A method for simulating a physical system of electrons, the method performed by a system comprising: quantum hardware, comprising: a plurality of qubits indexed according to a canonical ordering, a plurality of single qubit gates, and a plurality of two qubit gates; and one or more classical processors, the method comprising: transforming, by the one or more classical processors, a Hamiltonian describing the physical system of electrons into a qubit Hamiltonian describing a corresponding system of qubits using a Jordan Wigner transformation, the qubit Hamiltonian comprising a transformed kinetic energy operator; simulating, by the quantum hardware, evolution of the physical system under the Hamiltonian by performing evolution of the system of qubits under the qubit Hamiltonian, comprising simulating the evolution of the physical system under a kinetic energy operator included in the Hamiltonian by performing evolution of the system of qubits under the transformed kinetic energy operator by applying a quantum circuit to the system of qubits, wherein the quantum circuit comprises a plurality of fermionic simulation gates, wherein each fermionic simulation gate is indexed by a different index p, wherein each fermionic simulation gate is configured to simultaneously i) evolve the system of qubits under the operator X p X p +1 + Y p Y p +1 for a time φ, where X p represents a Pauli- X operator applied to qubit p and Y p represents a Pauli- Y operator applied to qubit p, ii) evolve the system of qubits under the operator Z p Z p +1 for a time θ, where Z p represents a Pauli- Z operator applied to qubit p and iii) apply a fermionic swap gate to qubits p and q = p + 1, the fermionic swap gate given by f swap = JordanWigner f swap p, q = 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 − 1:. and using, by the one or more classical processors, the simulated evolution of the system of qubits under the qubit Hamiltonian to determine properties of the physical system of electrons, wherein the properties of the physical system comprise an energy of the physical system of electrons. transforming, by the one or more classical processors, a Hamiltonian describing the physical system of electrons into a qubit Hamiltonian describing a corresponding system of qubits using a Jordan Wigner transformation, the qubit Hamiltonian comprising a transformed kinetic energy operator; simulating, by the quantum hardware, evolution of the physical system under the Hamiltonian by performing evolution of the system of qubits under the qubit Hamiltonian, comprising simulating the evolution of the physical system under a kinetic energy operator included in the Hamiltonian by performing evolution of the system of qubits under the transformed kinetic energy operator by applying a quantum circuit to the system of qubits, wherein the quantum circuit comprises a plurality of fermionic simulation gates, wherein each fermionic simulation gate is indexed by a different index p, wherein each fermionic simulation gate is configured to simultaneously i) evolve the system of qubits under the operator X p X p +1 + Y p Y p +1 for a time φ, where X p represents a Pauli- X operator applied to qubit p and Y p represents a Pauli- Y operator applied to qubit p, ii) evolve the system of qubits under the operator Z p Z p +1 for a time θ, where Z p represents a Pauli- Z operator applied to qubit p and iii) apply a fermionic swap gate to qubits p and q = p + 1, the fermionic swap gate given by f swap = JordanWigner f swap p, q = 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 − 1:. and i) evolve the system of qubits under the operator X p X p +1 + Y p Y p +1 for a time φ, where X p represents a Pauli- X operator applied to qubit p and Y p represents a Pauli- Y operator applied to qubit p, ii) evolve the system of qubits under the operator Z p Z p +1 for a time θ, where Z p represents a Pauli- Z operator applied to qubit p and iii) apply a fermionic swap gate to qubits p and q = p + 1, the fermionic swap gate given by f swap = JordanWigner f swap p, q = 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 − 1:. and using, by the one or more classical processors, the simulated evolution of the system of qubits under the qubit Hamiltonian to determine properties of the physical system of electrons, wherein the properties of the physical system comprise an energy of the physical system of electrons.