Quantum Computing for Developers: A Java-based introduction

Front matter

preface

acknowledgments

about this book

about the author

about the cover illustration

  

Part 1. Quantum computing introduction

  1 Evolution, revolution, or hype?

  1.1  Expectation management

Hardware

Software

Algorithms

Why start with QC today?

  1.2  The disruptive parts of QC: Getting closer to nature

Evolutions in classical computers

Revolution in quantum computers

Quantum physics

  1.3  Hybrid computing

  1.4  Abstracting software for quantum computers

  1.5  From quantum to computing or from computing to quantum

  2 “Hello World,” quantum computing style

  2.1  Introducing Strange

  2.2  Running a first demo with Strange

  2.3  Inspecting the code for HelloStrange

The build procedures

The code

Java APIs vs. implementations

  2.4  Obtaining and installing the Strange code

Downloading the code

A first look at the library

  2.5  Next steps

  3 Qubits and quantum gates: The basic units in quantum computing

  3.1  Classic bit vs. qubit

  3.2  Qubit notation

One qubit

Multiple qubits

  3.3  Gates: Manipulating and measuring qubits

  3.4  A first [quantum] gate: Pauli-X

  3.5  Playing with qubits in Strange

The QuantumExecutionEnvironment interface

The Program class

Steps and gates

Results

  3.6  Visualizing quantum circuits

Part 2. Fundamental concepts and how they relate to code

  4 Superposition

  4.1  What is superposition?

  4.2  The state of a quantum system as a probability vector

  4.3  Introducing matrix gate operations

The Pauli-X gate as a matrix

Applying the Pauli-X gate to a qubit in superposition

A matrix that works for all gates

  4.4  The Hadamard gate: The gate to superposition

  4.5  Java code using the Hadamard gate

  5 Entanglement

  5.1  Predicting heads or tails

  5.2  Independent probabilities: The classic way

  5.3  Independent probabilities: The quantum way

  5.4  The physical concept of entanglement

  5.5  A gate representation for quantum entanglement

Converting to probability vectors

CNot gate

  5.6  Creating a Bell state: Dependent probabilities

  5.7  Mary had a little qubit

  6 Quantum networking: The basics

  6.1  Topology of a quantum network

  6.2  Obstacles to quantum networking

Classical networking in Java

No-cloning theorem

Physical limitations on transferring qubits

  6.3  Pauli-Z gate and measurement

Pauli-Z gate

Measurements

  6.4  Quantum teleportation

The goal of quantum teleportation

Part 1: Entanglement between Alice and Bob

Part 2: Alice’s operations

Part 3: Bob’s operations

Running the application

Quantum and classical communication

  6.5  A quantum repeater

Part 3. Quantum algorithms and code

  7 Our HelloWorld, explained

  7.1  From hardware to high-level languages

  7.2  Abstractions at different levels

  7.3  Other languages for quantum computing simulators

Approaches

Resources for other languages

  7.4  Strange: High-level and low-level approaches

Top-level API

Low-level APIs

When to use what

  7.5  StrangeFX: A development tool

Visualization of circuits

Debugging Strange code

  7.6  Creating your own circuits with Strange

Quantum arithmetic as an introduction to Shor’s algorithm

Adding two qubits

Quantum arithmetic with a carry bit

Next steps

  7.7  Simulators, cloud services, and real hardware

  8 Secure communication using quantum computing

  8.1  The bootstrap problem

Issues with sending bits over a network

One-time pad to the rescue

Sharing a secret key

  8.2  Quantum key distribution

  8.3  Naive approach

  8.4  Using superposition

Applying two Hadamard gates

Sending qubits in superposition

  8.5  BB84

Confusing Eve

Bob is confused, too

Alice and Bob are talking

  8.6  QKD in Java

The code

Running the application

  9 Deutsch-Jozsa algorithm

  9.1  When the solution is not the problem

  9.2  Properties of functions

Constant and balanced functions

  9.3  Reversible quantum gates

Experimental evidence

Mathematical proof

  9.4  Defining an oracle

  9.5  From functions to oracles

Constant functions

Balanced functions

  9.6  Deutsch algorithm

  9.7  Deutsch-Jozsa algorithm

  9.8  Conclusion

10 Grover’s search algorithm

10.1  Do we need yet another search architecture?

Traditional search architecture

What is Grover’s search algorithm?

10.2  Classical search problems

General preparations

Searching the list

Searching using a function

10.3  Quantum search: Using Grover’s search algorithm

10.4  Probabilities and amplitudes

Probabilities

Amplitudes

10.5  The algorithm behind Grover’s search

Running the example code

Superposition

Quantum oracle

Grover diffusion operator: Increasing the probability

10.6  Conclusion

11 Shor’s algorithm

11.1  A quick example

11.2  The marketing hype

11.3  Classic factorization vs. quantum factorization

11.4  A multidisciplinary problem

11.5  Problem description

11.6  The rationale behind Shor’s algorithm

Periodic functions

Solving a different problem

Classic period finding

The post-processing step

11.7  The quantum-based implementation

11.8  Creating a periodic function using quantum gates

The flow and circuit

The steps

11.9  Calculating the periodicity

11.10 Implementation challenges

Appendix A. Getting started with Strange

Appendix B. Linear algebra

index