Application Opportunities of Quantum Computing

A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Quantum Science and Technology".

Deadline for manuscript submissions: closed (30 November 2022) | Viewed by 5583

Special Issue Editors

Department of Applied Mathematics, Faculty of Electrical Engineering, Mathematics, and Computer Science, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands
Interests: classical and quantum algorithms for fluid dynamic applications; high-performance computing; quantum-accelerated numerical linear algebra; numerical methods for simulation and optimization
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Computer Engineering Department, Technical University of Valencia, Camino de Vera s/n, 46022 Valencia, Spain
Interests: quantum computing; quantum computer architecture; compilation and mapping of quantum algorithms; quantum error correction; fault tolerant quantum computing
Special Issues, Collections and Topics in MDPI journals
Department of Chemistry, Purdue University College of Science, West Lafayette, IN, USA
Interests: developing quantum computing algorithms for open quantum dynamics and electronic strucure calculations; quantum phase transiotion; quantum machine learning for data analytics and material design

Special Issue Information

Dear Colleagues,

Quantum computing is an emerging technology that has the potential to radically change the way we will be solving computational problems in the future. While the development of quantum computing technologies (aka, the quantum computing hardware) is in full flight, the exploration of application domains where quantum computing may have significant impact has just begun. This goes along with the development of novel quantum algorithms for today's and near-future Noisy Intermediate-Scale Quantum (NISQ) devices and their adoption in practical applications (aka, the quantum computing software). The aim of this special issue is to assemble a collection of application opportunities that might benefit from the use of quantum computing in the (near) future.

We invite contributions from all scientific disciplines and application domains including but not limited to quantum chemistry, quantum biology, cryptography, quantum communications, quantum sensing, material design, and any other type of quantum-assisted simulation and/or optimization. We, in particular, encourage the submission of contributions from `exotic’ application areas where the opportunities of using quantum computers to speed up computations or enable unprecedented applications have hardly been explored so far.

Contributions should either demonstrate the successful realization of (prototypes of) quantum-assisted applications in software and/or on real quantum hardware, or present credible approaches to solve practical applications with the aid of quantum computers in the future.

Prof. Dr. Matthias Möller
Dr. Carmen G. Almudever
Prof. Dr. Sabre Kais
Guest Editors

Manuscript Submission Information

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Keywords

  • quantum information
  • quantum computing
  • quantum applications
  • quantum-accelerated scientific computing
  • practical quantum algorithms
  • quantum chemistry
  • quantum annealing
  • quantum finance

Published Papers (3 papers)

