Pith Number

pith:7BFAP66T

pith:2026:7BFAP66TTFVVFCBRRCXWPJWAQY

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Optimal Bounds, Barriers, and Extensions for Non-Hermitian Bivariate Quantum Signal Processing

Joshua M. Courtney

Bivariate quantum signal processing establishes a tight query complexity of Θ(β_I T + log(1/ε)/log log(1/ε)) for anti-Hermitian Hamiltonian simulation.

arxiv:2605.12656 v1 · 2026-05-12 · quant-ph · cs.CC · cs.DS

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Record completeness

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4 Citations open

5 Replications open

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Claims

C1strongest claim

We find the anti-Hermitian query complexity d_I = Θ(β_I T + log(1/ε)/log log(1/ε)) to be tight, established via Chebyshev coefficient bounds, modified Bessel function asymptotics, and Lambert W inversion.

C2weakest assumption

The bivariate polynomial model and walk-operator oracle model assumptions continue to apply without modification to the non-Hermitian setting and that the constant-ratio condition extends to non-identical signal operators.

C3one line summary

Tight anti-Hermitian query complexity d_I = Θ(β_I T + log(1/ε)/log log(1/ε)) is established for non-Hermitian M-QSP, with impossibility of √(β_I T) fast-forwarding, new angle-finding algorithms, and extensions to time-dependent cases.

References

48 extracted · 48 resolved · 1 Pith anchors

[1] Standard recursive:O(d·d R ·d I) =O(d 3)

[2] CRC-exploiting block peeling:O(dR ·d I) =O(d 2)

[3] ap- proximately2

[4] The warm-start basin guarantee (Theorem 10) requires a full-rank Jacobian, and the analytical basin radius de- cays polynomially with degree asρ analytical ∼d −4.62 (Eq

[5] Direct-access polynomial construction.A poly- nomial designed ab initio for the direct-access model that achievesλ=e ωT (1 +o(1))on the full bitorus (Problem 42) would establish exponential advantage

Receipt and verification

First computed	2026-05-18T03:09:50.626661Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f84a07fbd3996b52883188af67a6c086223797ccfb57f29eada0e22a18649314

Aliases

arxiv: 2605.12656 · arxiv_version: 2605.12656v1 · doi: 10.48550/arxiv.2605.12656 · pith_short_12: 7BFAP66TTFVV · pith_short_16: 7BFAP66TTFVVFCBR · pith_short_8: 7BFAP66T

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/7BFAP66TTFVVFCBRRCXWPJWAQY \
  | 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: f84a07fbd3996b52883188af67a6c086223797ccfb57f29eada0e22a18649314

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6045dd74df55ec8d7f7da502dbfafbe5f2951342b19c66011fcc4647972e7b65",
    "cross_cats_sorted": [
      "cs.CC",
      "cs.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-05-12T19:03:36Z",
    "title_canon_sha256": "81d6a2fa1aa4c5b555d464e453d33aa1930b71a0e42d515f97eef982e81ecab4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12656",
    "kind": "arxiv",
    "version": 1
  }
}