A technique relates to reducing qubits required on a quantum computer. A Fermionic system is characterized in terms of a Hamiltonian. The Fermionic system includes Fermions and Fermionic modes with a total number of 2M Fermionic modes. The Hamiltonian has a parity symmetry encoded by spin up and spin down parity operators. Fermionic modes are sorted such that the first half of 2M modes corresponds to spin up and the second half of 2M modes corresponds to spin down. The Hamiltonian and the parity operators are transformed utilizing a Fermion to qubit mapping that transforms parity operators to a first single qubit Pauli operator on a qubit M and a second single qubit Pauli operator on a qubit 2M. The qubit M having been operated on by the first single qubit Pauli operator and the qubit 2M having been operated on by the second single qubit Pauli operator are removed.