# Variational Quantum Eigensolver

The work presents a modular benchmarking framework that independently pairs search-direction estimators for parameterized quantum circuits (parameter-shift, finite differences, SPSA, PGPE, observable-curvature preconditioning) with classical update rules (SGD, Adam, RMSprop), evaluating them on MaxCut QAOA, Iris classification, a binary-MNIST QCNN, and molecular-hydrogen VQE under 256-shot finite-sampling simulation plus selected case studies on a 156-qubit processor; results show the preferred update rule depends on the estimator and workload, and that peak and across-seed average performance often favor different configurations.

The work presents a modular benchmarking framework that independently pairs search-direction estimators for parameterized quantum circuits (parameter-shift, finite differences, SPSA, PGPE, observable-curvature preconditioning) with classical update rules (SGD, Adam, RMSprop), evaluating them on MaxCut QAOA, Iris classification, a binary-MNIST QCNN, and molecular-hydrogen VQE under 256-shot finite-sampling simulation plus selected case studies on a 156-qubit processor; results show the preferred update rule depends on the estimator and workload, and that peak and across-seed average performance often favor different configurations.

The authors introduce a general framework based on Lie-algebraic properties that maps a pool of Pauli operators to a binary matrix ΓA over F2, proves that pool completeness and minimality can be decided in polynomial O(N³) time via the rank and congruence relations of that matrix, uses it to construct minimal complete pools (MCPs), proposes MB-ADAPT-VQE (adding a batch of k operators per iteration) to cut measurement overhead and accelerate convergence in quantum chemistry, and extends the fixed-ansatz NI-DUCC-VQE method, previously limited to N≤14 qubits by the MCP construction bottleneck, to a 26-qubit H2O system.

The authors introduce a general framework based on Lie-algebraic properties that maps a pool of Pauli operators to a binary matrix ΓA over F2, proves that pool completeness and minimality can be decided in polynomial O(N³) time via the rank and congruence relations of that matrix, uses it to construct minimal complete pools (MCPs), proposes MB-ADAPT-VQE (adding a batch of k operators per iteration) to cut measurement overhead and accelerate convergence in quantum chemistry, and extends the fixed-ansatz NI-DUCC-VQE method, previously limited to N≤14 qubits by the MCP construction bottleneck, to a 26-qubit H2O system.