index

A

abstractions 118

algebra. See linear algebra

algorithms 9–10

ancilla qubits 131

B

balanced functions 162–165

basis states 51

BB84 151–154

begin status 165, 167

Bell state 83, 85–86

bits

classic bit vs. qubit 32–33

issues with sending over network 138–139

modifying messages 139

reading messages 138–139

Boolean object 97

Boolean source 96

boolean type 56

breaking encryption 6

C

classical computers, evolutions in 12

classic bit vs. qubit 32–33

Classic class 26–27, 29

Classic.randomBit() method 26–29, 121

classicsearch application 188

Classic.search method 193, 196

CloudQuantumExcecutionEnvironment constructor 135

cloud services 133–135

CNot gate 80–83

communication. See secure communication

constant functions 162–165

control qubit 80

D

Deutsch-Jozsa algorithm

defining an oracle 167–170

from functions to oracles 170–173

balanced functions 172–173

constant functions 171–172

properties of functions 161–165

reversible quantum gates 165–167

experimental evidence 165–166

mathematical proof 166–167

when solution is not the problem 159–161

disruptive parts of quantum computing 11–13

evolutions in classical computers 12

quantum physics 12–13

revolution in quantum computers 12

doGrover method 197, 205

E

entanglement

creating bell state 83–86

gate representation for 79–83

CNot gate 80–83

converting to probability vectors 79–80

independent probabilities

classic way 69–72

quantum way 73–75

physical concept of 75–79

predicting heads or tails 69

evolutions in classical computers 12

expectation management 4–11

algorithms 9–10

hardware 4–5

reasons for learning quantum computing 10–11

software 6–9

exponential problems 55

exponential time 6

F

f(x) balanced function 180

f(x) constant function 180

f1 constant function 171, 175

f2 balanced function 172, 175

f4 constant function 172

factorization, classic vs. quantum 209–211

factor method 213

findPersonByAgeAndCountry method 188–189

functions

from functions to oracles 170–173

balanced functions 172–173

constant functions 171–172

periodic functions 214–215

properties of 161–165

G

gates 37 – 39

creating periodic function using 224–226

flow and circuit 224–225

steps 225–226

gate representation for quantum entanglement 79–83

CNot gate 80–83

converting to probability vectors 79–80

Pauli-X gate 39

reversible quantum gates 165–167

experimental evidence 165 – 166

mathematical proof 166–167

git commands 230

GPU (graphics processing unit) 13

Gradle

building “Hello World” program using 24–25

running HelloStrange program using 232–233

Grover's search 184

algorithm behind 196–205

diffusion operator 204–205

quantum oracle 200–204

running example code 197–199

superposition 199–200

amplitudes 195–196

classical search problems 185–191

general preparations 186–187

searching the list 187–188

searching using a function 189–191

overview 184

probabilities 193–194

using 191–193

H

Hadamard gates

applying two 146–147

general discussion 63–64

Java code using 65–67

H class 42

hellostrange demo application 232

HelloStrange program

running using Gradle 232–233

running using Maven 231–232

“Hello World” program

inspecting code for 23–28

build procedures 23–25

Java APIs vs. implementations 27–28

obtaining and installing Strange code 28–29

downloading code 28–29

library overview 29

running first demo with Strange 20–23

high-level Java API 19

high-level languages 116–117

hostname 95

I

IDE (integrated development environment) 229

IllegalArgumentException 42

independent probabilities

classic way 69–72

quantum way 73–75

installing Strange demo code 230

inverse quantum Fourier transform 226

inverter 37

J

Java

classical networking in 92–96

QKD application in 155–158

code 155–157

running application 157–158

using Hadamard gate 65–67

java command 229

JavaFX controls module 44

java.net.Socket class 93

L

languages

for quantum computing simulators 119

approaches 119

resources for other languages 119

high-level 116–117

linear algebra

matrix-matrix multiplication 235

matrix-vector multiplication 234

tensor product 236

linear time 6

List object 187

M

Main class 204–205

main method 71, 188, 212–213

makeCopy method 96–97

manyExecution function 66

Math.random() function 71

matrix gate operations 58–63

matrix that works for all gates 62–63

Pauli-X gate

applying to qubit in superposition 60–62

as matrix 59–60

matrix-matrix multiplication 235

matrix-vector multiplication 234

Maven

building Hello World program using 23–24

running HelloStrange program using 231–232

mavenLocal() method 29

measurement operation 101

mvn command 232

N

n/2 function evaluations 188, 191, 203

networking. See quantum networking

no-cloning theorem 96–98

nonpolynomial (exponential) scaling 16

nonpolynomial time 6

O

oracles 161

defining 167–170

from functions to 170–173

balanced functions 172–173

constant functions 171–172

org.redfx.javaqc.ch02.hellostrange package 26

org.redfx.strange.algorithm.Classic class 120

org.redfx.strangefx.render.Renderer class 44

org.redfx.strange.gate.Measurement class 101

org.redfx.strange.gate package 42

org.redfx.strange.local package 41

org.redfx.strange package 41

P

