Pith Number

pith:Q45ZBIXT

pith:2026:Q45ZBIXTBFNR6D2AMQCM4H6HNY

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MLMC-qDRIFT: Multilevel Variance Reduction for Randomized Quantum Hamiltonian Simulation

Pegah Mohammadipour, Xiantao Li

A multilevel coupling of qDRIFT estimators reduces total gate complexity for observable estimation from O(ε^{-3}) to O(ε^{-2} log²(1/ε)).

arxiv:2604.26865 v2 · 2026-04-29 · quant-ph · cs.NA · math.NA

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Claims

C1strongest claim

We prove that the resulting MLMC-qDRIFT estimator reduces the total gate complexity for fixed-precision observable estimation from the standard qDRIFT scaling O(ε^{-3}) to O(ε^{-2} log²(1/ε)), while preserving qDRIFT's lack of explicit dependence on the number of Hamiltonian terms.

C2weakest assumption

The variance of the coupled level differences decays sufficiently fast with increasing circuit depth so that the multilevel estimator achieves the claimed complexity improvement.

C3one line summary

MLMC-qDRIFT achieves O(ε^{-2} log²(1/ε)) gate complexity for observable estimation in quantum dynamics by using coupled multilevel qDRIFT estimators with variance decay across levels.

Receipt and verification

First computed	2026-05-20T02:05:44.010619Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

873b90a2f3095b1f0f406404ce1fc76e375010d77f7fc3d2ea7d802b8a5feb75

Aliases

arxiv: 2604.26865 · arxiv_version: 2604.26865v2 · doi: 10.48550/arxiv.2604.26865 · pith_short_12: Q45ZBIXTBFNR · pith_short_16: Q45ZBIXTBFNR6D2A · pith_short_8: Q45ZBIXT

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/Q45ZBIXTBFNR6D2AMQCM4H6HNY \
  | 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: 873b90a2f3095b1f0f406404ce1fc76e375010d77f7fc3d2ea7d802b8a5feb75

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "264fde3c530f5b911977e8c9b45477547c9898bdb36c0ba09684e4931172e11c",
    "cross_cats_sorted": [
      "cs.NA",
      "math.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-04-29T16:32:48Z",
    "title_canon_sha256": "3c83476edb2ec6f1fd530f635605d74022f8095f7f9a743005cdd6c6b6d22377"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.26865",
    "kind": "arxiv",
    "version": 2
  }
}