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

You can’t copy a qubit

The BB84 algorithm works because no eavesdropper can make a copy of a qubit’s state. Imagine that Eve intercepts one of Alice’s qubits, makes a measurement, and gets a value of 1. Eve has no way of knowing whether the qubit she measured was in the |1 state, the state, the state, or some other exotic in-between state. So, Eve doesn’t know exactly what to forward to Bob.

But wait! Can we be sure that Eve has no way to make a copy of Alice’s qubit? Yes, we can. The No-Cloning theorem shows that assuming that qubits can be copied leads to a nasty contradiction.

Let’s start by agreeing on three properties of tensor products:

  • For any three matrices, x, y, and z, a left distributive law holds – that is, {"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"\"><mstyle mathsize=\"16px\"><mi>x</mi><mo>&#xA0;</mo><mo>&#x2297;</mo><mo>&#xA0;</mo><mfenced><mrow><mi>y</mi><mo>&#xA0;</mo><mo>+</mo><mo>&#xA0;</mo><mi>z</mi></mrow></mfenced><mo>&#xA0;</mo><mo>=</mo><mo>&#xA0;</mo><mfenced><mrow><mi>x</mi><mo>&#xA0;</mo><mo>&#x2297;</mo><mo>&#xA0;</mo><mi>y</mi></mrow></mfenced><mo>&#xA0;</mo><mo>+</mo><mo>&#xA0;</mo><mfenced><mrow><mi>x</mi><mo>&#xA0;</mo><mo>&#x2297;</mo><mo>&#xA0;</mo><mi>z</mi></mrow></mfenced></mstyle></math>"}.

You can write out a formal proof of this fact, but I always like to test with a simple example:

An example is never as good as proof, but an example helps us...