Chapter 11 Arithmetic With Quantum Computers

 

This chapter covers:

  • Program with the Numerics library for Q#.
  • Implement Shor’s algorithm for factoring integers.
  • Recognize the implications of quantum computing to security infrastructure.
Figure 11.1. In this Chapter, we will be covering an application for quantum computers, namely factoring numbers.
CH11 FIGxx mental model

11.1 FACTORING IN QUANTUM COMPUTING TO SECURITY

In Part I, you saw how quantum concepts can be applied to send data securely, using techniques such as quantum key distribution. Even without QKD, though, important data is shared secretly over the internet all the time. The internet is used to share payment data, personal health data, dating preferences, and even to organize political movements. In this Chapter, you’ll take a look at how classical computers can protect your privacy, and how quantum computing changes how we make decisions about what tools we use to protect our data.

11.2 CONNECTING MODULAR MATH TO FACTORING

11.3 EXAMPLE OF FACTORING WITH SHOR’S ALGORITHM

11.3.1 Working through the steps of to factor 21.

11.4 CLASSICAL ALGEBRA AND FACTORING

11.5 QUANTUM ARITHMETIC

11.6 ADDING WITH QUBITS

11.7 MULTIPLYING WITH QUBITS IN SUPERPOSITION

11.8 MODULAR MULTIPLICATION IN SHOR’S ALGORITHM

11.9 PUTTING IT ALL TOGETHER

11.10 WRAPPING UP

11.11 Summary: