What you will learn in Building Quantum Software with Python
A developer’s guide
Chapter by chapter
Concepts explained in this book
- quantum stateA quantum state is the mathematical description of a quantum system that specifies the amplitudes and therefore the probabilities of its possible measurement outcomes.
- quantum amplitudeA quantum amplitude is a complex-valued coefficient of a quantum state whose squared magnitude determines an outcome probability and whose phase carries directional information.
- inverse quantum Fourier transformThe inverse quantum Fourier transform is the inverse unitary transformation of the quantum Fourier transform, mapping frequency-encoded amplitudes back to the corresponding computational-basis representation.
- probability theoryAn outcome probability is the probability assigned to a particular measurement outcome or specified combination of outcomes.
- quantum measurementQuantum measurement is the process of obtaining a classical outcome from a quantum system according to its state's probabilities, generally changing the state.
- quantum gateA single-qubit gate is a quantum gate whose transformation acts on one qubit.
- quantum oracleA quantum oracle is a computational subroutine that recognizes or marks states satisfying a specified condition.
- Hadamard gateThe Hadamard gate is a single-qubit quantum gate that transforms computational-basis states into equal-weight superpositions with relative phase differences.
- quantum computingQuantum computing, or quantum computation, is computation that exploits quantum-mechanical states and operations to process information.
- value registerA value register is a quantum register that encodes output values corresponding to function inputs.
- phaseWave phase is the horizontal or angular offset that specifies the position of a periodic waveform within its cycle.
- good outcomeA good outcome is an outcome that a quantum oracle recognizes or marks as satisfying its specified condition.
- Grover optimizerA Grover optimizer is a hybrid optimization algorithm that uses Grover adaptive search to seek an optimal solution.
- inversion operatorAn inversion operator is a quantum transformation that reflects amplitudes about their average value, equivalently the inversion-by-the-mean operation used in Grover search.
- amplitude amplificationAmplitude amplification is a quantum algorithmic technique that increases the probability of measuring states marked as desirable by an oracle.
- quantum Fourier transformThe quantum Fourier transform is a quantum algorithm that applies the Fourier transform to amplitudes of a quantum state, converting encoded phase relationships into measurable amplitude patterns.
- function encodingA function-encoding circuit is a quantum circuit that maps encoded function inputs to corresponding encoded function outputs in quantum registers.
- quantum phase estimationA phase estimation circuit is a quantum circuit that generates a phase-encoded state from an eigenstate and a unitary transformation for estimating an eigenvalue phase.
- state tableA state table is a tabular visualization that lists quantum-state outcomes and associated information such as probabilities.
- eigenvalueAn eigenvalue is the scalar by which a transformation multiplies an associated eigenstate, and for a quantum circuit it is a complex number of magnitude one.
- eigenvectorAn eigenstate, or eigenvector, is a nonzero state vector that a transformation maps to a scalar multiple of itself.
- quantum superpositionSuperposition is a quantum state formed by combining multiple possible basis-state outcomes before measurement.
- qubit systemA multi-qubit system is a quantum system composed of two or more qubits whose joint state can be represented and measured.
- quantum bitA qubit, or quantum bit, is the fundamental unit of quantum information and can exist in a superposition of two computational-basis states.
- phase gateThe Z gate is a single-qubit quantum gate that multiplies the amplitude of the one basis state by negative one.
- frequencyFrequency is the rate at which a periodic signal repeats its pattern, or the corresponding index in a discrete Fourier representation.
- Grover iterateA Grover iteration is one application of a Grover operator within a quantum search procedure.
- quantum parallelismQuantum parallelism is the ability of a quantum instruction to perform corresponding elementary operations simultaneously across many affected value pairs.
- bit oracleA bit oracle is a quantum oracle that marks satisfying inputs by changing an output bit or target qubit.
- samplingSampling is the process of generating outcomes according to a specified probability distribution.
- iteration scheduleAn iteration schedule is a rule or sequence specifying the numbers of Grover-operator iterations tried during an adaptive search.
- knapsack problemThe knapsack problem is an optimization problem that selects items with given weights and values to maximize total value without exceeding a weight capacity.
- key registerA key register is a quantum register whose computational-basis value represents the key in an encoded key-value pair.
- Grover's algorithmGrover’s algorithm is a quantum search algorithm that provides a quadratic speedup for finding a marked item in an unstructured search space.
- estimation registerAn estimation register is a quantum register whose measured outcomes encode an estimate computed by a quantum estimation algorithm.
- multi-qubit stateA multi-qubit state is the quantum state of a system containing multiple qubits, represented by one complex amplitude for each possible outcome.
- butterfly patternA butterfly pattern is a computational pattern that recombines pairs of values with a formula to produce updated values.
- target qubitA target qubit is the qubit position whose differing bit values determine which quantum-state amplitudes are paired for recombination.
- Bell stateA Bell state is one of four maximally entangled two-qubit quantum states with correlated measurement outcomes and equal probabilities for two basis states.
- phased discrete sinc stateA phased discrete sinc state is a quantum state whose computational-basis amplitudes follow a discretely sampled sinc profile with associated phase progression.
- bitA binary digit is a digit whose value is either 0 or 1 and that represents one position in a binary number.
- product stateA product state is a composite quantum state that can be expressed as the combination of independent states of its constituent qubits.
- quantum circuitA quantum circuit is an ordered representation of quantum gates, measurements, and related operations applied to qubits.
- Grover adaptive searchGrover adaptive search is a hybrid quantum-classical search technique that varies the number of Grover-operator iterations according to a schedule when the number of desired outcomes is unknown.
