A walk through of time series analysis on quantum computers

Daskin, Ammar

doi:10.48550/arxiv.2205.00986

Cited by 3 publications

(3 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As a future direction, we will apply this circuit to the sequence alignment and pattern matching problems. Since circulant matrices are used in convolutions, it can be also applied to problems in different areas such as convolution neural network, time series analysis [16,17].…”

Section: Discussionmentioning

confidence: 99%

Quantum implementation of circulant matrices and its use in quantum string processing

Daskin¹

2022

Preprint

Self Cite

View full text Add to dashboard Cite

Strings problems in general can be solved faster by using special data structures such as suffixes in many cases structured as trees and arrays. In this paper, we show that suffixes used in those data structures can be obtained by using circulant matrices as a quantum operator which can be implemented in logarithmic time. Hence, if the strings are given as quantum states, using the presented circuit implementation one can do string processing efficiently on quantum computers.

show abstract

Section: Discussionmentioning

confidence: 99%

Quantum implementation of circulant matrices and its use in quantum string processing

Daskin¹

2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…In this learning model, one of the fundamental tasks is to find a way to map a data vector x into a quantum state ψ without losing any information. This can be performed in two different ways [17,18,23,24]: (i) as performed in neural networks, we use one qubit for each feature x i . Because of the similarities to classical neural networks, this mapping provides a natural way to perform quantum machine learning with variational quantum circuits.…”

Section: Introductionmentioning

confidence: 99%

Dimension Reduction and Redundancy Removal through Successive Schmidt Decompositions

2023

View full text Add to dashboard Cite

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.

show abstract

“…In this learning model, one of the fundamental tasks is to find a way to map a data vector x into a quantum state |ψ without losing any information. This can be done in two different ways [14,15,20,21]: i) as done in neural networks, we use one qubit for each feature x i . Because of the similarities to classical neural networks, this mapping provides a natural way to do quantum machine learning with variational quantum circuits.…”

Section: Introductionmentioning

confidence: 99%

Dimension reduction and redundancy removal through successive Schmidt decompositions

Daskin¹,

Gupta²,

Kais³

2023

Preprint

View full text Add to dashboard Cite

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 is classical. Therefore, to process them on a quantum computer, there is a need for efficient methods which 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. And similarly, some quantum operations such as quantum Fourier transform and variational quantum circuits with a small depth also may 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.

show abstract

A walk through of time series analysis on quantum computers

Cited by 3 publications

References 31 publications

Quantum implementation of circulant matrices and its use in quantum string processing

Quantum implementation of circulant matrices and its use in quantum string processing

Dimension Reduction and Redundancy Removal through Successive Schmidt Decompositions

Dimension reduction and redundancy removal through successive Schmidt decompositions

Contact Info

Product

Resources

About