book

Quantum Computing in Action

by Johan Vos

February 2022

Beginner

264 pages

7h 33m

English

Manning Publications

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prefaceacknowledgmentsabout this bookWho should read this book?How this book is organized: a roadmapAbout the codeliveBook discussion forumabout the authorabout the cover illustration
1.1 Expectation management1.1.1 Hardware1.1.2 Software1.1.3 Algorithms1.1.4 Why start with QC today?1.2 The disruptive parts of QC: Getting closer to nature1.2.1 Evolutions in classical computers1.2.2 Revolution in quantum computers1.2.3 Quantum physics1.3 Hybrid computing1.4 Abstracting software for quantum computers1.5 From quantum to computing or from computing to quantumSummary
2.1 Introducing Strange2.2 Running a first demo with Strange2.3 Inspecting the code for HelloStrange2.3.1 The build procedures2.3.2 The code2.3.3 Java APIs vs. implementations2.4 Obtaining and installing the Strange code2.4.1 Downloading the code2.4.2 A first look at the library2.5 Next stepsSummary
3.1 Classic bit vs. qubit3.2 Qubit notation3.2.1 One qubit3.2.2 Multiple qubits3.3 Gates: Manipulating and measuring qubits3.4 A first [quantum] gate: Pauli-X3.5 Playing with qubits in Strange3.5.1 The QuantumExecutionEnvironment interface3.5.2 The Program class3.5.3 Steps and gates3.5.4 Results3.6 Visualizing quantum circuitsSummary

4.1 What is superposition?4.2 The state of a quantum system as a probability vector4.3 Introducing matrix gate operations4.3.1 The Pauli-X gate as a matrix4.3.2 Applying the Pauli-X gate to a qubit in superposition4.3.3 A matrix that works for all gates4.4 The Hadamard gate: The gate to superposition4.5 Java code using the Hadamard gateSummary
5.1 Predicting heads or tails5.2 Independent probabilities: The classic way5.3 Independent probabilities: The quantum way5.4 The physical concept of entanglement5.5 A gate representation for quantum entanglement5.5.1 Converting to probability vectors5.5.2 CNot gate5.6 Creating a Bell state: Dependent probabilities5.7 Mary had a little qubitSummary
6.1 Topology of a quantum network6.2 Obstacles to quantum networking6.2.1 Classical networking in Java6.2.2 No-cloning theorem6.2.3 Physical limitations on transferring qubits6.3 Pauli-Z gate and measurement6.3.1 Pauli-Z gate6.3.2 Measurements6.4 Quantum teleportation6.4.1 The goal of quantum teleportation6.4.2 Part 1: Entanglement between Alice and Bob6.4.3 Part 2: Alice’s operations6.4.4 Part 3: Bob’s operations6.4.5 Running the application6.4.6 Quantum and classical communication6.5 A quantum repeaterSummary
7.1 From hardware to high-level languages7.2 Abstractions at different levels7.3 Other languages for quantum computing simulators7.3.1 Approaches7.3.2 Resources for other languages7.4 Strange: High-level and low-level approaches7.4.1 Top-level API7.4.2 Low-level APIs7.4.3 When to use what7.5 StrangeFX: A development tool7.5.1 Visualization of circuits7.5.2 Debugging Strange code7.6 Creating your own circuits with Strange7.6.1 Quantum arithmetic as an introduction to Shor’s algorithm7.6.2 Adding two qubits7.6.3 Quantum arithmetic with a carry bit7.6.4 Next steps7.7 Simulators, cloud services, and real hardwareSummary
8.1 The bootstrap problem8.1.1 Issues with sending bits over a network8.1.2 One-time pad to the rescue8.1.3 Sharing a secret key8.2 Quantum key distribution8.3 Naive approach8.4 Using superposition8.4.1 Applying two Hadamard gates8.4.2 Sending qubits in superposition8.5 BB848.5.1 Confusing Eve8.5.2 Bob is confused, too8.5.3 Alice and Bob are talking8.6 QKD in Java8.6.1 The code8.6.2 Running the applicationSummary
9.1 When the solution is not the problem9.2 Properties of functions9.2.1 Constant and balanced functions9.3 Reversible quantum gates9.3.1 Experimental evidence9.3.2 Mathematical proof9.4 Defining an oracle9.5 From functions to oracles9.5.1 Constant functions9.5.2 Balanced functions9.6 Deutsch algorithm9.7 Deutsch-Jozsa algorithm9.8 ConclusionSummary
10.1 Do we need yet another search architecture?10.1.1 Traditional search architecture10.1.2 What is Grover’s search algorithm?10.2 Classical search problems10.2.1 General preparations10.2.2 Searching the list10.2.3 Searching using a function10.3 Quantum search: Using Grover’s search algorithm10.4 Probabilities and amplitudes10.4.1 Probabilities10.4.2 Amplitudes10.5 The algorithm behind Grover’s search10.5.1 Running the example code10.5.2 Superposition10.5.3 Quantum oracle10.5.4 Grover diffusion operator: Increasing the probability10.6 ConclusionSummary
11.1 A quick example11.2 The marketing hype11.3 Classic factorization vs. quantum factorization11.4 A multidisciplinary problem11.5 Problem description11.6 The rationale behind Shor’s algorithm11.6.1 Periodic functions11.6.2 Solving a different problem11.6.3 Classic period finding11.6.4 The post-processing step11.7 The quantum-based implementation11.8 Creating a periodic function using quantum gates11.8.1 The flow and circuit11.8.2 The steps11.9 Calculating the periodicity11.10 Implementation challengesSummary
A.1 RequirementsA.2 Obtaining and installing the demo codeA.3 The HelloStrange programRunning the program
B.1 Matrix-vector multiplicationB.2 Matrix-matrix multiplicationB.3 Tensor product

Content preview from Quantum Computing in Action

5 Entanglement

This chapter covers

The analogy between flipping a coin and getting a random number
Relating flipping coins and probability vectors
The physical concept of quantum entanglement
Using quantum entanglement to create connected random numbers
Understanding how to use superposition and entanglement in Java applications

In the previous chapter, we introduced and explained the concept of superposition. This concept does not exist in classical computing, and it is one of the reasons quantum computing is fundamentally different from classical computing. Nevertheless, we managed to describe superposition in such a way that a Java programmer can use it in their code. In this chapter, we introduce quantum entanglement, a concept that is ...