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

Epilogue – what does have to do with Grover’s algorithm?

When you run Grover’s algorithm, the optimal number of iterations is {"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"\"><mstyle mathsize=\"16px\"><mfrac><mi>&#x3C0;</mi><mn>4</mn></mfrac><msqrt><mi>N</mi></msqrt></mstyle></math>"}, where {"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"\"><mstyle mathsize=\"16px\"><mi>N</mi></mstyle></math>"} is the number of things you’re searching through. In this formula, you have {"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"\"><mstyle mathsize=\"16px\"><mi>n</mi></mstyle></math>"} qubits and {"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"\"><mstyle mathsize=\"16px\"><mi>N</mi><mo>&#xA0;</mo><mo>=</mo><mo>&#xA0;</mo><msup><mn>2</mn><mi>n</mi></msup></mstyle></math>"}.

Usually, the formula requires a few tweaks. For example, you can’t use the formula to search through exactly 1,000 items, because 1,000 isn’t a power of 2. Instead, you add 24 fake items to your list. Then, you use 10 qubits to search through {"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"\"><mstyle mathsize=\"16px\"><msup><mn>2</mn><mn>10</mn></msup><mo>&#xA0;</mo><mo>=</mo><mo>&#xA0;</mo><mn>1024</mn></mstyle></math>"} items. And what if {"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"\"><mstyle mathsize=\"16px\"><mfrac><mi>&#x3C0;</mi><mn>4</mn></mfrac><msqrt><mi>N</mi></msqrt></mstyle></math>"} isn’t an integer? The value of {"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"\"><mstyle mathsize=\"16px\"><mfrac><mi>&#x3C0;</mi><mn>4</mn></mfrac><msqrt><mn>1024</mn></msqrt></mstyle></math>"} is approximately 25.1327, and you can’t apply the Grover iterate 25.1327 times. In this case, there are ways to decide whether Grover’s sweet spot is 25 or 26, but we won’t get into that here.

In this section, our goal is to convey some idea of the role {"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"\"><mstyle mathsize=\"16px\"><mfrac><mi>&#x3C0;</mi><mn>4</mn></mfrac></mstyle></math>"} plays in the number of Grover iterate applications. Our explanation has many gaps and involves several approximations. We won’t come to...