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Research

17 pages, 1027 KiB  
Article
Dimension Reduction and Redundancy Removal through Successive Schmidt Decompositions
Appl. Sci. 2023, 13(5), 3172; https://doi.org/10.3390/app13053172 - 01 Mar 2023
Cited by 2 | Viewed by 1262
Abstract
Quantum computers are believed to have the ability to process huge data sizes, which can be seen in machine learning applications. In these applications, the data, in general, are classical. Therefore, to process them on a quantum computer, there is a need for [...] Read more.
Quantum computers are believed to have the ability to process huge data sizes, which can be seen in machine learning applications. In these applications, the data, in general, are classical. Therefore, to process them on a quantum computer, there is a need for efficient methods that can be used to map classical data on quantum states in a concise manner. On the other hand, to verify the results of quantum computers and study quantum algorithms, we need to be able to approximate quantum operations into forms that are easier to simulate on classical computers with some errors. Motivated by these needs, in this paper, we study the approximation of matrices and vectors by using their tensor products obtained through successive Schmidt decompositions. We show that data with distributions such as uniform, Poisson, exponential, or similar to these distributions can be approximated by using only a few terms, which can be easily mapped onto quantum circuits. The examples include random data with different distributions, the Gram matrices of iris flower, handwritten digits, 20newsgroup, and labeled faces in the wild. Similarly, some quantum operations, such as quantum Fourier transform and variational quantum circuits with a small depth, may also be approximated with a few terms that are easier to simulate on classical computers. Furthermore, we show how the method can be used to simplify quantum Hamiltonians: In particular, we show the application to randomly generated transverse field Ising model Hamiltonians. The reduced Hamiltonians can be mapped into quantum circuits easily and, therefore, can be simulated more efficiently. Full article
(This article belongs to the Special Issue Application Opportunities of Quantum Computing)
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18 pages, 478 KiB  
Article
Fock-Space Schrieffer–Wolff Transformation: Classically-Assisted Rank-Reduced Quantum Phase Estimation Algorithm
Appl. Sci. 2023, 13(1), 539; https://doi.org/10.3390/app13010539 - 30 Dec 2022
Cited by 1 | Viewed by 1265
Abstract
We present an extension of many-body downfolding methods to reduce the resources required in the quantum phase estimation (QPE) algorithm. In this paper, we focus on the Schrieffer–Wolff (SW) transformation of the electronic Hamiltonians for molecular systems that provides significant simplifications of quantum [...] Read more.
We present an extension of many-body downfolding methods to reduce the resources required in the quantum phase estimation (QPE) algorithm. In this paper, we focus on the Schrieffer–Wolff (SW) transformation of the electronic Hamiltonians for molecular systems that provides significant simplifications of quantum circuits for simulations of quantum dynamics. We demonstrate that by employing Fock-space variants of the SW transformation (or rank-reducing similarity transformations (RRST)) one can significantly increase the locality of the qubit-mapped similarity-transformed Hamiltonians. The practical utilization of the SW-RRST formalism is associated with a series of approximations discussed in the manuscript. In particular, amplitudes that define RRST can be evaluated using conventional computers and then encoded on quantum computers. The SW-RRST QPE quantum algorithms can also be viewed as an extension of the standard state-specific coupled-cluster downfolding methods to provide a robust alternative to the traditional QPE algorithms to identify the ground and excited states for systems with various numbers of electrons using the same Fock-space representations of the downfolded Hamiltonian. The RRST formalism serves as a design principle for developing new classes of approximate schemes that reduce the complexity of quantum circuits. Full article
(This article belongs to the Special Issue Application Opportunities of Quantum Computing)
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36 pages, 754 KiB  
Article
Quantum Circuit Implementation of Multi-Dimensional Non-Linear Lattice Models
Appl. Sci. 2023, 13(1), 529; https://doi.org/10.3390/app13010529 - 30 Dec 2022
Cited by 3 | Viewed by 1480
Abstract
The application of Quantum Computing (QC) to fluid dynamics simulation has developed into a dynamic research topic in recent years. With many flow problems of scientific and engineering interest requiring large computational resources, the potential of QC to speed-up simulations and facilitate more [...] Read more.
The application of Quantum Computing (QC) to fluid dynamics simulation has developed into a dynamic research topic in recent years. With many flow problems of scientific and engineering interest requiring large computational resources, the potential of QC to speed-up simulations and facilitate more detailed modeling forms the main motivation for this growing research interest. Despite notable progress, many important challenges to creating quantum algorithms for fluid modeling remain. The key challenge of non-linearity of the governing equations in fluid modeling is investigated here in the context of lattice-based modeling of fluids. Quantum circuits for the D1Q3 (one-dimensional, three discrete velocities) Lattice Boltzmann model are detailed along with design trade-offs involving circuit width and depth. Then, the design is extended to a one-dimensional lattice model for the non-linear Burgers equation. To facilitate the evaluation of non-linear terms, the presented quantum circuits employ quantum computational basis encoding. The second part of this work introduces a novel, modular quantum-circuit implementation for non-linear terms in multi-dimensional lattice models. In particular, the evaluation of kinetic energy in two-dimensional models is detailed as the first step toward quantum circuits for the collision term of two- and three-dimensional Lattice Boltzmann methods. The quantum circuit analysis shows that with O(100) fault-tolerant qubits, meaningful proof-of-concept experiments could be performed in the near future. Full article
(This article belongs to the Special Issue Application Opportunities of Quantum Computing)
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