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

The idea behind Grover’s algorithm

The strategy underlying Grover’s algorithm is quite clever. Instead of thinking about 64 boxes the way we did in the previous section, let’s imagine that you have only four boxes. This set of four boxes is called the search space.

You’re a quantum computing enthusiast, so you’ve electronically coded the contents of these boxes and labeled the boxes |00, |01, |10, and |11. Now your search space consists of the four values |00, |01, |10, and |11. In your quantum computing circuit, you represent these values with two qubits, both of which are in the {"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"\"><mstyle mathsize=\"16px\"><mfenced><mtable><mtr><mtd><mfrac><mn>1</mn><msqrt><mn>2</mn></msqrt></mfrac></mtd></mtr><mtr><mtd><mfrac><mn>1</mn><msqrt><mn>2</mn></msqrt></mfrac></mtd></mtr></mtable></mfenced></mstyle></math>"} state. When you take the tensor product, you get {"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"\"><mstyle mathsize=\"16px\"><mfenced><mtable><mtr><mtd><mfrac bevelled=\"true\"><mn>1</mn><mn>2</mn></mfrac></mtd></mtr><mtr><mtd><mfrac bevelled=\"true\"><mn>1</mn><mn>2</mn></mfrac></mtd></mtr><mtr><mtd><mfrac bevelled=\"true\"><mn>1</mn><mn>2</mn></mfrac></mtd></mtr><mtr><mtd><mfrac bevelled=\"true\"><mn>1</mn><mn>2</mn></mfrac></mtd></mtr></mtable></mfenced></mstyle></math>"}. Remember that each of the numbers in this vector is an amplitude. The square of each amplitude is the probability of getting a certain outcome when you measure the two qubits. (See Figure 8.1.)

Figure 8.1 – A state vector’s entries correspond to probabilities of measuring values

Figure 8.1 – A state vector...