Skip to main content

Advanced Search

Projected result for your current search: 0

Search Operators:

You can use operators in your search query to narrow down your results even more. Click on the search operator to see an explanation of how it works.
Finds documents with exactly this word group, in exactly this word order and spelling (e.g. "employer branding").
Finds documents with both search terms (e.g. sales AND bonus).
Finds documents with one or the other search term (e.g. porsche OR volkswagen).
Finds documents with all search terms. Blank space is understood as AND (e.g. man robot production).
Finds documents with no appearance of the word behind NOT (e.g. ford NOT "harrison ford").
Finds documents where the search term is mentioned at least "n" times."n" may be any number (e.g. COUNT(gear)>8).
Finds documents with both search terms in any word order, permitting "n" words as a maximum distance between them. Best choose between 15 and 30 (e.g. NEAR(recruit, professionals, 20)).
Finds documents with the search term in word versions or composites. The asterisk * marks whether you wish them BEFORE, BEHIND, or BEFORE and BEHIND the search term (e.g. lightweight*, *lightweight, *lightweight*).
Finds documents with the search term in different spellings. "?" allows only one character (e.g. organi?ation).
Special characters are understood as AND (e.g. Miller Bros. & Sons).

Semantic Search

powered by (Link opens in a new window)
loading …
Log in
Top

2. Polynomial Approximations

  • 2026
  • OriginalPaper
  • Chapter
Published in:
Authors
Osama M. Raisuddin
Suvranu De
Published in
Quantum Computing for Engineers
Publisher
Springer Nature Switzerland

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

This chapter delves into the essential role of polynomial approximations in the development and analysis of quantum algorithms. It begins by introducing two primary categories of approximation techniques: pointwise approximations, exemplified by Taylor expansions, and uniform approximations over an interval, illustrated by Chebyshev polynomial expansions. The Taylor series is explored for approximating functions around a point, with a focus on the approximation error and the radius of convergence. The chapter then shifts to Chebyshev polynomials, detailing their properties, recurrence relations, and the significance of Chebyshev nodes in achieving uniform approximations. The concept of evaluating analytic functions of matrices using Taylor series is also discussed, highlighting the challenges and solutions in matrix exponentiation, particularly in quantum computing. The chapter touches on the Hamiltonian simulation problem and the use of Trotter–Suzuki formulas for approximating matrix exponentials. It concludes by mentioning the Baker–Campbell–Hausdorff formula and the Lie–Trotter approximation, setting the stage for further exploration in subsequent chapters.
AI Generated

This summary of the content was generated with the help of AI.

Already a customer? Then log in here to gain access.

Customer login

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Business + Economics & Engineering + Technology"

Online-Abonnement

Springer Professional "Business + Economics & Engineering + Technology" gives you access to:

  • more than 130.000 books
  • more than 540 journals

from the following subject areas:

  • Automotive
  • Construction + Real Estate
  • Business IT + Informatics
  • Electrical Engineering + Electronics
  • Energy + Sustainability
  • Finance + Banking
  • Management + Leadership
  • Marketing + Sales
  • Mechanical Engineering + Materials
  • Surfaces + Materials Technology
  • Insurance + Risk


Secure your knowledge advantage now!

inform now

Springer Professional "Engineering + Technology"

Online-Abonnement

Springer Professional "Engineering + Technology" gives you access to:

  • more than 75.000 books
  • more than 390 journals

from the following specialised fileds:

  • Automotive
  • Business IT + Informatics
  • Construction + Real Estate
  • Electrical Engineering + Electronics
  • Energy + Sustainability
  • Mechanical Engineering + Materials
  • Surfaces + Materials Technology





 

Secure your knowledge advantage now!

inform now

Springer Professional "Business + Economics"

Online-Abonnement

Springer Professional "Business + Economics" gives you access to:

  • more than 100.000 books
  • more than 340 journals

from the following specialised fileds:

  • Construction + Real Estate
  • Business IT + Informatics
  • Finance + Banking
  • Management + Leadership
  • Marketing + Sales
  • Insurance + Risk



Secure your knowledge advantage now!

inform now

For explorers: Get to know our platforms better with a free registration.

Register for free
previous chapter Linear Algebra and Probability
next chapter Theory of Computing
Title
Polynomial Approximations
Authors
Osama M. Raisuddin
Suvranu De
Copyright Year
2026
Book
Quantum Computing for Engineers

Print ISBN: 978-3-032-03324-6

Electronic ISBN: 978-3-032-03325-3

Copyright Year: 2026

DOI
https://doi.org/10.1007/978-3-032-03325-3_2
This content is only visible if you are logged in and have the appropriate permissions.

Premium Partner

    Image Credits
    Neuer Inhalt/© ITandMEDIA, Nagarro GmbH/© Nagarro GmbH, AvePoint Deutschland GmbH/© AvePoint Deutschland GmbH, AFB Gemeinnützige GmbH/© AFB Gemeinnützige GmbH, USU GmbH/© USU GmbH, Ferrari electronic AG/© Ferrari electronic AG