Pith Number

pith:FC6TQZBJ

pith:2026:FC6TQZBJLNGAMBPMSJVUZX67JT

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Complexity scaling and optimal policy degeneracy in quantum reinforcement learning via analytically solvable unitary-control-then-measure models

Alessandro Michelangeli, Andrea Cintio, Dmitrii Tsutskov

Quantum RL with unitary control and measurement reduces expected return complexity from exponential to power-law scaling while revealing distinct optimal policy degeneracy patterns.

arxiv:2604.13096 v2 · 2026-04-09 · math.GM

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Claims

C1strongest claim

we identify and quantify a two-level reduction in the computational complexity of the expected return, from the nominally exponential O(e^N) scaling in the trajectory length N to an explicit power-law O(N^I): a trajectory-based level, arising from equivalence classes of paths sharing the same unordered state counts and transition frequencies, and a policy-based level, arising from the sparsity of the transition graph enforced by constrained unitary actions.

C2weakest assumption

The specific choice of unitary controls and projective measurements onto a fixed reference basis in finite-dimensional spaces is assumed to permit closed-form derivations and to capture the essential complexity and degeneracy features relevant to broader quantum RL.

C3one line summary

Analytically solvable QRL models reduce expected-return computation from O(e^N) to O(N^I) via path equivalence and transition sparsity, while exhibiting unique optima governed by Zeno effect or discrete/plateau degeneracy at critical energies.

Cited by

1 paper in Pith

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Receipt and verification

First computed	2026-07-03T01:17:20.453111Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

28bd3864295b4c0605ec926b4cdfdf4cfe46fc36bd4128b9205d806cdbc3946f

Aliases

arxiv: 2604.13096 · arxiv_version: 2604.13096v2 · doi: 10.48550/arxiv.2604.13096 · pith_short_12: FC6TQZBJLNGA · pith_short_16: FC6TQZBJLNGAMBPM · pith_short_8: FC6TQZBJ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/FC6TQZBJLNGAMBPMSJVUZX67JT \
  | 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: 28bd3864295b4c0605ec926b4cdfdf4cfe46fc36bd4128b9205d806cdbc3946f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "233285fa19e4e8dbe4af27ece30669e61ae7cb46b64d67f78986f36670cd2b8b",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GM",
    "submitted_at": "2026-04-09T17:42:37Z",
    "title_canon_sha256": "f66f7849f8e7b4fc0ab922a2c176833e6180851daaef8ec745a9fd6cd0742ec3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.13096",
    "kind": "arxiv",
    "version": 2
  }
}