fix bug in hadamard test where counts was empty, add deuteron test using hadamard test and lambdas

#include <qcor_hadamard_test>

int main() {

  // Create the Deuteron Hamiltonian

  auto H = 5.907 - 2.1433 * X(0) * X(1) - 2.1433 * Y(0) * Y(1) + .21829 * Z(0) -

           6.125 * Z(1);

  for (auto x : linspace(-constants::pi, constants::pi, 10)) {

    auto terms = H.getNonIdentitySubTerms();

    double sum = H.getIdentitySubTerm()->coefficient().real();

    for (auto term : terms) {

      auto pop = std::dynamic_pointer_cast<PauliOperator>(term);

      assert(pop && pop->nTerms() == 1);

      auto [zv, xv] = pop->toBinaryVectors(2);

      auto sp = qpu_lambda(

          [](qreg q) {

            X(q.head());

            Ry(q.tail(), x);

            X::ctrl(q.tail(), q.head());

          },

          x);

      auto l = qpu_lambda(

          [](qreg q) {

            for (auto [i, x_val] : enumerate(xv)) {

              auto z_val = zv[i];

              if (x_val == z_val && x_val == 1) {

                Y(q[i]);

              } else if (x_val == 1) {

                X(q[i]);

              } else if (z_val == 1) {

                Z(q[i]);

              }

            }

          },

          xv, zv);

      auto val = qcor::hadamard_test(sp, l, 2);

      sum += pop->coefficient().real() * val;

    }

    print("E(", x, ") = ", sum);

  }

}

 No newline at end of file

  auto q = qalloc(n_state_qubits + 1);

  __quantum_hadamard_test(q, state_prep, unitary);

  // Compute <psi|U|psi>

  // First make sure we have counts, 

  // if not, grab exp-val-z key in buffer

  auto counts = q.counts();

  if (counts.empty()) {

    return q.results()->getExpectationValueZ();

  }

  // We have counts, so use that

  double count1 = (double)q.counts().find("1")->second;

  double count2 = (double)q.counts().find("0")->second;

  return std::fabs((count1 - count2) / (count1 + count2));