Book Image

Dancing with Qubits

By : Robert S. Sutor
5 (1)
Book Image

Dancing with Qubits

5 (1)
By: Robert S. Sutor

Overview of this book

Quantum computing is making us change the way we think about computers. Quantum bits, a.k.a. qubits, can make it possible to solve problems that would otherwise be intractable with current computing technology. Dancing with Qubits is a quantum computing textbook that starts with an overview of why quantum computing is so different from classical computing and describes several industry use cases where it can have a major impact. From there it moves on to a fuller description of classical computing and the mathematical underpinnings necessary to understand such concepts as superposition, entanglement, and interference. Next up is circuits and algorithms, both basic and more sophisticated. It then nicely moves on to provide a survey of the physics and engineering ideas behind how quantum computing hardware is built. Finally, the book looks to the future and gives you guidance on understanding how further developments will affect you. Really understanding quantum computing requires a lot of math, and this book doesn't shy away from the necessary math concepts you'll need. Each topic is introduced and explained thoroughly, in clear English with helpful examples.
Table of Contents (16 chapters)
Preface
13
Afterword

6.3 Wrong again?

Suppose you have a very faulty calculator that does not always compute the correct result.

If the probability of getting the wrong answer is p, the probability of getting the correct answer is 1 − p. This called the complementary probability. Assuming there is no connection between the attempts, the probability of getting the wrong answer two times in a row is p2 and the probability of getting the correct answer two times in a row is (1 − p)2.

Question 6.3.1

Compute p2 and (1 − p)2 for p = 0, p = 0.5, and p = 1.0.

To make this useful, we want the probability of failure p to be non-zero.

For n independent attempts, the probability of getting the wrong answer is pn. Let’s suppose p = 0.6. We get the wrong answer 60% of the time in many attempts. We get the correct answer 40% of the time.

After 10 attempts, the probability of having gotten the wrong answer every time is 0.610 ...