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Mathematics
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Quantum Algorithms and Quantum Computing
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Quantum Algorithms and Quantum Computing

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Computational and Applied Mathematics".

Deadline for manuscript submissions: closed (31 March 2024) | Viewed by 1633

Special Issue Editor

Dr. Kamil Khadiev

E-Mail Website
Guest Editor
Institute of Computational Mathematics and Information Technologies, Kazan Federal University, Kremlevskaya 18, 420008 Kazan, Russia
Interests: quantum computing; computer science; computational complexity; branching program

Special Issue Information

Dear Colleagues,

In the last few decades, quantum algorithms have been a hot topic. Different computational models were explored from the quantum point of view. The most standard model for quantum algorithms is the query model. At the same time, automata-like models (automata, branching programs, stream processing algorithms, online algorithms and others), communication protocols and others have also been explored by researchers.

The purpose of this Special Issue is to gather a collection of articles reflecting the latest developments in quantum algorithms and computational complexity for different quantum computational models. We invite researchers to submit their theoretical or experimental contributions on topics including but not limited to: quantum algorithms, quantum query model, quantum automata, quantum stream processing algorithms and quantum communication complexity.

Dr. Khadiev Kamil
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (2 papers)

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Research

18 pages, 332 KiB  
Article
Noisy Tree Data Structures and Quantum Applications
by Kamil Khadiev, Nikita Savelyev, Mansur Ziatdinov and Denis Melnikov
Mathematics 2023, 11(22), 4707; https://doi.org/10.3390/math11224707 - 20 Nov 2023
Cited by 1 | Viewed by 764
Abstract
We suggest a new technique for developing noisy tree data structures. We call it a “walking tree”. As applications of the technique we present a noisy Self-Balanced Binary Search Tree (we use a Red–Black tree as an implementation) and a noisy segment tree. [...] Read more.
We suggest a new technique for developing noisy tree data structures. We call it a “walking tree”. As applications of the technique we present a noisy Self-Balanced Binary Search Tree (we use a Red–Black tree as an implementation) and a noisy segment tree. The asymptotic complexity of the main operations for the tree data structures does not change compared to the case without noise. We apply the data structures in quantum algorithms for several problems on strings like the string-sorting problem and auto-complete problem. For both problems, we obtain quantum speed-up. Moreover, for the string-sorting problem, we show a quantum lower bound. Full article
(This article belongs to the Special Issue Quantum Algorithms and Quantum Computing)
9 pages, 474 KiB  
Article
Dimensionality Reduction with Variational Encoders Based on Subsystem Purification
by Raja Selvarajan, Manas Sajjan, Travis S. Humble and Sabre Kais
Mathematics 2023, 11(22), 4678; https://doi.org/10.3390/math11224678 - 17 Nov 2023
Viewed by 599
Abstract
Efficient methods for encoding and compression are likely to pave the way toward the problem of efficient trainability on higher-dimensional Hilbert spaces, overcoming issues of barren plateaus. Here, we propose an alternative approach to variational autoencoders to reduce the dimensionality of states represented [...] Read more.
Efficient methods for encoding and compression are likely to pave the way toward the problem of efficient trainability on higher-dimensional Hilbert spaces, overcoming issues of barren plateaus. Here, we propose an alternative approach to variational autoencoders to reduce the dimensionality of states represented in higher dimensional Hilbert spaces. To this end, we build a variational algorithm-based autoencoder circuit that takes as input a dataset and optimizes the parameters of a Parameterized Quantum Circuit (PQC) ansatz to produce an output state that can be represented as a tensor product of two subsystems by minimizing Tr(ρ2). The output of this circuit is passed through a series of controlled swap gates and measurements to output a state with half the number of qubits while retaining the features of the starting state in the same spirit as any dimension-reduction technique used in classical algorithms. The output obtained is used for supervised learning to guarantee the working of the encoding procedure thus developed. We make use of the Bars and Stripes (BAS) dataset for an 8 × 8 grid to create efficient encoding states and report a classification accuracy of 95% on the same. Thus, the demonstrated example provides proof for the working of the method in reducing states represented in large Hilbert spaces while maintaining the features required for any further machine learning algorithm that follows. Full article
(This article belongs to the Special Issue Quantum Algorithms and Quantum Computing)
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