jaydeep \ Kumar Basak , author Bidyut \ Dey , author Kunal \ Pal , and\ author Kuntal \ Pal ( year 2023 ),\ title title Time evolution of spread complexity in que 2023 · doi:10.1088/1742-5468/ad0032

[4] author author Aguilar-Gutierrez , Sergio E ( year 2024 ),\ title title Towards complexity in de Sitter space from the doubled-scaled Sachdev-Ye-Kitaev model , \ https://doi.org/10.1007/JHEP10(2024)107 2024 · doi:10.1007/jhep10(2024)107

[5] Aguilar-Gutierrez,Building the Holographic Dictionary of the DSSYK from Chords, Complexity & Wormholes with Matter,2505.22716 2025

Formal links

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Cited by

32 papers in Pith

Krylov Complexity and Mixed-State Phase Transition

Recursion method for out-of-equilibrium many-body dynamics: strengths and limitations

Complexity of Quantum Trajectories

Resource generation and dynamical complexities in open random quantum circuits

Scrambling of Entanglement from Integrability to Chaos: Bootstrapped Time-Integrated Spread Complexity

Receipt and verification

First computed	2026-05-17T23:38:47.529943Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

39a3859e2740a6d7a6cf5687447ace4aca8d2110eec357dc7093c4dd774a00aa

Aliases

arxiv: 2507.06286 · arxiv_version: 2507.06286v1 · doi: 10.48550/arxiv.2507.06286 · pith_short_12: HGRYLHRHICTN · pith_short_16: HGRYLHRHICTNPJWP · pith_short_8: HGRYLHRH

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/HGRYLHRHICTNPJWPK2DUI6WOJL \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 39a3859e2740a6d7a6cf5687447ace4aca8d2110eec357dc7093c4dd774a00aa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ef3d98ce978da63fc123aafcf75d403510906c5c4694f00f7a06b557b528c011",
    "cross_cats_sorted": [
      "cond-mat.str-el",
      "quant-ph"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2025-07-08T18:00:00Z",
    "title_canon_sha256": "340e7f7dd7ab3456fc0db34ac5517c1be6b2b081cf1033d5c081a873ec4d01a4"
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  "source": {
    "id": "2507.06286",
    "kind": "arxiv",
    "version": 1
  }
}