Quantum computing

A model of computation that encodes information in quantum states and transforms it with quantum operations. It can outperform classical methods on certain problems, but offers no general speedup for every computation.

Qubit: A two-level quantum system used as the basic unit of quantum information. Its superposition and measurement behavior distinguish quantum bits from classical bits.
Shor's algorithm: A quantum algorithm that factors integers and computes discrete logarithms in polynomial time. It threatens widely used public-key cryptography if sufficiently large fault-tolerant computers exist.
Quantum mechanics: The physical theory describing matter and energy at atomic and subatomic scales. Quantum computing relies on the theory’s rules for states, operations, and measurement.
Classical computing: Computation using information represented by classical bits and processed by classical devices. It is the baseline against which quantum algorithms and hardware are evaluated.
Quantum gate: A reversible operation that transforms one or more qubits. Quantum circuits compute by applying sequences of these operations.
Grover's algorithm: A quantum search algorithm that finds a marked item among N possibilities using order √N queries. Its quadratic speedup illustrates a broad but limited form of quantum advantage.
Linear algebra: The mathematics of vectors, matrices, and linear transformations. Quantum states are represented by vectors, while gates act as matrices.
Quantum annealing: A quantum optimization approach that seeks low-energy solutions by evolving a physical system. It uses a specialized computational strategy rather than the general gate model.
Quantum circuit: A computational model representing qubits and their ordered quantum gates. It makes an algorithm’s sequence of state transformations explicit.
Quantum simulation: The use of a controllable quantum system to model another quantum system. Simulating quantum matter is a natural target because classical descriptions can grow prohibitively large.

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