Glossary

Quantum Computing Glossary

Plain-English definitions of 22 quantum computing terms. From qubit to quantum supremacy, no math degree required.

Written by

Sohum Thakkar

CEO, Qolour · Ex-Apple, Ex-QCWare · UC Berkeley

Reviewed by academic advisors

John Preskill · Richard P. Feynman Professor of Theoretical Physics

Iordanis Kerenidis · Director

Yasser Omar · Professor

Qubit(Quantum bit): The fundamental unit of quantum information. Unlike a classical bit (which is 0 or 1), a qubit can be in a superposition of 0 and 1 simultaneously. Physically, a qubit can be made from a superconducting circuit, a trapped ion, a photon, or any other two-level quantum system.
Superposition: The ability of a quantum system to exist in a combination of multiple states at once. A qubit in superposition is neither 0 nor 1 — it has a probability amplitude for each. When measured, the superposition collapses to a single classical outcome with probability determined by the amplitudes.
Entanglement: A quantum correlation between two or more particles such that their states cannot be described independently. Measuring one entangled particle instantly determines the result of measuring the other, even at large distances. Entanglement is the resource that powers quantum teleportation, quantum key distribution, and many quantum algorithms.
Bloch sphere: A geometric representation of a single qubit's state as a point on the surface of a 3D sphere. The north pole represents |0⟩, the south pole represents |1⟩, and every other point represents a superposition. The Bloch sphere is the most common visualization tool in quantum computing education.
Quantum gate: An operation that transforms the state of one or more qubits. Quantum gates are reversible (unlike most classical logic gates) and are represented by unitary matrices. Common gates include the Hadamard (H), Pauli-X/Y/Z, CNOT, and rotation gates Rx, Ry, Rz.
Quantum circuit: A sequence of quantum gates applied to qubits, ending in measurement. Quantum circuits are the lowest-level abstraction for programming a quantum computer — they're the quantum equivalent of an assembly-language program.
Measurement: The act of reading out the classical state of a qubit. Measurement causes a qubit's superposition to collapse to either 0 or 1, with probabilities given by the squared amplitudes of the quantum state. Once a qubit is measured, the original superposition is destroyed.
Born rule: The rule that gives the probability of measuring a particular outcome from a quantum state. If a qubit is in state α|0⟩ + β|1⟩, the probability of measuring 0 is |α|², and the probability of measuring 1 is |β|². Named after Max Born, who won the 1954 Nobel Prize for it.
Decoherence: The process by which a quantum system loses its quantum properties (superposition and entanglement) due to interaction with its environment. Decoherence is the main obstacle to building large-scale quantum computers — qubits must be isolated from heat, vibration, and stray electromagnetic fields to maintain their quantum state.
Quantum error correction(QEC): A set of techniques for protecting quantum information from decoherence and gate errors by encoding a single logical qubit into many physical qubits. Common codes include the Shor code, Steane code, and the surface code.
Hadamard gate(H gate): A single-qubit gate that creates an equal superposition. Applied to |0⟩, it produces (|0⟩ + |1⟩)/√2. The Hadamard gate is the workhorse of quantum algorithms and appears at the start of nearly every quantum circuit.
CNOT gate(Controlled-NOT): A two-qubit gate that flips the second (target) qubit if and only if the first (control) qubit is in state |1⟩. CNOT is the most common entangling gate and, combined with single-qubit rotations, is universal for quantum computing.
Bell state: One of four maximally entangled two-qubit states. The four Bell states form a basis for the two-qubit Hilbert space and are the simplest examples of entanglement. Generated by applying a Hadamard gate followed by a CNOT.
Quantum supremacy(Quantum advantage): The point at which a quantum computer can solve a problem that no classical computer can solve in any reasonable amount of time. Google claimed quantum supremacy in 2019 with the Sycamore processor on a random circuit sampling task.
Shor's algorithm: A quantum algorithm developed by Peter Shor in 1994 that factors large integers exponentially faster than the best known classical algorithm. Shor's algorithm threatens RSA cryptography and is one of the key motivators for post-quantum cryptography.
Grover's algorithm: A quantum algorithm developed by Lov Grover in 1996 that searches an unsorted database of N items in O(√N) operations, quadratically faster than the best classical algorithm. Used as a subroutine in many other quantum algorithms.
BB84: The first quantum key distribution protocol, invented by Charles Bennett and Gilles Brassard in 1984. BB84 lets two parties share a secret encryption key with security guaranteed by the laws of physics — any eavesdropper is necessarily detected.
CHSH inequality: A mathematical inequality (Clauser–Horne–Shimony–Holt) that any classical theory must satisfy. Quantum mechanics violates the CHSH inequality, and experimental violations prove that the universe cannot be described by local hidden variables. The 2022 Nobel Prize was awarded for verifying this experimentally.
NISQ(Noisy Intermediate-Scale Quantum): A term coined by John Preskill describing the current era of quantum computing: hundreds to thousands of qubits, but with significant noise and no full error correction. NISQ devices include IBM's Eagle and Heron processors and IonQ's trapped-ion machines.
Quantum teleportation: A protocol for transmitting an unknown quantum state from one location to another using a shared entangled pair and two classical bits of communication. Despite the name, no matter or energy is teleported — only quantum information.
Wave function: A mathematical description of the quantum state of a system. The wave function contains all the information needed to compute the probabilities of every possible measurement outcome via the Born rule.
Pauli operators(Pauli matrices): A set of three single-qubit gates (X, Y, Z) named after Wolfgang Pauli. X is the quantum analog of NOT (it flips |0⟩ ↔ |1⟩), Y combines a flip and a phase, and Z flips the phase of |1⟩. Together with the identity, they form a basis for all single-qubit operations.

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