One technique relates to reducing qubits needed on a quantum computer. A fermion system is characterized as a Hamiltonian. The fermion system includes fermions and fermion modes with a total of 2M fermion modes. The Hamiltonian has a parity symmetry coded by spin-up and spin-down parity operators. Fermion modes are ordered so that the first half of the 2M modes corresponds to the spin-up and the second half of the 2M modes to the spin-down. The Hamiltonian and the parity operators are transformed using a Fermion-Qubit mapping that transforms parity operators into a first single-qubit Pauli operator on a qubit M and into a second single-qubit Pauli operator on a qubit 2M , The qubit M to which the first single-qubit Pauli operator was applied and the qubit 2M to which the second single-qubit Pauli operator was applied are removed
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