A method for simulating a physical system, the physical system comprising a system of electrons, the method comprising: transforming, using one or more classical processors, a Hamiltonian describing the physical system into a qubit Hamiltonian describing a corresponding system of qubits by applying a Jordan-Wigner transformation, wherein: the qubit Hamiltonian comprises a transformed kinetic energy operator comprising one or more operators that act on multiple non-adjacent qubits; and the system of qubits is arranged as a one dimensional chain of qubits with nearest neighbour interactions; simulating, using quantum hardware, evolution of the system of qubits under the qubit Hamiltonian, comprising simulating the evolution of the system of qubits under the transformed kinetic energy operator by applying a fermionic swap network to the system of qubits, the fermionic swap network comprising multiple layers of fermion swap gates; 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, wherein simulating the evolution of the system of qubits under the transformed kinetic energy operator using the fermionic swap network comprises sequentially applying each of the multiple layers of fermionic swap gates to the system of qubits to change a canonical ordering of the qubits until the canonical ordering is reversed and each index has been adjacent to all others once, wherein sequentially applying each of the multiple layers of fermionic swap gates to the system of qubits to change the canonical ordering of the qubits comprises indexing the qubits by the canonical ordering from 1 to N and sequentially applying: fermionic swap gates between odd numbered qubits and even numbered qubits to the right; and fermionic swap gates between even numbered qubits and odd numbered qubits to the right, wherein a fermionic swap gate acting on qubit p and qubit q=p+1 is 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. transforming, using one or more classical processors, a Hamiltonian describing the physical system into a qubit Hamiltonian describing a corresponding system of qubits by applying a Jordan-Wigner transformation, wherein: the qubit Hamiltonian comprises a transformed kinetic energy operator comprising one or more operators that act on multiple non-adjacent qubits; and the system of qubits is arranged as a one dimensional chain of qubits with nearest neighbour interactions; the qubit Hamiltonian comprises a transformed kinetic energy operator comprising one or more operators that act on multiple non-adjacent qubits; and the system of qubits is arranged as a one dimensional chain of qubits with nearest neighbour interactions; simulating, using quantum hardware, evolution of the system of qubits under the qubit Hamiltonian, comprising simulating the evolution of the system of qubits under the transformed kinetic energy operator by applying a fermionic swap network to the system of qubits, the fermionic swap network comprising multiple layers of fermion swap gates; 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, wherein simulating the evolution of the system of qubits under the transformed kinetic energy operator using the fermionic swap network comprises sequentially applying each of the multiple layers of fermionic swap gates to the system of qubits to change a canonical ordering of the qubits until the canonical ordering is reversed and each index has been adjacent to all others once, wherein sequentially applying each of the multiple layers of fermionic swap gates to the system of qubits to change the canonical ordering of the qubits comprises indexing the qubits by the canonical ordering from 1 to N and sequentially applying: fermionic swap gates between odd numbered qubits and even numbered qubits to the right; and fermionic swap gates between even numbered qubits and odd numbered qubits to the right, wherein a fermionic swap gate acting on qubit p and qubit q=p+1 is 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.