Abstract: The present invention relates to methods and systems for enumerating and generating relatively low cost mappings from fermionic operators to qubits. The method identifies a set including every Pauli operator implementable on the quantum information processor and assigns a first fermionic operator to a first Pauli operator. The method then assigns a Pauli operator to each subsequent fermionic operator in a manner which respects commutation relations and/or anticommutation relations in the set of fermionic operators. The method iterates through the set of fermionic operators until a complete mapping is found. The method also includes applying a cost model to partial or complete mappings to decide which Pauli operator from a set of legitimate candidates is the preferred Pauli operator for assigning to the fermionic operator.

Abstract: A method of simulating condensed matter systems on quantum computers includes reducing the Hamiltonian of the system to adapt it to being implementable on a given quantum computer. Part of this adaptation is identifying an active space and associated degrees of freedom within the active space. This effective Hamiltonian is provided a localised representation to assist in reducing the depth of the quantum circuit which used to simulate the system. The quadratic and quartic interaction matrix and coefficients between modes of the localised Hamiltonian are calculated and the modes of the localised Hamiltonian are encoded onto the qubits of the quantum computer. Qubit interactions corresponding to interactions between modes of the localised Hamiltonian are implemented between the qubits and the resulting state is measured to extract a simulation of the active space of the effective Hamiltonian.