Pith Number

pith:EDCPWQPU

pith:1995:EDCPWQPUO6FO7KJYJ7UCPZNRVQ

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Quantum measurements and the Abelian Stabilizer Problem

A.Yu.Kitaev (L.D.Landau Institute for Theoretical Physics, Moscow)

A quantum algorithm solves the Abelian stabilizer problem in polynomial time, covering factoring and discrete logarithm.

arxiv:quant-ph/9511026 v1 · 1995-11-20 · quant-ph

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Claims

C1strongest claim

We present a polynomial quantum algorithm for the Abelian stabilizer problem which includes both factoring and the discrete logarithm.

C2weakest assumption

The group action (or the function whose stabilizer is sought) can be implemented as an efficient quantum circuit realizing the corresponding unitary operator.

C3one line summary

Kitaev presents a polynomial quantum algorithm for the Abelian stabilizer problem based on measuring eigenvalues of unitary operators, generalizing Shor's factoring and discrete-log algorithms.

References

16 extracted · 16 resolved · 0 Pith anchors

[1] Quantum mechanical Hamiltonian models of Tu ring machines 1982

[2] Reversible logic and quantum computers 1985

[3] Quantum mechanical computers 1985

[4] Quantum theory, the Church-Turing princip le and the universal quantum computer 1985

[5] Quantum computational networks 1989

Formal links

2 machine-checked theorem links

Cited by

80 papers in Pith

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Receipt and verification

First computed	2026-07-04T14:47:03.525645Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

20c4fb41f4778aefa9384fe827e5b1ac0cb36dfbedc5824e4a914218acffb847

Aliases

arxiv: quant-ph/9511026 · arxiv_version: quant-ph/9511026v1 · doi: 10.48550/arxiv.quant-ph/9511026 · pith_short_12: EDCPWQPUO6FO · pith_short_16: EDCPWQPUO6FO7KJY · pith_short_8: EDCPWQPU

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/EDCPWQPUO6FO7KJYJ7UCPZNRVQ \
  | 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: 20c4fb41f4778aefa9384fe827e5b1ac0cb36dfbedc5824e4a914218acffb847

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b74975f8f3ce0120af5e418a3f1ae905fc923dddf1f39446eb4b68635dbe15a5",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "quant-ph",
    "submitted_at": "1995-11-20T20:39:33Z",
    "title_canon_sha256": "fa185c89991489a57118af967fca74940d69c844b1c8d31a6963faf277e4c763"
  },
  "schema_version": "1.0",
  "source": {
    "id": "quant-ph/9511026",
    "kind": "arxiv",
    "version": 1
  }
}