Quantum Mechanics Glossary
Plain-language definitions for every term used across the platform. Each entry is linkable — share /glossary#term to drop someone directly on the definition.
39 terms across 4 categories.
Concept
- amplitude
- A complex number (with magnitude and phase) attached to each possible measurement outcome. Square the magnitude to get the probability. The phase determines how amplitudes interfere with each other.
- basis
- A complete set of reference states used to describe the system. |0⟩ and |1⟩ form the computational basis. Changing basis changes which questions look simple — the physics doesn't change.
- bloch sphere
- A geometric picture of a single-qubit state as a point on the surface of a sphere. North pole = |0⟩, south pole = |1⟩. Any quantum gate is a rotation on this sphere.
- born rule
- The rule connecting amplitude to probability: P(outcome) = |amplitude|². The bridge between abstract quantum math and what you actually observe.
- decoherence
- The process by which a quantum system loses its superposition due to unwanted interaction with the environment — gradually turning quantum behavior into classical-looking behavior.
- eigenstate
- A special state of an operator that doesn't change direction when the operator acts on it — only its magnitude scales by a number called the eigenvalue. Measurement results correspond to eigenvalues of the observable.
- eigenvalue
- The number an eigenstate gets multiplied by when an operator acts on it. For a physical observable, eigenvalues are the possible measurement results.
- entanglement
- A quantum correlation between two or more systems that can't be described by separate independent states. Measuring one instantly determines the other's outcome — regardless of distance.
- hilbert space
- The mathematical space of all possible quantum states for a system. For one qubit it is 2-dimensional; for n qubits, 2ⁿ-dimensional.
- interference
- When amplitudes from different paths combine — adding up (constructive) or canceling (destructive) — changing outcome probabilities. The core mechanism behind quantum speedup.
- measurement
- The act of extracting a classical result from a quantum system. Irreversibly collapses a superposition to one definite outcome, with probabilities given by the Born rule.
- observable
- Any physical quantity that can be measured — position, momentum, energy, spin along an axis. Represented by a Hermitian operator; its eigenvalues are the only possible measurement results.
- operator
- A mathematical transformation that acts on quantum states. Physical observables are represented by special operators called Hermitian operators whose eigenvalues are the possible measurement outcomes.
- phase
- The 'direction' part of a complex amplitude. Doesn't change measurement probabilities directly, but determines whether amplitudes add up (constructive interference) or cancel (destructive interference).
- phase kickback
- A quantum trick where applying a controlled gate causes the eigenvalue's phase to 'kick back' onto the control qubit instead of changing the target. It is the key mechanism behind many quantum algorithms.
- quantum state
- A complete mathematical description of a quantum system — a recipe that specifies the amplitude (and therefore probability) of every possible measurement outcome.
- qubit
- The basic unit of quantum information: a two-level quantum system that can be in any superposition of |0⟩ and |1⟩. The quantum analog of a classical bit.
- spin
- An intrinsic angular momentum carried by quantum particles. Unlike everyday spinning, it has only discrete values (e.g. +½ or −½ for electrons). Spin is the physical basis for many qubit implementations.
- superposition
- A quantum system being in a combination of multiple states at once, described by a sum of amplitudes. Not 'secretly one or the other' — a genuinely new kind of description that collapses to one outcome when measured.
- teleportation
- A protocol that transfers a quantum state from one qubit to another using entanglement and classical communication. No physical particle moves — only the state information is transferred.
- uncertainty
- Heisenberg's result: incompatible observables (like position and momentum) can't both have definite values simultaneously. Not a measurement limitation — a fundamental property of quantum states.
- unitary
- A transformation that preserves total probability. All quantum gates are unitary — they rotate the state vector without losing normalization.
- wavefunction
- Another name for the quantum state, often written ψ(x,t). Squaring its magnitude at any point gives the probability density of finding a particle there.
Quantum gate
- cnot
- A two-qubit gate that flips the target qubit when the control qubit is |1⟩. When the control is in superposition, CNOT creates entanglement between the two qubits.
- hadamard
- A quantum gate that creates a 50/50 superposition from a definite state. It is the most common starting point in quantum circuits because it opens the door to interference.
- pauli-x
- A quantum gate that swaps |0⟩ and |1⟩ — the quantum version of a NOT gate. Also called a bit-flip gate.
- pauli-z
- A quantum gate that flips the sign of the |1⟩ amplitude without changing measurement probabilities. The effect is hidden until a later gate reveals it through interference.
- quantum gate
- An operation that transforms a qubit's state. Every quantum gate is reversible and preserves total probability. Gates are the building blocks of quantum circuits.
- toffoli
- A three-qubit gate that flips the target only when both control qubits are |1⟩. It acts as a reversible AND gate and is used in quantum error correction and arithmetic.
Experiment or setup
- bell state
- One of four maximally entangled two-qubit states. The simplest example of entanglement: each qubit alone looks random, but together they are perfectly correlated.
- double-slit experiment
- A landmark experiment where particles are sent through two narrow slits. An interference pattern forms on the screen — evidence that quantum mechanics uses amplitudes, not just probabilities.
- ghz state
- A maximally entangled state of three or more qubits. Like a Bell state but with more qubits — measuring any one instantly determines all the others.
- quantum circuit
- A sequence of quantum gates applied to qubits, read left to right. It is the standard way to describe a quantum computation — analogous to a classical logic circuit.
- quantum computer
- A machine that processes information using qubits instead of classical bits. It exploits superposition, entanglement, and interference to solve certain problems faster than any classical computer.
Algorithm
- deutsch-jozsa
- One of the first quantum algorithms to show a clear advantage over classical computing. It determines whether a function is constant or balanced using a single evaluation.
- grover's algorithm
- A quantum search algorithm that finds a target in an unsorted list using roughly √N steps instead of N. It provides a quadratic speedup over brute-force classical search.
- quantum algorithm
- A step-by-step procedure designed to run on a quantum computer. Quantum algorithms use interference to amplify correct answers and suppress wrong ones.
- quantum fourier transform
- A quantum version of the classical Fourier transform that runs exponentially faster. It is the key subroutine inside Shor's algorithm for factoring large numbers.
- shor's algorithm
- A quantum algorithm that factors large numbers exponentially faster than any known classical method. It threatens current encryption and is a major motivation for building quantum computers.