# Lie algebra generator pools

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.