QubitThe fundamental unit of quantum information, a two-level quantum system that can exist in a superposition of |0> and |1> with complex probability amplitudes.
Bloch SphereA unit sphere in three dimensions used to geometrically represent the pure state of a single qubit, where the north and south poles correspond to |0> and |1> respectively.
SuperpositionThe quantum mechanical principle that a quantum system can exist in a linear combination of multiple basis states simultaneously, collapsing to a definite state only upon measurement.
EntanglementA quantum correlation between two or more qubits where the quantum state of the composite system cannot be described independently for each qubit, famously called 'spooky action at a distance' by Einstein.
Hadamard GateA single-qubit quantum gate that creates an equal superposition: H|0> = (|0>+|1>)/sqrt(2) and H|1> = (|0>-|1>)/sqrt(2). Geometrically, it is a 180-degree rotation about the X+Z axis on the Bloch sphere.
Pauli X GateThe quantum NOT gate that flips |0> to |1> and vice versa. On the Bloch sphere, it is a 180-degree rotation about the X-axis.
Pauli Y GateA single-qubit gate that performs a 180-degree rotation about the Y-axis on the Bloch sphere, combining bit-flip and phase-flip operations.
Pauli Z GateA single-qubit gate that applies a phase flip: Z|0> = |0> and Z|1> = -|1>. On the Bloch sphere, it is a 180-degree rotation about the Z-axis.
CNOT GateControlled-NOT gate, a two-qubit gate that flips the target qubit if and only if the control qubit is |1>. Essential for creating entanglement and implementing quantum algorithms.
Probability AmplitudeA complex number whose squared modulus gives the probability of measuring a particular outcome. Unlike classical probabilities, amplitudes can interfere constructively or destructively.
MeasurementThe process of observing a quantum system, which causes the state to collapse from a superposition to a definite basis state with probability determined by the squared amplitude.
Quantum GateA unitary operation applied to qubits that transforms the quantum state in a reversible way, analogous to logic gates in classical computing but operating on continuous state spaces.
FidelityA measure of how close two quantum states are, ranging from 0 (orthogonal) to 1 (identical). Used to benchmark quantum operations and characterize noise in quantum devices.
Hilbert SpaceThe mathematical space of all possible quantum states, a complex vector space with an inner product. For n qubits, it is a 2^n-dimensional complex Hilbert space.
Unitary MatrixA complex matrix U satisfying U*U_dagger = I (identity), representing reversible quantum operations. All quantum gates and time evolution are described by unitary matrices.
Bell StateOne of four maximally entangled two-qubit states that form a basis for two-qubit Hilbert space, fundamental to quantum teleportation, superdense coding, and entanglement-based quantum protocols.
Quantum CircuitA sequence of quantum gates applied to qubits, representing a quantum computation as a diagram that flows from left to right, analogous to classical logic circuit diagrams.
Quantum TeleportationA protocol that transfers a quantum state from one qubit to another using shared entanglement and classical communication, without physically transmitting the qubit.
No-Cloning TheoremA fundamental result in quantum mechanics proving that it is impossible to create an identical copy of an arbitrary unknown quantum state, a cornerstone of quantum cryptography.
Born RuleThe rule that the probability of measuring a particular outcome is the squared modulus of the corresponding probability amplitude, connecting the mathematical formalism of quantum states to observable predictions.
Quantum RegisterA collection of qubits that together form a multi-qubit quantum state, used to encode the input and output of quantum algorithms. An n-qubit register exists in a 2^n-dimensional Hilbert space.
PhaseThe argument (angle) of a complex probability amplitude, which influences interference effects but does not affect the measurement probability of a single qubit. Global phases are unobservable; relative phases are physically meaningful.
T GateA single-qubit gate that applies a phase of pi/4 to the |1> state, essential for achieving universal quantum computation when combined with Hadamard and CNOT gates.
Quantum Error CorrectionTechniques for protecting quantum information from noise and decoherence by encoding logical qubits in multiple physical qubits, detecting and correcting errors without measuring the quantum state directly.
Toffoli GateA three-qubit gate (controlled-controlled-NOT) that flips the target qubit only when both control qubits are |1>. Universal for classical reversible computation and useful in quantum error correction.
Quantum Process TomographyThe experimental characterization of a quantum operation (gate or channel) by applying it to a set of known input states and performing state tomography on the outputs, reconstructing the full process matrix.
Schmidt DecompositionA way to express any pure bipartite quantum state as a sum of products of orthonormal states, revealing the entanglement structure. The number of non-zero Schmidt coefficients measures the entanglement dimension.
Quantum FidelityThe overlap between two quantum states, F(rho, sigma) = (Tr sqrt(sqrt(rho) sigma sqrt(rho)))^2, measuring how close an experimentally prepared state is to the target state. A fidelity of 1 means perfect agreement.