book

Building Quantum Software with Python

by Charlee Stefanski, Constantin Gonciulea

April 2025

Intermediate to advanced

376 pages

9h 41m

English

Manning Publications

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1.1 Why quantum computing?1.2 Becoming quantum ready1.3 The superpowers of quantum computing1.3.1 The power of quantum parallelism1.3.2 The random nature of quantum measurement1.4 The anatomy of a quantum computation1.4.1 Computing with a single classical bit1.4.2 Computing with a single quantum bit1.4.3 Computing with multiple quantum bits1.4.4 Putting it together1.5 Patterns of quantum computations1.5.1 Sampling from probability distributions1.5.2 Searching for specific outcomes1.5.3 Estimating the probability of specific outcomes
2.1 A quick overview of optimization problems2.1.1 The knapsack problem2.1.2 Problem setup2.2 The steps of a quantum computation2.2.1 Outcomes as binary strings2.2.2 Quantum state and probabilities2.3 A quantum solution to the knapsack problem2.3.1 Encoding the problem2.3.2 Knapsack problem solution2.4 Tools for programming a quantum solution
3.1 Single-qubit state: A pair of complex numbers3.1.1 Visualizing single-qubit states with tables3.1.2 The general form of a single-qubit state3.1.3 Programmatically encoding single-qubit states with lists3.1.4 Implementing a single-qubit quantum computing simulator in Python3.2 Changing amplitudes with single-qubit gates3.2.1 Rotation is multiplication3.2.2 Basic single-qubit gates3.2.3 The general form of a single-qubit gate3.2.4 More basic single-qubit gates3.2.5 Single-qubit gate inverses3.3 Simulating changing amplitudes with gates3.3.1 Printing and visualizing the state3.3.2 Transforming a single-qubit state3.3.3 Single-qubit circuits3.4 Simulating measurement of single-qubit states3.4.1 Encoding the uniform distribution in a single-qubit quantum state3.5 Applications of single-qubit computations3.5.1 Encoding a Bernoulli distribution in a single-qubit quantum state3.5.2 Encoding a number with a single qubit
4.1 Computing with more than one qubit4.1.1 Measurement counts4.1.2 Sampling from a probability distribution4.1.3 Understanding quantum computations with a simple Python simulator4.2 A quantum state is a list of complex numbers4.2.1 Two-qubit states4.2.2 Multi-qubit states4.2.3 Simulating multi-qubit states in Python4.3 Changing amplitudes with quantum transformations4.3.1 Selecting pairs of amplitudes based on the target qubit4.3.2 Pair selection in Python4.3.3 Simulating amplitude changes4.3.4 Encoding a uniform distribution in a multi-qubit quantum system4.4 Controlled quantum transformations4.4.1 Simulating controlled gate transformations in Python4.4.2 Simulating multicontrol gate transformations in Python4.5 Simulating quantum circuits4.5.1 Simulating measurement of multi-qubit states4.5.2 Quantum registers and circuits in code4.5.3 Reimplementing the uniform distribution with registers and circuits4.5.4 Encoding the binomial distribution in a multi-qubit state4.5.5 Implementing the Bell states
5.1 Describing outcomes with quantum oracles: Intuition and classical implementation5.1.1 Phase oracles5.1.2 Bit oracles5.2 Quantum implementation of oracles5.2.1 Creating quantum circuits from building blocks5.2.2 Phase oracle5.2.3 Bit oracle5.3 Converting between phase and bit quantum oracles5.3.1 Converting a phase oracle to a bit oracle5.3.2 Converting a bit oracle to a phase oracle5.4 Fibonacci numbers and the golden ratio with good outcomes
6.1 Amplitude amplification: Intuition and classical implementation6.1.1 Finding good outcomes with oracles6.1.2 Computing similarity with inner products6.1.3 The inversion operator6.1.4 Putting it together: The Grover iterate6.1.5 A classical but quantum-friendly implementation of the inversion operator6.2 Magnitude amplification: Quantum circuit implementation6.2.1 Quantum oracle6.2.2 The inversion operator6.2.3 Grover iterate6.2.4 Putting it all together: Grover’s algorithm
7.1 Periodic patterns in sound waves and quantum states7.1.1 Periodic patterns in sound waves7.1.2 Periodic patterns in quantum states7.1.3 Roots of unity and their geometric sequences7.2 Converting from phase to magnitude encoding with the Hadamard gate7.3 From classical to quantum Fourier transforms7.3.1 The classical (discrete) Fourier transform7.3.2 Introducing the QFT and IQFT7.4 Quantum circuits for the QFT and IQFT7.4.1 Understanding the effect of the IQFT on a geometric sequence state
