Quantum Phase Estimation and the Aharonov-Bohm effect

K. Splittorff

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Quantum Phase Estimation and the Aharonov-Bohm effect

K. Splittorff

Quantum Physics · Submitted 15 Jul 2024

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

The authors' main claim We consider the time evolution of a particle on a ring with a long solenoid through and show that due to the Aharonov-Bohm effect this system naturally makes up a physical implementation of the quantum phase estimation algorithm for a $U(1)$ unitary operator.

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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, 3,632 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.08 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.09 · 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 consider the time evolution of a particle on a ring with a long solenoid through and show that due to the Aharonov-Bohm effect this system naturally makes up a physical implementation of the quantum phase estimation algorithm for a $U(1)$ unitary operator. The implementation of the full quantum phase estimation algorithm with a $U(N)$ unitary operator is realised through the non-abelian Aharonov-Bohm effect. The implementation allows for a more physically intuitive understanding of the algorithm. As an example we use the path integral formulation of the implemented quantum phase estimation algorithm to analyse the classical limit $\hbar\to0$.

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 consider the time evolution of a particle on a ring with a long solenoid through and show that due to the Aharonov-Bohm effect this system naturally makes up a physical implementation of the quantum phase estimation algorithm for a $U(1)$ unitary operator.	contribution 0.81	0.85	0.71	asserted 1.00
s1	The implementation of the full quantum phase estimation algorithm with a $U(N)$ unitary operator is realised through the non-abelian Aharonov-Bohm effect.	contribution 0.78	0.77	0.31	asserted 1.00
s2	The implementation allows for a more physically intuitive understanding of the algorithm.	interpretation 0.98	0.49	0.11	asserted 0.99
s3	As an example we use the path integral formulation of the implemented quantum phase estimation algorithm to analyse the classical limit $\hbar\to0$.	method 0.58	0.89	0.05	asserted 0.93

What kind of paper the classifier reports this is: theoretical result 0.80 · evidence from proof or derivation 0.99.

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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 consider the time evolution of a particle on a ring with a long solenoid through and show that due to the Aharonov-Bohm effect this system naturally makes up a physical implementation of the quantum phase estimation algorithm for a $U(1)$ unitary operator. The implementation of the full quantum phase estimation algorithm with a $U(N)$ unitary operator is realised through the non-abelian Aharonov-Bohm effect. The implementation allows for a more physically intuitive understanding of the algorithm. As an example we use the path integral formulation of the implemented quantum phase estimation algorithm to analyse the classical limit $\hbar\to0$.

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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 whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 1 paper

Here we show that the time evolution of a particle on a ring with a coil through performs the key quantum algorithm known as Quantum Phase Estimation.

Building intuition for Quantum Algorithms using the Aharonov-Bohm effect · 0.88

What it cites · 3 sentences without a confident label

Cites as background 3 papers

To set the notation we start by briefly recalling the quantum phase estimation (QPE) algorithm [ref] .

Quantum measurements and the Abelian Stabilizer Problem · Quantum Phase Estimation · 0.97
Our aim is to examine the classical limit where $ħ→0$ of the implemented QPE algorithm, and hence it is natural to consider the system in the path integral formalism[For discussions of quantum computing, computational paths and path integrals, see e.g. [ref] .] [ref] .

Quantum computing and polynomial equations over the finite field Z_2 · The classical limit of implemented QPE algorithm · 0.88
It enters as the central building block in quantum algorithms, such as for example Shors algorithm [ref] , which provide an exponential speed-up as compared to classical algorithms.

Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer · Introduction · 0.82

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