- geometric sequence stateA geometric sequence state is a quantum state whose amplitude phases follow a geometric progression associated with a signal frequency.
- quantum entanglementQuantum entanglement is a quantum correlation in which a composite system's state cannot be represented as independent states of its constituent systems.
- probability distributionA probability distribution is a function assigning probabilities to possible outcomes, with the probabilities summing to one.
- Fourier basisA Fourier basis state is a normalized quantum state whose amplitudes form a geometric sequence associated with a particular frequency index.
- quantum amplitude estimationQuantum amplitude estimation is a quantum algorithm that estimates the probability or count associated with marked outcomes by estimating a rotation angle of a Grover operator.
- hybrid approachA hybrid algorithm combines classical and quantum computation in a single procedure, typically using classical processing to guide repeated quantum computations.
- target registerA target register is a quantum register containing the qubits whose marked outcomes are being counted or amplitude-estimated.
- control qubitA control qubit is a qubit whose state conditionally determines whether or how a controlled quantum operation acts on another qubit.
- binary stringA binary string is a finite sequence of symbols drawn from the binary alphabet, typically 0 and 1.
- quantum systemA quantum system is a physical system described by a quantum state and subject to quantum evolution and measurement.
- discrete Fourier transformThe discrete Fourier transform is a mathematical operation that converts a finite sequence of discrete signal samples into its frequency components.
- quantum operationA quantum operation is a transformation that changes the state of one or more qubits.
- state collapseState collapse is the post-measurement transition in which the measured outcome has probability one and all other outcomes have probability zero.
- sinusoidal functionA sinusoid is a waveform described by a sine or cosine function and characterized by a frequency and phase.
- QuantumRegisterA quantum register is a grouped collection of qubits used to represent a multi-bit quantum value or variable.
- nonproduct stateA nonproduct state is a composite quantum state that cannot be expressed as a product of independent states of its constituent qubits.
- x gateThe X gate is a single-qubit quantum gate that swaps the amplitudes associated with the two computational-basis outcomes.
- periodic quantum stateA periodic quantum state is a quantum state whose amplitude pattern repeats periodically across computational-basis outcomes.
- controlled quantum operationA multicontrolled transformation is a quantum transformation applied to a target qubit only when every specified control qubit has the required control value.
- controlled phase gateA controlled phase gate is a controlled quantum gate that applies a phase rotation to a target state conditional on the control state.
- table comprehensionA table comprehension is a tabular representation of quantum-state values corresponding to the entries generated by a state expression.
- rotational gateA Y rotation gate is a single-qubit quantum gate that rotates a qubit's state by an angle about the Y axis of the Bloch sphere.
- HumeHume is the educational Python quantum-computing simulator developed for this book.
- quantum countingQuantum counting is an amplitude-estimation application that estimates the number of solutions or marked outcomes in a search space.
- quantum computerA quantum computer, or quantum computing system, is a machine that processes information using quantum-mechanical states and operations.
- Fourier transformA Fourier transform is a mathematical operation that represents a signal or function in terms of its frequency components.
- quantum supremacyQuantum advantage is a performance improvement on a computational task that a quantum computer achieves over available classical approaches.
- default quantum stateA default quantum state is the all-zero computational-basis state used as the initial state before quantum operations are applied.
- rz gateThe RZ gate is a single-qubit quantum gate that rotates the zero and one amplitudes in opposite directions by half of a specified angle.
- Y gateThe Y gate is a single-qubit quantum gate that rotates the two amplitudes in opposite quarter turns and then swaps them.
- raised cosine distributionA raised cosine distribution is a bounded continuous probability distribution whose density follows a shifted and scaled cosine curve over a finite interval.
- computational basisThe computational basis is the standard basis of quantum states formed from basis states corresponding to definite bit-string outcomes.
- controlled-X gateA controlled-X gate is a controlled quantum gate that applies the X gate to a target qubit when its control condition is satisfied.
- phase shiftA phase shift is an angular change in the phase of a periodic or complex-valued quantity.
- uniform distributionA uniform distribution is a probability distribution that assigns equal probability to every possible outcome.
- weight registerA weight register is a quantum register that stores the weight associated with an encoded item selection.
- QiskitQiskit is an open-source software development kit for constructing, simulating, compiling, and executing quantum circuits.
- binary representationA binary representation expresses a value using digits or states based on the two-element binary system.
- selection registerA selection register is a quantum register whose qubits encode whether corresponding items are included in a selection.
- sound waveA sound wave is a mechanical wave that propagates through a medium and can be perceived as sound.
- Fibonacci sequenceThe Fibonacci sequence is the sequence whose successive terms are formed by adding the two preceding terms, conventionally starting with 0 and 1.
- golden ratioThe irrational number equal to (1 + √5) / 2, approached by ratios of consecutive Fibonacci numbers.
- grid stateA grid state is a two-dimensional visual arrangement of quantum-state outcomes in rows and columns, often used to display selection and encoded-value coordinates.
- state vectorA state vector is an ordered list of complex amplitudes representing a quantum state in a chosen basis.
- binary decompositionBinary decomposition expresses an integer as the sum of powers of two selected by the positions of its one-valued binary digits.
- two's complementTwo's complement is a signed binary representation in which the leading bit distinguishes nonnegative values from negative values and an m-bit string represents values from −2^(m−1) through 2^(m−1)−1.
- inverse Fourier transformThe inverse discrete Fourier transform is the mathematical operation that reconstructs a discrete signal from its frequency components.
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