Glossary
Short definitions and deeper explanations for the concepts used across the course.
A two-level quantum state used as the basic unit of quantum information.
A qubit is represented by amplitudes over a chosen basis, not by a hidden classical bit. Its state supports phase and interference effects.
Example: |ψ⟩ = α|0⟩ + β|1⟩ with |α|² + |β|² = 1.
Related: basis state, superposition, probability amplitude
A vector used as a reference element of a basis for state expansion.
For one qubit in the computational basis, the basis states are |0⟩ and |1⟩. Any pure state is a linear combination of them.
Related: computational basis, qubit
The standard qubit basis {|0⟩, |1⟩} used for digital-style measurement.
Most introductory circuits and measurements are described in the computational basis. Other bases are possible and change observed distributions.
Related: basis state, measurement
A coherent linear combination of basis states.
Superposition is not classical uncertainty. Relative phase between amplitudes affects later interference outcomes.
Example: |+⟩ = (|0⟩ + |1⟩)/√2.
Related: probability amplitude, relative phase, interference
A complex coefficient in a state expansion whose magnitude squared gives probability.
Amplitudes carry both magnitude and phase. The phase part does not appear directly as probability but governs interference.
Related: superposition, relative phase, born rule
Phase difference between amplitudes of basis components.
Relative phase changes how amplitudes combine after gates. Two states with equal probabilities can still evolve differently.
Related: global phase, interference, hadamard gate
A uniform phase factor multiplying the whole state.
Multiplying |ψ⟩ by e^{iγ} leaves all measurement statistics unchanged. Global phase is physically unobservable in isolated state descriptions.
Related: relative phase, probability amplitude
A geometric representation of single-qubit pure states up to global phase.
Points on the sphere encode relative amplitude and phase. Gate actions can often be interpreted as rotations on this sphere.
Example: |0> is the north pole and |1> is the south pole.
Related: global phase, relative phase, quantum gate
A basis-dependent process that returns a classical outcome from a quantum state.
Measurement probabilities follow the Born rule. Post-measurement state depends on the observed outcome and basis used.
Example: Measuring α|0⟩ + β|1⟩ in the computational basis yields 0 with |α|².
Related: computational basis, born rule
Rule mapping amplitudes to measurement probabilities.
For projective measurement in a basis, each outcome probability is the squared magnitude of the corresponding amplitude component.
Related: measurement, probability amplitude
A unitary operation applied to one or more qubits.
Gates transform state vectors reversibly (until measurement). Algorithms are built by composing many such operations.
Related: hadamard gate, pauli x gate
A single-qubit gate that maps basis states into equal superpositions.
H introduces and resolves interference structure. The sign difference in H|1⟩ is crucial for algorithmic behavior.
Example: H|0> = (|0> + |1>)/sqrt(2).
Related: superposition, relative phase, interference
A bit-flip gate exchanging |0⟩ and |1⟩.
The Pauli-X gate is the quantum analog of NOT on computational basis states, though on superpositions it acts linearly on all components.
Example: X(α|0⟩ + β|1⟩) = α|1⟩ + β|0⟩.
Related: quantum gate, computational basis
A non-separable multi-qubit state with correlations not reducible to independent parts.
Entangled systems cannot be described as products of single-qubit states. Their joint amplitudes encode correlations across subsystems.
Related: interference, quantum circuit
Constructive or destructive combination of amplitudes under evolution.
Interference determines which outcomes are amplified or suppressed in an algorithm, making phase control computationally meaningful.
Example: Applying H twice can recover deterministic outcomes due to interference.
Related: relative phase, hadamard gate
