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On Universal and Fault-Tolerant Quantum Computing

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P. Oscar Boykin, Tal Mor, Matthew Pulver, Vwani Roychowdhury, Farrokh Vatan

Quantum Physics · Submitted 16 Jun 1999

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim A novel universal and fault-tolerant basis (set of gates) for quantum computation is described.

how it is stated · asserted 1.00 read the record →

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arXiv IDquant-ph/9906054 (version 1)
Pith IDQM6N4EBM, Pith's permanent record of this paper and its review
CitationFarrokh Vatan, Matthew Pulver, P. Oscar Boykin, Tal Mor, Vwani Roychowdhury. "On Universal and Fault-Tolerant Quantum Computing." arXiv:quant-ph/9906054 (1999). https://pith.science/paper/QM6N4EBM
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,309 input tokens.

What the abstract itself states, as probabilities: claims first 0.14 · states limitation 0.23 · human participants 0.01 · controlled comparison 0.07 · randomized assignment 0.01 · states quantitative result 0.56 · compares with prior results 0.95 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

A novel universal and fault-tolerant basis (set of gates) for quantum computation is described. Such a set is necessary to perform quantum computation in a realistic noisy environment. The new basis consists of two single-qubit gates (Hadamard and ${\sigma_z}^{1/4}$), and one double-qubit gate (Controlled-NOT). Since the set consisting of Controlled-NOT and Hadamard gates is not universal, the new basis achieves universality by including only one additional elementary (in the sense that it does not include angles that are irrational multiples of $\pi$) single-qubit gate, and hence, is potentially the simplest universal basis that one can construct. We also provide an alternative proof of universality for the only other known class of universal and fault-tolerant basis proposed by Shor and by Kitaev.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 A novel universal and fault-tolerant basis (set of gates) for quantum computation is described. contribution 1.00 0.92 0.76 asserted 1.00
s1 Such a set is necessary to perform quantum computation in a realistic noisy environment. background 0.98 0.09 0.07 asserted 1.00
s2 The new basis consists of two single-qubit gates (Hadamard and ${\sigma_z}^{1/4}$), and one double-qubit gate (Controlled-NOT). contribution 0.92 0.86 0.23 asserted 1.00
s3 Since the set consisting of Controlled-NOT and Hadamard gates is not universal, the new basis achieves universality by including only one additional elementary (in the sense that it does not include angles that are irrational multiples of $\pi$) single-qubit gate, and hence, is potentially the simplest universal basis that one can construct. interpretation 0.85 0.73 0.33 hedged possibility 0.74
s4 We also provide an alternative proof of universality for the only other known class of universal and fault-tolerant basis proposed by Shor and by Kitaev. contribution 0.98 0.89 0.10 asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.60 · evidence from proof or derivation 0.98.

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  • C citations
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

A novel universal and fault-tolerant basis (set of gates) for quantum computation is described. Such a set is necessary to perform quantum computation in a realistic noisy environment. The new basis consists of two single-qubit gates (Hadamard and ${\sigma_z}^{1/4}$), and one double-qubit gate (Controlled-NOT). Since the set consisting of Controlled-NOT and Hadamard gates is not universal, the new basis achieves universality by including only one additional elementary (in the sense that it does not include angles that are irrational multiples of $\pi$) single-qubit gate, and hence, is potentially the simplest universal basis that one can construct. We also provide an alternative proof of universality for the only other known class of universal and fault-tolerant basis proposed by Shor and by Kitaev.

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References
How the literature uses it

31 arXiv papers cite this in 47 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 37 sentences without a confident label

Uses its method or tool 2 papers
  • The original fault-tolerant construction due to Boykin et al. [ref] can be used verbatim as the logical gadget for the $T$ gate in the trap scheme.

    Quantum one-time programs · The $π/8$-phase gate · 0.98

  • The techniques used in this section are based on cyclotomic polynomials and they were used in the similar context in [ref] .

    Universality of beamsplitters · Introduction · 0.99

Cites it as background 8 papers
  • The second level is the Clifford Group [ref] , $𝒞^(2)$, which can be generated using the unitaries Hadamard, Phase, and either of Controlled-NOT (C$X$) or Controlled-$Z$ (C$Z$) defined respectively as [equation] The Clifford group in combination with any unitary from a higher level can be used to approximate any unitary operator arbitrarily well [ref] .

    Divisible Codes for Quantum Computation · The Clifford Hierarchy · 0.96

  • Various methods of decomposing an arbitrary quantum gate into a sequence of gates drawn from a universal, discrete set are known [ref] , and typically require first decomposing the operation into controlled single-qubit unitaries [ref] , and then decomposing the single-qubit unitaries into a circuit of gates from a universal basis [ref] .

    A Depth-Optimal Canonical Form for Single-qubit Quantum Circuits · Introduction · 0.94

  • A common minimal choice is ${H,CNOT,T}$ [ref] .

    Universal Weakly Fault-Tolerant Quantum Computation via Code Switching in the [[8,3,2]] Code · Introduction · 0.80

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