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The adiabatic theorem states that a quantum system will stay in its ground state if the Hamiltonian that governs it changes slowly enough. Example: Evolution of a quantum annealer's Hamiltonian from an initial easy-to-prepare ground state to the final problem Hamiltonian.

Quantum fluctuations are temporary changes in energy at a point in space, which allow quantum annealing to overcome local minima. Example: Fluctuations that assist in exploring various states of the qubits during annealing.

The Ising Model is a mathematical model used in quantum annealing to represent magnetic spin interactions. Example: Representing a combinatorial optimization problem in a quantum annealer.

Superposition is the ability of a quantum system to be in multiple states simultaneously. Example: Quantum bits in a quantum annealer initially representing all possible solutions.

The annealing schedule is the controlled process by which quantum annealing progresses from the initial Hamiltonian to the problem Hamiltonian. Example: Varying the transverse magnetic field over time in a quantum annealer.

Quantum coherence characterizes the ability of a quantum system to exhibit interference effects due to phase relationships between quantum states. Example: Maintaining qubit states during the annealing process.

Quantum tunneling allows quantum annealers to bypass local minima and reach the global minimum by transitioning through energy barriers, not possible in classical systems. Example: Escaping a local minimum in an energy landscape.

A qubit is the fundamental unit of quantum information, analogous to a classical bit but can be in a state of 0, 1, or a superposition of both. Example: Representing solutions in a quantum annealer.

The ground state is the lowest energy state of a quantum system, and the goal in quantum annealing is to reach the ground state that corresponds to the optimal solution. Example: The solution state for an optimization problem in quantum annealing.

Quantum error correction involves protocols to protect quantum information from errors due to decoherence and other quantum noises. Example: Methods used in quantum annealers to maintain solution fidelity despite errors.

Entanglement is a quantum phenomenon where pairs or groups of particles cannot be described independently of the state of the others. Example: Correlated qubit states in quantum annealing.

The transverse field is applied to quantum bits to induce superposition and tunneling during the quantum annealing process. Example: Creating a non-commuting Hamiltonian to kick off the annealing process.

Decoherence is the loss of quantum coherence, where the system transitions from a quantum to a classical state, often detrimental to quantum annealing. Example: A quantum annealer losing its superposition capabilities due to interaction with the environment.

Quantum annealing is a quantum computing method used to find the global minimum of an objective function over a given set of candidate solutions by utilizing quantum fluctuations. Example: Finding the ground state of a spin glass system.