Reference
Glossary
Terminology from every tutorial, in one alphabetical reference. Click any entry with a linked tutorial to jump into the deep dive.
A
- Amplitude
- The complex coefficient of a basis state in a quantum superposition; its squared magnitude is the Born-rule probability. → See: Born rule
- Amplitude amplification
- Generalized form of Grover's algorithm that boosts the amplitude of any 'good' subspace from sin θ to near 1 in O(1/√p) iterations. → See: Grover tutorial
- Ancilla
- A helper qubit introduced to make an otherwise irreversible computation reversible, then (usually) uncomputed back to |0⟩ for reuse.
- Ansatz
- A parameterized quantum circuit used as a variational model — e.g., in VQE, QAOA, or QML classifiers. → See: VQE
B
- Barren plateau
- A pathology of variational quantum algorithms: gradients vanish exponentially with qubit count, making optimization intractable.
- Bell state
- One of the four maximally entangled two-qubit states (|Φ±⟩, |Ψ±⟩). The 'hello world' of entanglement. → See: Entanglement
- Bloch sphere
- Geometric representation of a single-qubit state as a point on the surface of a unit sphere.
- Born rule
- The postulate that the probability of measuring outcome |x⟩ from |ψ⟩ = Σ αx|x⟩ equals |αx|².
C
- Clifford gate
- A gate in the group generated by H, S, and CNOT. Circuits made entirely of Clifford gates are efficiently classically simulable (Gottesman-Knill).
- CNOT / CX
- Controlled-NOT — flips the target qubit iff the control is |1⟩. The canonical two-qubit entangling gate.
- Coherence time (T₁, T₂)
- T₁ is energy-relaxation time; T₂ is dephasing time. T₂ ≤ 2T₁ always. Set the maximum useful circuit depth on real hardware. → See: Noise & decoherence
D
- Density matrix (ρ)
- A positive-semidefinite trace-1 operator generalizing state vectors to mixed states. Rank 1 ⇔ pure state.
- Dequantization
- Producing a classical algorithm matching a quantum algorithm's asymptotic complexity — e.g., Ewin Tang's recommendation-system result (2018). → See: Is QML worth it?
E
- Eigenstate
- A state |ψ⟩ such that U|ψ⟩ = λ|ψ⟩ for some scalar λ. For unitary U, |λ| = 1.
- Entanglement
- A quantum state that cannot be written as a tensor product of single-qubit states. The resource behind most quantum speedups. → See: Entanglement tutorial
- Error correction (QEC)
- Encoding one logical qubit into many physical qubits so errors can be detected and fixed. Surface code is the dominant scheme. → See: Surface code
F
- Fault-tolerant quantum computing (FTQC)
- Regime where QEC suppresses logical error rate exponentially with code distance. Requires per-operation error below the threshold (~1% for surface code).
- Fidelity
- A measure of how close two quantum states or operations are. 1 = identical; 0 = orthogonal. Gate error = 1 − fidelity.
G
- Grover's algorithm
- Quantum unstructured search in O(√N) queries, provably optimal. → See: Grover tutorial
H
- Hadamard (H)
- Maps |0⟩ → |+⟩ and |1⟩ → |−⟩. The gate that creates superposition out of basis states.
- Harvest now, decrypt later
- Attack model: adversary records encrypted traffic today and decrypts it once a Shor-capable quantum computer exists. Motivates near-term PQC migration. → See: PQC threat model
J
- Jordan-Wigner transformation
- Standard mapping from fermion creation/annihilation operators to Pauli strings on qubits, used in quantum chemistry simulations.
K
- Ket (|ψ⟩)
- Dirac notation for a state vector in a complex Hilbert space.
- Kraus operators
- A decomposition of a quantum channel ε(ρ) = Σ Kk ρ Kk† with Σ Kk†Kk = I. The general language of noisy quantum evolution.
L
- Logical qubit
- A qubit encoded across many physical qubits using an error-correcting code. The surface code uses ~d² physical qubits for one logical qubit at distance d.
