You're reading from Quantum Computing with Silq Programming Get up and running with quantum computing with the simplicity of this new high-level programming language

Product type Paperback

Published in Apr 2021

Publisher Packt

ISBN-13 9781800569669

Length 310 pages

Edition 1st Edition

Languages

C++

Tools

Quantum Development Kit

Concepts

Programming Language

Authors (2):

Thomas Cambier

Srinjoy Ganguly

View More author details

Table of Contents (19) Chapters

Preface

1. Section 1: Essential Background and Introduction to Quantum Computing

2. Chapter 1: Essential Mathematics and Algorithmic Thinking FREE CHAPTER

3. Chapter 2: Quantum Bits, Quantum Measurements, and Quantum Logic Gates

4. Chapter 3: Multiple Quantum Bits, Entanglement, and Quantum Circuits

5. Chapter 4: Physical Realization of a Quantum Computer

6. Section 2: Challenges in Quantum Programming and Silq Programming

7. Chapter 5: Challenges in Quantum Computer Programming

8. Chapter 6: Silq Programming Basics and Features

9. Chapter 7: Programming Multiple-Qubit Quantum Circuits with Silq

10. Section 3: Quantum Algorithms Using Silq Programming

11. Chapter 8: Quantum Algorithms I – Deutsch-Jozsa and Bernstein-Vazirani

12. Chapter 9: Quantum Algorithms II – Grover's Search Algorithm and Simon's Algorithm

13. Chapter 10: Quantum Algorithms III – Quantum Fourier Transform and Phase Estimation

14. Section 4: Applications of Quantum Computing

15. Chapter 11: Quantum Error Correction

16. Chapter 12: Quantum Cryptography – Quantum Key Distribution

17. Chapter 13: Quantum Machine Learning

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Grover's search for multiple solutions using Silq programming

Until now, we have looked into Grover's search for finding only one solution, which we termed as the marked element. But Grover's algorithm can also be used to find multiple solutions, which means multiple marked elements. The number of iterations in the case of multiple solutions is around , where M is the number of marked elements. Let's now start with the extensive mathematical treatment for the case of multiple solutions in the next section.

Mathematical treatment of Grover's search for multiple solutions

Consider that the number of marked elements is M such that ; so, therefore, we start with state , which is the superposition of all the M marked elements.

We also have our original state prepared, which is . Now, the original state can be written in terms of N and M as coefficients by a bit of mathematical manipulation, as follows: