A topological quantum error correction code that arranges physical qubits in a 2D lattice. It's the leading approach for fault-tolerant quantum computing with a threshold error rate of ~1%.

A quantum state where a particle exists in multiple states simultaneously. For qubits, this means being in a combination of |0⟩ and |1⟩ at the same time, described as |ψ⟩ = α|0⟩ + β|1⟩ where α and β are complex amplitudes.

A quantum algorithm for integer factorization that runs in polynomial time O((log N)³), exponentially faster than the best known classical algorithm. It threatens RSA encryption.

The basic unit of quantum information. Unlike a classical bit (0 or 1), a qubit can exist in a superposition of both |0⟩ and |1⟩ states simultaneously, enabling quantum parallelism.

The demonstration that a quantum computer can solve a problem that is practically infeasible for classical computers. Google claimed this in 2019 with their Sycamore processor.

A basic quantum operation that acts on qubits. Quantum gates are represented by unitary matrices and transform qubit states. Common gates include Hadamard (H), Pauli-X/Y/Z, CNOT, and Toffoli gates.

A single-qubit quantum gate that creates superposition. It transforms |0⟩ to (|0⟩+|1⟩)/√2 and |1⟩ to (|0⟩-|1⟩)/√2. Represented by matrix H = (1/√2)[[1,1],[1,-1]].

A quantum search algorithm that finds an item in an unsorted database in O(√N) time, compared to O(N) classically. It provides a quadratic speedup for search problems.

A quantum phenomenon where two or more particles become correlated such that the state of one cannot be described independently of the other, regardless of the distance separating them.

The loss of quantum coherence (superposition and entanglement) due to interaction with the environment. Decoherence is the primary challenge in building practical quantum computers.

The Controlled-NOT gate is a two-qubit quantum gate that flips the target qubit if and only if the control qubit is |1⟩. It's essential for creating entanglement.

A geometrical representation of a single qubit's state as a point on a unit sphere. The north pole represents |0⟩, the south pole |1⟩, and equatorial points are equal superpositions.