params parameter 135

Pauli-X gate 39

applying to qubit in superposition 60–62

as matrix 59–60

Pauli-Z gate 100–101

periodic functions 214–215

creating using quantum gates 224–226

flow and circuit 224–225

steps 225–226

example 162

periodicity 214

Person class 187

Person instance 187

polynomial in quantum 8

polynomial time 6

portnumber 95

prepareStep 155

probabilities

independent probabilities

classic way 69–72

quantum way 73–75

probability vectors 54–58, 79–80

probability vector 70, 193

Program class 41

Program.initializeQubit (int index, double alpha) method 107

Program instance 65–66, 122

Q

Q# language 119

QKD (quantum key distribution) 137

QKD application in Java 155–158

code 155–157

executing application 156

filling steps 155–156

initializing variables 155

preparing steps 155

processing results 156–157

running 157–158

-q option 232

-q parameter 233

QPU (quantum processing unit) 13

quantum black box 167

quantum circuits, visualizing 43–45

quantum computing

abstracting software for quantum computers 14–16

disruptive parts of 11–13

evolutions in classical computers 12

quantum physics 12–13

revolution in quantum computers 12

expectation management 4–11

algorithms 9–10

hardware 4–5

reasons for learning quantum computing 10–11

software 6–9

from quantum to computing or from computing to quantum 17–18

hybrid computing 13–14

revolution in quantum computers 12

quantum entanglement 75

QuantumExecutionEnvironment 41–42, 65–66, 135

quantum Fourier transform, inverse 226

quantum networking

measurements 101

obstacles to 92–99

classical networking in Java 92 – 96

no-cloning theorem 96–98

physical limitations on transferring qubits 99

Pauli-Z gate 100–101

quantum repeater 109–112

quantum teleportation 102–109

goal of 102

quantum and classical communication 108–109

running application 105–108

topology of quantum network 90–92

quantum NOT gate 100

quantum physics 12–13

Qubit class 97

qubits 5, 12

in Strange 40–43

Program class 41

QuantumExecutionEnvironment interface 41

results 42–43

steps and gates 41–42

manipulating and measuring 37–39

notation 33–37

multiple qubits 34–37

one qubit 34

physical limitations on transferring 99

vs. classic bits 32–33

R

randomBit() function 25, 27, 29, 71, 122

repeaters 99

Result class 42–43

reversible quantum gates 165–167

experimental evidence 165–166

mathematical proof 166–167

revolution in quantum computers 12

runProgram() method 42, 66

S

search algorithm. See Grover’s search

search architecture, traditional 183–184

secure communication

BB84 151–154

bootstrap problem 137–142

issues with sending bits over network 138–139

one-time pad 140–141

sharing secret key 141–142

naive approach 142–145

QKD in Java 155–158

code 155–157

running application 157–158

quantum key distribution 142

using superposition 145–150

applying two Hadamard gates 146–147

sending qubits in superposition 147–150

Shor’s algorithm

calculating the periodicity 226–227

classic factorization vs. quantum factorization 209–211

creating periodic function using quantum gates 224–226

flow and circuit 224–225

steps 225–226

implementation challenges 227–228

marketing hype 208–209

multidisciplinary problem 211

problem description 212–213

quantum arithmetic as introduction to 128

quantum-based implementation 222–224

quick example 207–208

rationale behind 214–222

classic period finding 218–219

periodic functions 214–215

post-processing step 219–222

solving different problem 215–218

summary 228

SimpleQuantumExecutionEnvironment 41, 89, 135

simulators 133–135

singleExecution function 66

software 6–9

solution argument 197

someFunction function 56–57

source instance 97

spin property 12, 51, 76

state vector 193

Step instance 65

Strange 119–123

creating own circuits with 128–133

adding two qubits 128–130

next steps 133

quantum arithmetic as introduction to Shor’s algorithm 128

quantum arithmetic with carry bit 131–133

HelloStrange program

running using Gradle 232–233

running using Maven 231–232

low-level APIs 121–122

obtaining and installing code for Strange library 28–29

downloading code 28–29

library overview 29

obtaining and installing demo code 230

qubits in 40–43

Program class 41

QuantumExecutionEnvironment interface 41

results 42–43

steps and gates 41–42

requirements 229–230

running first demo with 20–23

top-level API 120–121

when to use what 122–123

StrangeBridge class 87

StrangeFX tool 123–128

debugging Strange code 124–128

visualization of circuits 123–124

superposition

Hadamard gate

general discussion 63–64

Java code using 65–67

matrix gate operations 58–63

matrix that works for all gates 62–63

Pauli-X gate 59–62

overview 50–54

secure communication using 145–150

applying two Hadamard gates 146–147

sending qubits in superposition 147–150

state of quantum system as probability vector 54–58

superPositionStep 156

superPositionStep2 156

T

target qubit 80

teleportation, quantum 102–109

goal of 102

quantum and classical communication 108–109

running application 105–108

tensor product 236

ToIntFunction function 189

U

user interface (presentation layer) 183

V

version key 29

-version parameter 229

X

X class 42