using-nctssos

You can compute certified lower bounds for noncommutative polynomial optimization by constructing structured SDP relaxations via the moment-SOHS hierarchy using NCTSSoS.jl. This framework applies to quantum many-body physics and operator algebra analysis.

The moment-SOHS hierarchy solves noncommutative polynomial optimization problems by building increasingly tight semidefinite programming relaxations. It yields certified lower bounds for quantum ground-state energies and Bell inequalities.

Yes, you can use Clarabel or Mosek as compatible SDP backends for noncommutative optimization in Julia. The NCTSSoS.jl package requires Julia and a compatible SDP solver to solve the structured relaxations.

To calculate ground state energy lower bounds for a 1D Heisenberg spin chain, define the Pauli variables in Julia and pass the Hamiltonian to the polyopt solver within NCTSSoS.jl to compute certified energy bounds.

To scale semidefinite programming for complex quantum systems, leverage correlative and term sparsity alongside Wedderburn block-diagonalization. These techniques reduce computational complexity in noncommutative optimization relaxations.

You can recover optimal operators and states from noncommutative optimization through GNS reconstruction when the SDP relaxation is numerically exact. This enables precise state-polynomial recovery in quantum many-body analysis.