8.1 The single-slit experiment: Wave diffraction8.1.1 Introducing the discrete sinc function8.2 Encoding a periodic signal using discrete sinc quantum states8.2.1 Phase-to-magnitude frequency encoding with the IQFT8.2.2 Some useful numerical forms of the frequency encoding pattern8.2.3 Reversed qubit implementation of phased discrete sinc quantum states8.3 Discrete sinc as a sequence of coin flips8.4 Encoding trigonometric distributions in a quantum state8.4.1 Raised cosine8.4.2 Other trigonometric functions
9.1 Estimating the frequency of a periodic quantum state9.1.1 Getting better angle estimates with more qubits9.1.2 Reading between the ticks: Getting better estimates with interpolation9.2 Quantum circuits as rotations with eigenstates and eigenvalues9.3 The quantum phase estimation algorithm9.4 Circuit-level implementation of the quantum phase estimation algorithm9.5 An alternative implementation of the phase estimation circuit without qubit swaps9.6 Amplitude estimation and quantum counting9.6.1 Amplitude estimation9.6.2 Estimating the number of good outcomes with quantum counting9.6.3 Estimating the probability of good outcomes with amplitude estimation
10.1 Encoding function inputs and outputs10.1.1 Encoding a simple function10.1.2 Encoding the knapsack problem10.1.3 Encoding polynomials of binary variables10.1.4 Complexity of polynomial-encoding circuits10.1.5 Representing negative values10.2 Searching for function values10.3 Finding zeros of polynomial functions
11.1 Finding desired outcomes with Grover adaptive search11.2 Finding optimal outcomes with the Grover optimizer11.3 Solving the knapsack problem with a Grover optimizer11.3.1 Preparing the state11.3.2 Encoding constraints11.3.3 Defining the parameters of the Grover optimizer
12.1 Quantum concepts in review12.1.1 Quantum readiness12.1.2 Quantum advantage and its limitations12.2 Building quantum software and running on real quantum computers12.2.1 The importance of a fast, flexible quantum simulator12.2.2 Source-level compatibility between Hume and Qiskit12.2.3 Running on real quantum hardware12.2.4 Quantum assistant12.3 Revisiting quantum gates and the butterfly pattern12.3.1 Another look at single-qubit gates and the butterfly pattern12.4 Quantum states as an image12.4.1 Visualizing quantum state evolution12.5 Combinatorial optimization problems12.5.1 Encoding polynomials with noninteger coefficients12.5.2 Shor’s factorization algorithm
A.1 Diving deeper into binary stringsA.1.1 Converting between binary and decimal valuesA.1.2 Adding a digit to a binary stringA.1.3 Visualizing binary strings with binary treesA.1.4 Joining and splitting binary strings with prefixes and suffixesA.1.5 Encoding negative integersA.2 Using complex numbers to represent amplitudesA.2.1 Amplitudes as arrows inside the unit circleA.2.2 Amplitudes as complex numbers: The algebraic formA.2.3 Amplitudes as complex numbers: The trigonometric (polar) formA.2.4 Conjugates of complex numbersA.2.5 Combining amplitude pairsA.2.6 Amplitudes as colored bars
B.1 The Bloch sphereB.2 Building any gate from Hadamard and phase gatesB.2.1 Example: The Z gateB.2.2 Example: The X gate
C.1 Additional strategies for pair selection in PythonC.1.1 Recognizing pairs by checking the digit for the target qubitC.1.2 Generating pairs by concatenating the prefix, target, and suffix

Content preview from Building Quantum Software with Python

8 Using the quantum Fourier transform

This chapter covers

Introducing the discrete sinc distribution and phased discrete sinc quantum states
Using the IQFT to find the encoded frequency of periodic quantum states
Using the QFT to encode some trigonometric distributions in quantum states

Now that we understand what happens when the quantum Fourier transform (QFT) and inverse QFT (IQFT) are applied to a quantum state, let’s look at how we can use them. We will look at examples of two of the most common uses of the QFT: converting difference in phase to difference in magnitude and efficiently preparing some useful quantum states.

In the previous chapter, we saw how to encode a certain frequency into a quantum state in the form of a geometric ...