Qubit order
q0 is the most-significant displayed bit unless a chapter explicitly declares a different external SDK convention.
For two qubits, |q0 q1> = |10> has state-vector index 2.Publication record
Quantum computing glossary
Precise definitions of qubits, amplitudes, gates, measurement, error correction, fault tolerance, compilation, and quantum evidence, linked to full explanations.
Notation used across the book
These conventions apply unless a chapter explicitly declares an external SDK or domain-specific alternative.
State vectors
State vectors are column vectors; gates multiply them from the left.
|psi_after> = U |psi_before>.Circuit time
Circuit diagrams run left to right. Algebraic operator products act right to left.
A circuit that applies H and then Z has state ZH|psi>.Inner product
The bra is conjugate-transposed, so <phi|psi> is conjugate-linear in its first argument and linear in its second.
<psi|psi> = 1 for a normalized pure state.Born probabilities
Measurement probabilities are squared magnitudes of amplitudes in the declared measurement basis.
If |psi> = alpha|0> + beta|1>, then P(1) = |beta|^2.Logarithms
log means base two in information and complexity contexts; ln denotes the natural logarithm.
n qubits span a vector space of dimension 2^n.Physical units
Physical quantities carry SI units or an explicitly named alternative. Rates and probabilities are never presented as interchangeable error metrics.
A 1 microsecond cycle time and a 0.1% error probability describe different dimensions.Complexity claims
Query complexity, logical gate count, circuit depth, physical-qubit count, wall time, and end-to-end runtime are reported separately.
O(sqrt(N)) oracle queries does not by itself establish an O(sqrt(N)) application runtime.Global phase
Pure states that differ only by a unit-magnitude global phase represent the same physical state; relative phase remains observable through interference.
|psi> and -|psi> are equivalent, but (|0>+|1>)/sqrt(2) and (|0>-|1>)/sqrt(2) are not.Numerical precision
Worked examples state rounding explicitly. Companion tests use exact expressions when practical and otherwise declare a tolerance.
The core simulator tests complex amplitudes to absolute tolerance 1e-12.AmplitudeBasisBloch sphereCircuit depthCoherenceControlled gateDensity matrixEntanglementError mitigationGate fidelityHamiltonianInterferenceLogical qubitMeasurementNISQObservableOraclePhysical qubitQubitQuantum advantageQuantum Fourier transformShotStabilizerSurface codeTranspilationUnitary
Amplitude
A complex number attached to a basis state. Probabilities come from squared magnitudes, so amplitudes can reinforce or cancel before measurement.
Read the working explanation →Basis
A set of mutually distinguishable states used to represent a quantum state and define a measurement.
Read the working explanation →Bloch sphere
A geometric representation of a pure one-qubit state, useful for seeing rotations, phase, and measurement axes.
Read the working explanation →Circuit depth
The number of sequential layers of operations after gates that can run together are grouped. Depth helps estimate exposure to noise.
Read the working explanation →Coherence
The preservation of phase relationships needed for interference. Environmental coupling degrades those relationships.
Read the working explanation →Controlled gate
An operation applied to one subsystem conditional on the state of another, such as CNOT.
Read the working explanation →Density matrix
A state representation that handles both pure states and classical uncertainty over quantum states.
Read the working explanation →Entanglement
A joint quantum state that cannot be factored into independent states for its subsystems.
Read the working explanation →Error mitigation
A family of techniques that estimates or reduces noise effects without encoding a fully error-corrected logical computation.
Read the working explanation →Gate fidelity
A measure of how closely an implemented operation matches its intended quantum operation under a stated protocol.
Read the working explanation →Hamiltonian
The operator that specifies a quantum system's energy and generates its time evolution.
Read the working explanation →Interference
The addition of amplitudes so some outcomes become more likely and others less likely. It is the mechanism algorithms must control.
Read the working explanation →Logical qubit
Encoded quantum information whose error rate is suppressed through repeated error detection and correction.
Read the working explanation →Measurement
A physical interaction that produces a classical outcome distributed according to a chosen measurement and the quantum state.
Read the working explanation →NISQ
A label for noisy, intermediate-scale quantum devices that lack full fault tolerance; the label does not by itself establish usefulness.
Read the working explanation →Observable
A Hermitian operator representing a measurable quantity; its eigenvalues are possible outcomes.
Read the working explanation →Oracle
An abstract operation that exposes a problem's structure through queries. Query speedups must still be connected to an implementable cost model.
Read the working explanation →Physical qubit
A quantum degree of freedom used by hardware. Many physical qubits may be needed for one reliable logical qubit.
Read the working explanation →Qubit
A controllable two-level quantum system whose state is described by two complex amplitudes subject to normalization and global-phase equivalence.
Read the working explanation →Quantum advantage
A demonstrated advantage over a relevant classical method on a specified task and metric; the claim is only as strong as its baseline and validation.
Read the working explanation →Quantum Fourier transform
The unitary Fourier transform on amplitudes. Its value comes from algorithms that can extract useful global structure without reading every amplitude.
Read the working explanation →Shot
One execution and measurement of a quantum circuit. Repeated shots estimate an outcome distribution or expectation value.
Read the working explanation →Stabilizer
An operator that leaves a state unchanged. Stabilizer measurements reveal error syndromes without directly measuring encoded logical information.
Read the working explanation →Surface code
A topological error-correcting code with local checks on a two-dimensional layout, studied because of its threshold and hardware locality.
Read the working explanation →Transpilation
The conversion of a logical circuit into operations, connectivity, and scheduling supported by a target device.
Read the working explanation →Unitary
A linear operation that preserves inner products and therefore total probability; closed-system quantum gates are represented this way.
Read the working explanation →