Quantum computation over continuous variables

Samuel L. Braunstein; Seth Lloyd

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Quantum computation over continuous variables

Seth Lloyd, Samuel L. Braunstein

Quantum Physics · Submitted 27 Oct 1998

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

The authors' main claim This paper provides necessary and sufficient conditions for constructing a universal quantum computer over continuous variables.

how it is stated · asserted 1.00 read the record →

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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, 3,539 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.63 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.06 · 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.

This paper provides necessary and sufficient conditions for constructing a universal quantum computer over continuous variables. As an example, it is shown how a universal quantum computer for the amplitudes of the electromagnetic field might be constructed using simple linear devices such as beam-splitters and phase shifters, together with squeezers and nonlinear devices such as Kerr-effect fibers and atoms in optical cavities. Such a device could in principle perform `quantum floating point' computations. Problems of noise, finite precision, and error correction are discussed.

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	This paper provides necessary and sufficient conditions for constructing a universal quantum computer over continuous variables.	contribution 0.93	0.89	0.80	asserted 1.00
s1	As an example, it is shown how a universal quantum computer for the amplitudes of the electromagnetic field might be constructed using simple linear devices such as beam-splitters and phase shifters, together with squeezers and nonlinear devices such as Kerr-effect fibers and atoms in optical cavities.	method 0.52	0.85	0.10	asserted 0.40
s2	Such a device could in principle perform `quantum floating point' computations.	interpretation 0.98	0.22	0.06	hedged possibility 1.00
s3	Problems of noise, finite precision, and error correction are discussed.	contribution 0.63	0.52	0.04	asserted 0.82

What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from proof or derivation 0.95.

What was examined, and what was not

sources read

arXiv listing abstract v1

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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

This paper provides necessary and sufficient conditions for constructing a universal quantum computer over continuous variables. As an example, it is shown how a universal quantum computer for the amplitudes of the electromagnetic field might be constructed using simple linear devices such as beam-splitters and phase shifters, together with squeezers and nonlinear devices such as Kerr-effect fibers and atoms in optical cavities. Such a device could in principle perform `quantum floating point' computations. Problems of noise, finite precision, and error correction are discussed.

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References

Forward citations

Cited by 3 Pith papers

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

Encoding Compact U(1) Gauge Fields in Bosonic Modes with GKP Stabilization
quant-ph 2026-08 accept novelty 7.0 of 10

A single-oscillator-per-mode encoding of compact U(1) gauge fields is enforced by a GKP stabilizer, enabling simulation on bosonic hardware without truncation errors.
Trigonometric Continuous-Variable Quantum Gates: Realization with Trapped Ions and Nonperturbative Wigner Negativity
quant-ph 2026-07 conditional novelty 6.0 of 10

Cosine gates exp(-iθ cos(c x̂)) in one- and two-mode versions were implemented on trapped-ion motional modes and benchmarked against noise-inclusive simulations via Fock-space transition probabilities.
A Quantum Path to Partial Differential Equations
quant-ph 2026-07 accept novelty 3.5 of 10

Lecture notes that organize quantum PDE algorithms around block encodings of finite-difference and finite-element operators, tracking discretization, preparation, normalization, postselection, and measurement costs.

How later papers used it

248 later papers cite it

Evidence: substantial. 248 of the citing papers share no author with it, and 15 of those carry a confident label from Pith's citation classifier.

Pith read 40 of the 379 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

1 later paper by other authors is listed below: 1 used its method or tool.

Uses its method or tool 1 of 6 papers with this label

Following Ref. [ref] , we select a set of CV gates made up of displacements in position $X(c)$, squeezing $S(r)$, rotations $R(θ)$, and Kerr gates $K_LB(κ)$, defined as [equation] with ${c, r, θ, κ}∈ℝ$.

Towards fault-tolerant quantum computation with universal continuous-variable gates (2025) · Introduction · 0.87

How the literature uses it

19 arXiv papers cite this in 30 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 · 18 sentences without a confident label

Cites it as background 9 papers

There is a fully quantum version of analogue computing, usually known as continuous variable quantum computing (CVQC) and first described by [ref] .

Quantum Analogue Computing · Continuous variable quantum computing · 0.95
Gaussian operations, generated by Hamiltonians at most quadratic in the quadratures, together with a suitable non-Gaussian resource, provide a universal gate set [ref] .

Trigonometric Continuous-Variable Quantum Gates: Realization with Trapped Ions and Nonperturbative Wigner Negativity · Introduction · 0.90
To date, several models studied in the literature seem to have these desirable properties, including Clifford circuits [ref] , nearest-neighbor matchgates [ref] , Gaussian operations [ref] , the one-clean qubit (DQC1) model [ref] , and commuting circuits [ref] (a more complete list is given at the end of this section).

The computational power of normalizer circuits over black-box groups · Introduction · 0.88

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