Pith. sign in

REVIEW 5 cited by

Universal fault-tolerant quantum computation with only transversal gates and error correction

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1304.3709 v2 pith:QG42ZMWH submitted 2013-04-12 quant-ph

Adam Paetznick , Ben W. Reichardt This is my paper · ORCID
classification quant-ph
keywords transversalgatesdistillationfault-tolerantuniversalbravyicomputationcontrolled-controlled-z
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
read the original abstract

Transversal implementations of encoded unitary gates are highly desirable for fault-tolerant quantum computation. Though transversal gates alone cannot be computationally universal, they can be combined with specially distilled resource states in order to achieve universality. We show that "triorthogonal" stabilizer codes, introduced for state distillation by Bravyi and Haah [Phys. Rev. A 86 052329 (2012)], admit transversal implementation of the controlled-controlled-Z gate. We then construct a universal set of fault-tolerant gates without state distillation by using only transversal controlled-controlled-Z, transversal Hadamard, and fault-tolerant error correction. We also adapt the distillation procedure of Bravyi and Haah to Toffoli gates, improving on existing Toffoli distillation schemes.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Finding diagonal logical gates in CSS codes and circuits

    quant-ph 2026-07 conditional novelty 7.0 of 10

    Diagonal logical gates of a CSS code or circuit are exactly the kernel of a pullback map on phase functions, and that kernel can be computed in cubic time.

  2. The Utility of Sparse Error Detection in Quantum Simulations

    quant-ph 2026-08 conditional novelty 6.0 of 10

    Sparse error detection in small Iceberg codes reduces systematic errors in simulated Schwinger-model observables under depolarizing noise, with diminishing returns after a few detection layers.

  3. Realizing Error Suppression in Partially Fault-Tolerant Quantum Simulations with IBM Quantum Computers

    quant-ph 2026-07 conditional novelty 6.0 of 10

    Partially fault-tolerant [[4,2,2]] Iceberg-code simulations on ibm_boston improve local Ising observables over unencoded baselines by a few percent in 1D and over 200% in 2D at late times via Observable-Ranked Postselection.

  4. No-Go Theorem on Fault Tolerant Gadgets for Multiple Logical Qubits

    quant-ph 2026-02 reject novelty 6.0 of 10

    No stabilizer code can implement the full logical Clifford group on multiple logical qubits using transversal gates, fold-transversal gates beyond two qubits, or code automorphisms.

  5. A small and interesting architecture for early fault-tolerant quantum computers

    quant-ph 2025-07 conditional novelty 5.0 of 10

    An early fault-tolerant quantum computer architecture that uses teleportation between the [[4,2,2]] and [[8,3,2]] color codes for a universal transversal gate set, plus a mirror-circuit benchmarking protocol.

Pith tools