Added the deuteron example

IterativeQpeWorkflow::execute(const QuantumSimulationModel &model) {

  ham_converter.fromObservable(model.observable);

  auto stretchedObs = ham_converter.stretchObservable(model.observable);

  // std::cout << "Stretched Obs: " << stretchedObs->toString() << "\n";

  auto provider = xacc::getIRProvider("quantum");

  // Iterative Quantum Phase Estimation:

  // We're using XACC IR construction API here, since using QCOR kernels here

#include "qcor_qsim.hpp"

// Validate the ground-state energy of the Deuteron Hamiltonian operator by the

// iterative QPE procedure.

// Compile and run with:

/// $ qcor -qpu qpp IterativeQpeVqe.cpp

/// $ ./a.out

/// Ansatz to bring the state into an eigenvector state of the Hamiltonian.

/// This optimized ansatz was found by VQE.

__qpu__ void eigen_state_prep(qreg q) {

  X(q[0]);

  // Theta angle found by VQE.

  double opt_theta = 0.297113;

  auto exponent_op = X(0) * Y(1) - Y(0) * X(1);

  exp_i_theta(q, opt_theta, exponent_op);

}

int main(int argc, char **argv) {

  // Create Hamiltonian:

  auto H = 5.907 - 2.1433 * X(0) * X(1) - 2.143 * Y(0) * Y(1) + 0.21829 * Z(0) -

           6.125 * Z(1);

  auto problemModel =

      qsim::ModelBuilder::createModel(eigen_state_prep, H, 2, 0);

  // Instantiate an IQPE workflow.

  auto workflow =

      qsim::getWorkflow("iqpe", {{"time-steps", 8}, {"iterations", 8}});

  auto result = workflow->execute(problemModel);

  const double phaseValue = result.get<double>("phase");

  const double energy = result.get<double>("energy");

  std::cout << "Final phase = " << phaseValue << "\n";

  // Expect: ~ -1.7 (due to limited bit precision)

  std::cout << "Energy = " << energy << "\n";

  return 0;

}

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