Abstract: A computing system can be configured to determine a quantum circuit architecture, for a quantum computer, based on a physical system comprising a plurality of fermions. The computing system can comprise a classical computing system configured to: receive a reference quantum state for the physical; receive a cut-off energy; determine a Fermionic Unitary Operator based on a parameter dependent Fermionic operator, wherein the parameter dependent Fermionic operator comprises a sum of products of: an operator string with a parameter for the operator string. Each operator string of the sum of products has a transition energy less than the cut-off energy. The quantum circuit architecture can be based on the Fermionic Unitary Operator.

Abstract: A computing system can be configured to determine a compressed quantum circuit architecture, for a quantum computer, based on a point-symmetry group of a physical system. The computing system can comprise a classical computer operatively coupled to the quantum computer. The classical computer can be configured to transmit a symmetrized-unitary operator to the quantum computer to enable configuration of the compressed quantum circuit architecture and application of the compressed quantum circuit architecture to a quantum memory containing a first quantum basis state of the physical system stored in a plurality of qubits. The first quantum basis state transforms according to a first irreducible representation of the point-symmetry group.