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

9.4 Arithmetic

In section 2.5

I’m going to keep to a straightforward approach to help bridge the gap between classical and quantum approaches. The gates we use are simple, and we replace bits with qubits. That is, instead of 0 and 1 we use |0 and |1, respectively. The data input qubits are called |x and |y, and each are in the state |0 or |1 at any given time. We are essentially mimicking what we would do in the classical case.

If we do not worry about carry-in and carry-out qubits, our circuit looks like

tikz JPG figure

where ‘‘⊕’’ is addition modulo 2. This is implemented as a CNOT gate acting as an xor. We use q1 to store this output as well as the |y input.

To include a carry-out state |cout we employ a Toffoli CCNOT gate and use a third qubit, q2, to hold the value.

tikz JPG figure

Question 9.4.1

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