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 Grover’s algorithm

As we saw in the previous sections, each application of the Grover iterate has two parts:

  1. In the first part, the oracle marks the target amplitude.
  2. In the second part, the diffuser inverts all amplitudes about the mean.

Each part is a collection of quantum gates, and those gates apply a matrix to the circuit’s qubits. In this section, we’ll describe the matrix representations of the oracle and the diffuser.

A matrix for the oracle

Let’s assume that we have only two qubits. After these qubits go through Hadamard gates, we have a matrix representation of {"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"\"><mstyle mathsize=\"16px\"><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>&#xA0;</mo><mfenced><mtable><mtr><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></mstyle></math>"}. If we want to mark the |10 amplitude, we must do the following:

In general, the oracle’s matrix is the identity matrix with one of the 1s along the diagonal changed to a -1. Simple as this is, it’s also somewhat disconcerting. To know which diagonal element becomes -1, you have to know which item is...