Pith Number

pith:6FWKIL4A

pith:2026:6FWKIL4AYJGZE3A5CHLF377HCC

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Low Rank Structure of the Reduced Transition Matrix

Bruno Bertini, Cathy Li, Katja Klobas, Tianci Zhou

The reduced transition matrix for local observables in chaotic dual-unitary circuits admits a low-rank approximation because its entropy grows at most logarithmically in time.

arxiv:2605.12665 v1 · 2026-05-12 · quant-ph

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Claims

C1strongest claim

We then prove that, for chaotic dual-unitary circuits, the associated entropy grows at most logarithmically in time. Our conclusions follow from exact results for random dual-unitary circuits and are further supported by numerical results for fixed instances of both dual-unitary and random circuits.

C2weakest assumption

The truncation error is controlled by the singular-value spectrum of the reduced transition matrix, and the systems considered are chaotic dual-unitary circuits where the entropy bound holds.

C3one line summary

The reduced transition matrix in chaotic dual-unitary quantum circuits has low-rank structure with entropy growing at most logarithmically in time, enabling efficient approximation for local expectation values.

References

56 extracted · 56 resolved · 2 Pith anchors

[1] Vidal, Efficient classical simulation of slightly entan- gled quantum computations, Phys 2003

[2] U.Schollwöck,Thedensity-matrixrenormalizationgroup in the age of matrix product states, Ann. Phys.326, 96 (2011) 2011

[3] J. I. Cirac, D. Pérez-García, N. Schuch, and F. Ver- straete, Matrix product states and projected entangled pair states: Concepts, symmetries, theorems, Rev. Mod. Phys.93, 045003 (2021) 2021

[4] Vidal, Efficient simulation of one-dimensional quan- tum many-body systems, Phys 2004

[5] A. J. Daley, C. Kollath, U. Schollwöck, and G. Vidal, Time-dependent density-matrix renormalization-group using adaptive effective hilbert spaces, Journal of Statis- tical Mechanics: Theory and Experi 2004

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-18T03:09:50.357426Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f16ca42f80c24d926c1d11d65dffe7108913f652b00694c6e0f5cdb9897567e3

Aliases

arxiv: 2605.12665 · arxiv_version: 2605.12665v1 · doi: 10.48550/arxiv.2605.12665 · pith_short_12: 6FWKIL4AYJGZ · pith_short_16: 6FWKIL4AYJGZE3A5 · pith_short_8: 6FWKIL4A

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/6FWKIL4AYJGZE3A5CHLF377HCC \
  | 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: f16ca42f80c24d926c1d11d65dffe7108913f652b00694c6e0f5cdb9897567e3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9199b5c064ccc355c71a4f2cc3c980c9d7c8564e2a0eb31aaa7bf58e65f692b5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-05-12T19:13:34Z",
    "title_canon_sha256": "b4589df58da41198a2a97017162d6b5a299ecbbe3c7ffecd64c0b4e8c432d0ba"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12665",
    "kind": "arxiv",
    "version": 1
  }
}