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#### 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.
Introduction to Quantum Computing
Free Chapter
Part 1 Nuts and Bolts
Chapter 1: New Ways to Think about Bits
Chapter 2: What Is a Qubit?
Chapter 3: Math for Qubits and Quantum Gates
Chapter 4: Qubit Conspiracy Theories
Part 2 Making Qubits Work for You
Chapter 5: A Fanciful Tale about Cryptography
Chapter 6: Quantum Networking and Teleportation
Part 3 Quantum Computing Algorithms
Chapter 7: Deutsch’s Algorithm
Chapter 8: Grover’s Algorithm
Chapter 9: Shor’s Algorithm
Part 4 Beyond Gate-Based Quantum Computing
Chapter 10: Some Other Directions for Quantum Computing
Index
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# Working with matrices

A matrix is a rectangle of numbers. For example:

The matrix shown previously has two rows and three columns, so we call it a 2×3 matrix (pronounced as two-by-three matrix).

Tip

The plural of matrix is matrices (pronounced as MAY-trih-sees). To sound like a pro, never say matrixes or matricee.

It’s common to use an uppercase to represent a matrix. You refer to the entries in a matrix using the entries’ row numbers and column numbers. Some authors start with row number 1 and column number 1, but, for our purposes, it’s better to start with row number 0 and column number 0.

When you talk about matrices, you need a name that refers to a single number – a number that isn’t inside of a matrix. For example, if you write the number 12 with no parentheses around it, you’re referring to one of these single numbers. A number of this kind is called a scalar.

So, what can you do with...