Book Image

Quantum Computing Algorithms

By : Barry Burd
5 (1)
Book Image

Quantum Computing Algorithms

5 (1)
By: Barry Burd

Overview of this book

Navigate the quantum computing spectrum with this book, bridging the gap between abstract, math-heavy texts and math-avoidant beginner guides. Unlike intermediate-level books that often leave gaps in comprehension, this all-encompassing guide offers the missing links you need to truly understand the subject. Balancing intuition and rigor, this book empowers you to become a master of quantum algorithms. No longer confined to canned examples, you'll acquire the skills necessary to craft your own quantum code. Quantum Computing Algorithms is organized into four sections to build your expertise progressively. The first section lays the foundation with essential quantum concepts, ensuring that you grasp qubits, their representation, and their transformations. Moving to quantum algorithms, the second section focuses on pivotal algorithms — specifically, quantum key distribution and teleportation. The third section demonstrates the transformative power of algorithms that outpace classical computation and makes way for the fourth section, helping you to expand your horizons by exploring alternative quantum computing models. By the end of this book, quantum algorithms will cease to be mystifying as you make this knowledge your asset and enter a new era of computation, where you have the power to shape the code of reality.
Table of Contents (19 chapters)
Free Chapter
Part 1 Nuts and Bolts
Part 2 Making Qubits Work for You
Part 3 Quantum Computing Algorithms
Part 4 Beyond Gate-Based Quantum Computing

Finding a sequence’s period

In the section entitled How Shor’s algorithm works, we saw how knowing the period of a certain repeating sequence of numbers helps an eavesdropper factor a large public key and decrypt a message. How can quantum computing help the eavesdropper discover a sequence’s period?

Consider the following sequence of numbers:

1, 2, 7, 10, 15, 3, 1, 2, 7, 10, 15, 3, 1, 2, 7, 10, 15, 3, 1, 2, 7, 10, 15, 3

For want of a better name, we’ll call this my sequence. In my sequence, the pattern 1, 2, 7, 10, 15, 3 occurs four times:

  • Since the pattern contains six numbers, we say that my sequence’s period is 6
  • Since the pattern occurs four times in my sequence, we say that the pattern’s frequency is 4

My sequence contains 24 numbers. So, the period and frequency in my sequence are related by the following formula:

{"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"\"><mstyle mathsize=\"16px\"><mtext>period&#xA0;=&#xA0;</mtext><mfrac><mtext>24</mtext><mi>frequency</mi></mfrac></mstyle></math>"}

Mathematicians refer to my sequence’s period and its frequency as dual variables...