Hybrid Monte Carlo Without Pseudofermions
  We introduce a dynamical fermion algorithm which is based on the hybrid Monte Carlo (HMC) algorithm, but without pseudofermions. The molecular dynamics steps in HMC are retained except the derivatives with respect to the gauge fields are calculated with the $Z_2$ noise. The determinant ratios are estimated with the Pa\`{d}e - $Z_2$ method. Finally, we use the Kennedy-Kuti linear accept/reject method for the Monte Carlo step which is shown to respect detailed balance. We comment on the comparison of this algorithm with the pseudofermion algorithm. 
K. F. Liu, S. J. Dong and C. Thron