Method of performing a quantum computation

A computer-implemented method for representing a plurality of states conforming to a set of one or more constraints of an electronic structure when performing a quantum computation using a hybrid computer system comprising a quantum computer and a classical computer, the computer-implemented method comprising:

• using the classical computer to:
• identify a subspace of states conforming to a set of one or more constraints of the electronic structure;
• perform a linear bijective mapping between a plurality of states of the subspace of states and an unconstrained Hilbert space, wherein no constraints are enforced, the linear bijective mapping equalising a dimension of the unconstrained Hilbert space to a dimension of the subspace of states;
• and
• generate a representation of an electronic structure Hamiltonian in the unconstrained Hilbert space;
• and using the quantum computer to:
• generate a representation of the unconstrained Hilbert space comprising a plurality of qubits in a register of the quantum computer;
• and
• execute quantum circuits, based on the representation of the unconstrained Hilbert space on the quantum computer to calculate an expectation value in a Hamiltonian of at least one state belonging to the subspace of states conforming to the set of one or more constraints of the electronic structure.