Linear-Depth Quantum Circuits for n-qubit Toffoli gates with no Ancilla

Massoud Pedram; Mehdi Saeedi

RECORD

Linear-Depth Quantum Circuits for n-qubit Toffoli gates with no Ancilla

Mehdi Saeedi, Massoud Pedram

Quantum Physics · Submitted 14 Mar 2013

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

The authors' main claim We design a circuit structure with linear depth to implement an $n$-qubit Toffoli gate.

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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-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,691 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.28 · human participants 0.02 · controlled comparison 0.26 · randomized assignment 0.01 · states quantitative result 0.77 · compares with prior results 0.97 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We design a circuit structure with linear depth to implement an $n$-qubit Toffoli gate. The proposed construction uses a quadratic-size circuit consists of elementary 2-qubit controlled-rotation gates around the x axis and uses no ancilla qubit. Circuit depth remains linear in quantum technologies with finite-distance interactions between qubits. The suggested construction is related to the long-standing construction by Barenco et al. (Phys. Rev. A, 52: 3457-3467, 1995, arXiv:quant-ph/9503016), which uses a quadratic-size, quadratic-depth quantum circuit for an $n$-qubit Toffoli gate.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We design a circuit structure with linear depth to implement an $n$-qubit Toffoli gate.	contribution 1.00	0.95	0.74	asserted 1.00
s1	The proposed construction uses a quadratic-size circuit consists of elementary 2-qubit controlled-rotation gates around the x axis and uses no ancilla qubit.	method 0.69	0.91	0.48	asserted 1.00
s2	Circuit depth remains linear in quantum technologies with finite-distance interactions between qubits.	interpretation 0.45	0.23	0.18	asserted 0.98
s3	The suggested construction is related to the long-standing construction by Barenco et al. (Phys. Rev. A, 52: 3457-3467, 1995, arXiv:quant-ph/9503016), which uses a quadratic-size, quadratic-depth quantum circuit for an $n$-qubit Toffoli gate.	background 1.00	0.08	0.07	asserted 0.96

What kind of paper the classifier reports this is: method or tool 0.95 · evidence from proof or derivation 0.80.

What was examined, and what was not

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arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

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P abstract

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S sections
T body sentences
C citations
R cross-paper relations

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

We design a circuit structure with linear depth to implement an $n$-qubit Toffoli gate. The proposed construction uses a quadratic-size circuit consists of elementary 2-qubit controlled-rotation gates around the x axis and uses no ancilla qubit. Circuit depth remains linear in quantum technologies with finite-distance interactions between qubits. The suggested construction is related to the long-standing construction by Barenco et al. (Phys. Rev. A, 52: 3457-3467, 1995, arXiv:quant-ph/9503016), which uses a quadratic-size, quadratic-depth quantum circuit for an $n$-qubit Toffoli gate.

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2 arXiv papers cite this in 2 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

What it cites · 12 sentences without a confident label

Uses the method or tool of 2 papers

For this case, we apply a linear-depth circuit with depth $n+5$, and size $4n-6$ [ref] to restore the ordering $1,2,⋯, n-1, n$.

Computation at a distance · Depth Analysis · 0.89
Reusing optimizations in [ref] in the proposed circuit structure is straightforward.

Quantum Circuit Simplification and Level Compaction · Comparison with prior art · 0.83

Compares with 2 papers

The method in [ref] benefits from a recursive construction with quadratic-depth $2n^2+O(n)$.

Reversible Logic Synthesis by Quantum Rotation Gates · Comparison with prior art · 0.95
The optimizations in [ref] improve the linear-cost implementation of a multiple-control Toffoli gates with one ancilla from $48n+O(1)$ to $24n+O(1)$.

Quantum Circuit Simplification and Level Compaction · Comparison with prior art · 0.89

Cites as background 1 paper

In the recent years, several protocols have been proposed to realize the 3-qubit Toffoli gate and its variants in different physical quantum technologies, e.g., with superconducting qubits [ref] , trapped ions [ref] , optical elements [ref] , and cavity quantum electrodynamics [ref] .

Implementation of a Toffoli Gate with Superconducting Circuits · Introduction · 0.94

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