Variational Quantum Eigensolver (VQE)A hybrid algorithm that finds molecular ground state energies by iteratively optimizing a parameterized quantum circuit using classical feedback.
QAOAQuantum Approximate Optimization Algorithm - a hybrid method for solving combinatorial optimization problems using alternating quantum operations.
AnsatzA parameterized quantum circuit template used in variational algorithms, whose parameters are optimized by a classical computer.
Cost FunctionA mathematical function that quantifies how good a particular solution is, which the hybrid algorithm seeks to minimize or maximize.
Barren PlateauA phenomenon where the gradient of the cost function vanishes exponentially with the number of qubits, making classical optimization extremely difficult.
Classical OptimizerThe classical algorithm (like COBYLA, Adam, or L-BFGS) that adjusts the quantum circuit parameters based on measurement results.
Circuit DepthThe number of sequential gate layers in a quantum circuit, directly affecting computation time and noise accumulation.
Gate SynthesisThe decomposition of complex quantum operations into sequences of elementary gates native to specific hardware.
TranspilationConverting a quantum circuit to satisfy hardware constraints including native gate sets and qubit connectivity.
Error MitigationTechniques to reduce the impact of noise on quantum computations without full quantum error correction, such as zero-noise extrapolation.
Noise ModelA mathematical description of the errors affecting a quantum processor, including gate errors, measurement errors, and decoherence.
ConvergenceThe process of the optimization algorithm approaching the optimal solution, measured by the decreasing difference between successive iteration results.
Measurement ShotsThe number of times a quantum circuit is executed and measured to build up statistics for estimating expectation values.
Ground State EnergyThe lowest possible energy of a quantum system, which VQE algorithms aim to find for molecular simulation applications.
Qubit ConnectivityThe physical layout of connections between qubits on a quantum processor, determining which two-qubit gates can be performed directly.
Hardware-Efficient AnsatzA parameterized circuit design that uses only gates native to the target hardware and respects its qubit connectivity, minimizing transpilation overhead.
COBYLAConstrained Optimization BY Linear Approximations - a gradient-free classical optimizer commonly used in VQE that works well with noisy quantum measurements.
MaxCut ProblemA graph theory optimization problem asking for the maximum number of edges between two groups of vertices, commonly used to benchmark QAOA.
HamiltonianA mathematical operator describing the total energy of a quantum system, whose ground state VQE algorithms seek to find.
Variational PrincipleThe quantum mechanical principle that the expectation value of the Hamiltonian for any trial state is always greater than or equal to the true ground state energy.
Gradient DescentA classical optimization algorithm that iteratively adjusts parameters in the direction of steepest decrease of the cost function.
Expectation ValueThe average result of measuring a quantum observable over many repeated measurements of identically prepared quantum states.
FidelityA measure of how close two quantum states are to each other, ranging from 0 (orthogonal) to 1 (identical).
Pauli DecompositionExpressing a Hamiltonian as a weighted sum of tensor products of Pauli matrices, enabling measurement on quantum hardware.
Quantum VolumeA metric combining qubit count, connectivity, and gate fidelity to measure the overall capability of a quantum processor.
Quantum AdvantageA demonstration that a quantum computer solves a practical problem faster or more efficiently than any classical computer.
Adiabatic TheoremA principle stating that a quantum system remains in its ground state if external conditions change slowly enough, the basis for quantum annealing.