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

Matrices for qubit states and operations

In Chapter 1, New Ways to Think about Bits, we represented bits with kets and vectors:

Let’s expand that notation for qubits.

When you apply a Hadamard (h) gate to a |0 qubit, the qubit goes into a halfway state. Here’s how we represent that halfway state in Dirac notation:

And here’s how we represent that state with a vector:

This qubit state crops up so often in quantum computing that it’s convenient to give the state its own symbol. We put a plus sign inside a ket and say that .

In vector notation, the vector’s top number represents the amount of |0’ness, while the bottom number represents an equal amount of |1’ness. But what do the square roots do? What follows is a slight simplification.

Important note

A qubit’s state has two parts. When you take the square of either...