M
- Magic state distillation
- Process for preparing low-error T-eigenstates (ancillas for non-Clifford gates) by sacrificing many noisy ones. Dominant cost in fault-tolerant computing.
- Measurement basis
- The set of eigenstates against which a measurement projects. Z-basis = {|0⟩, |1⟩}; X-basis = {|+⟩, |−⟩}; Y-basis = {|i⟩, |−i⟩}.
- ML-DSA (FIPS 204)
- NIST-standardized lattice-based digital signature — replaces RSA/ECDSA/Ed25519.
- ML-KEM (FIPS 203)
- NIST-standardized lattice-based key encapsulation — replaces RSA/ECDH in PQC migrations. → See: ML-KEM in practice
N
- NISQ
- Noisy Intermediate-Scale Quantum era — roughly 50-10,000 qubits without full error correction (Preskill 2018). Today.
O
- Oracle
- A black-box unitary Uf |x⟩|y⟩ = |x⟩|y ⊕ f(x)⟩ that lets a quantum algorithm query a Boolean function f reversibly.
P
- Parameter-shift rule
- Exact identity for derivatives of expectation values in parameterized circuits: ∂⟨H⟩/∂θ = ½[⟨H⟩θ+π/2 − ⟨H⟩θ−π/2]. Makes gradient-based QML training work on real hardware.
- Pauli matrices
- The three 2×2 matrices X, Y, Z that generate all single-qubit rotations and form the backbone of quantum error-correction stabilizer codes.
- Phase estimation (QPE)
- Recovers the eigenvalue phase φ of a unitary given an eigenvector, using O(1/ε) controlled applications to reach precision ε. → See: QFT + QPE
- Phase kickback
- When an oracle acts on |−⟩ in the target register, the output f(x) appears as a phase (−1)^{f(x)} on the input register. Central to Deutsch-Jozsa, Grover, Shor.
- Post-quantum cryptography (PQC)
- Cryptographic primitives (lattice, code, hash, isogeny based) believed secure against quantum computers with Shor's algorithm.
- Projector
- An operator P with P² = P, corresponding to a measurement outcome; for |φ⟩, P = |φ⟩⟨φ|.
Q
- QFT — Quantum Fourier Transform
- The quantum analog of the discrete Fourier transform, implemented in O(n²) gates. The engine of Shor, QPE, and many algorithms. → See: QFT tutorial
- Qubit
- The quantum unit of information: α|0⟩ + β|1⟩ with |α|² + |β|² = 1.
S
- Shor's algorithm
- Factors N-bit integers in time polynomial in N, using quantum phase estimation on a modular-exponentiation unitary. → See: Shor tutorial
- Stabilizer
- A Pauli operator that leaves a codeword unchanged. Surface codes are defined by mutually commuting X- and Z-stabilizers.
- Superposition
- A linear combination α|0⟩ + β|1⟩ (or higher-dimensional analog) of basis states. → See: Superposition tutorial
- Surface code
- 2D topological error-correcting code on a qubit lattice with local stabilizer measurements. Current experimental leader (see Willow).
T
- T gate
- The π/8 phase gate. Non-Clifford. Its count (T-count) dominates fault-tolerant-circuit cost.
- Threshold theorem
- Below a code-dependent physical error threshold (~1% for surface code), increasing code distance reduces logical error rate exponentially.
- Toffoli (CCNOT)
- Three-qubit reversible AND gate. Universal for classical reversible computation; costs 6 CNOTs + 7 T-gates in the surface code.
U
- Unitary
- A linear operator U with U†U = UU† = I. Every non-measurement quantum operation is a unitary.
V
- VQE
- Variational Quantum Eigensolver — hybrid classical/quantum algorithm for estimating ground-state energies of quantum systems. → See: VQE tutorial
W
- Willow
- Google's 105-qubit superconducting chip (Dec 2024) — first experimental demonstration of below-threshold surface-code error correction. → See: Surface code + Willow
Y
- Y2Q
- Shorthand for the quantum apocalypse — the year a Shor-capable quantum computer breaks RSA. Commonly used in PQC migration planning.