Pith Number

pith:YZXB4G6T

pith:2000:YZXB4G6TNDPLNQQSCYGYXDCTAC

not attested not anchored not stored refs resolved

Quantum Amplitude Amplification and Estimation

(2) BRICS University of Aarhus, (3) CACR University of Waterloo), Alain Tapp (3) ((1) DIRO Universite de Montreal, Gilles Brassard (1), Michele Mosca (3), Peter Hoyer (2)

Amplitude amplification finds a good element after a number of steps proportional to one over the square root of its initial probability.

arxiv:quant-ph/0005055 v1 · 2000-05-15 · quant-ph

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\usepackage{pith}
\pithnumber{YZXB4G6TNDPLNQQSCYGYXDCTAC}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

Amplitude amplification finds a good x after expected applications of A and inverse proportional to 1/sqrt(a), generalizing Grover's algorithm.

C2weakest assumption

Algorithm A makes no measurements and is unitary.

C3one line summary

Amplitude amplification finds solutions quadratically faster than classical methods and enables quantum estimation of solution counts.

References

15 extracted · 15 resolved · 1 Pith anchors

[1] Quantum lower bounds by polynomials 1998

[2] Notes on the history of reversible computatio n 1988

[3] Tight bounds on quantum searching 1998

[4] An exact quantum polynomial- time algorithm for Simon’s problem 1997

[5] Quantum count- ing 1998

Formal links

2 machine-checked theorem links

Cited by

24 papers in Pith

Benincasa-Dowker-Glaser causal set actions by quantum counting

Automatic De-Quantization of Quantum Programs Using Constant Propagation

Query and Depth Upper Bounds for Quantum Unitaries via Grover Search

A shortcut to an optimal quantum linear system solver

QuantFPFlow: Quantum Amplitude Estimation for Fokker--Planck Policy Optimisation in Continuous Reinforcement Learning

Receipt and verification

First computed	2026-05-17T23:38:49.186344Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c66e1e1bd368deb6c212160d8b8c53008ec368e35bf5018a7bdb71322c94b685

Aliases

arxiv: quant-ph/0005055 · arxiv_version: quant-ph/0005055v1 · doi: 10.48550/arxiv.quant-ph/0005055 · pith_short_12: YZXB4G6TNDPL · pith_short_16: YZXB4G6TNDPLNQQS · pith_short_8: YZXB4G6T

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/YZXB4G6TNDPLNQQSCYGYXDCTAC \
  | 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: c66e1e1bd368deb6c212160d8b8c53008ec368e35bf5018a7bdb71322c94b685

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "07210f9413dd2b64df518d4ff6beb29a9f396ee56692751fb5d6132a9ad8c043",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "quant-ph",
    "submitted_at": "2000-05-15T18:19:59Z",
    "title_canon_sha256": "a7ad7296667be27d18c159bf309f34f05cfe9adedc40ff5029dbd5675b147e95"
  },
  "schema_version": "1.0",
  "source": {
    "id": "quant-ph/0005055",
    "kind": "arxiv",
    "version": 1
  }
}