Pith Number

pith:SMR4QIYY

pith:1998:SMR4QIYYQI2Q6UF3AM2QSFSACK

not attested not anchored not stored refs resolved

The Heisenberg Representation of Quantum Computers

Daniel Gottesman

The Heisenberg representation describes quantum computers by tracking the evolution of operators rather than states.

arxiv:quant-ph/9807006 v1 · 1998-07-01 · quant-ph

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\usepackage{pith}
\pithnumber{SMR4QIYYQI2Q6UF3AM2QSFSACK}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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

States used in error correction and certain communication protocols can be described by their stabilizer, a group of tensor products of Pauli matrices. Even this simple group structure is sufficient to allow a rich range of quantum effects, although it falls short of the full power of quantum computation.

C2weakest assumption

That the relevant quantum operations preserve the stabilizer structure and that the class of states and operations considered is representative of useful quantum computation tasks.

C3one line summary

Quantum states for error correction are described by their stabilizer, a commuting group of tensor products of Pauli matrices, enabling analysis of a rich class of quantum effects short of full quantum computation.

References

13 extracted · 13 resolved · 0 Pith anchors

[1] Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer 1997 · arXiv:quant-ph/9508027

[2] A Theory of Fault-Tolerant Quantum Computation 1998 · arXiv:quant-ph/9702029

[3] Expressing the operations of quantum computing in multiparticle geome tric algebra 1998

[4] Class of quantum error-correcting c odes saturating the quantum Hamming bound 1996

[5] Quantum Error Correction and Orthogonal Geometry 1997 · arXiv:quant-ph/9605005

Formal links

2 machine-checked theorem links

Cited by

107 papers in Pith

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Unitary Designs from Doped Matchgate Circuits

Hierarchy of mixed symmetry protected topological states in extended cluster states under subsystem decoherence

Receipt and verification

First computed	2026-07-04T15:48:09.337668Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9323c8231882350f50bb033509164012be5997b60df0972e6c3bfb757b7d3a51

Aliases

arxiv: quant-ph/9807006 · arxiv_version: quant-ph/9807006v1 · doi: 10.48550/arxiv.quant-ph/9807006 · pith_short_12: SMR4QIYYQI2Q · pith_short_16: SMR4QIYYQI2Q6UF3 · pith_short_8: SMR4QIYY

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/SMR4QIYYQI2Q6UF3AM2QSFSACK \
  | 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: 9323c8231882350f50bb033509164012be5997b60df0972e6c3bfb757b7d3a51

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6ac87f296acf1f5fad37770744df1e12815d024f359c32d9e8310ae716520e22",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "quant-ph",
    "submitted_at": "1998-07-01T19:34:39Z",
    "title_canon_sha256": "c316c5489c72d8f4571a297f41edb669bdec506912651e36755daa57870999cc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "quant-ph/9807006",
    "kind": "arxiv",
    "version": 1
  }
}