Quantum device simulation using natural-orbital basis

A method of simulating a quantum device using a computing device, the method comprising:

• receiving a single-particle Hamiltonian matrix that describes an initial Hamiltonian operator, wherein the initial Hamiltonian operator models a plurality of parts of the quantum device;
• based at least in part on the single-particle Hamiltonian matrix, estimating a reduced density matrix associated with a first part of the plurality of parts;
• estimating a plurality of eigenvectors and the corresponding plurality of eigenvalues of the reduced density matrix;
• generating a transformed Hamiltonian matrix associated with the first part, wherein:
• generating the transformed Hamiltonian matrix includes transforming the single-particle Hamiltonian matrix into a natural-orbital basis of the first part such that the transformed Hamiltonian matrix has a reduced dimensionality relative to the single-particle Hamiltonian matrix;
• the natural-orbital basis is spanned by a subset of the plurality of eigenvectors of the reduced density matrix;
• and
• the eigenvectors included in the subset respectively have a predetermined number of largest eigenvalues among the corresponding plurality of eigenvalues of the reduced density matrix, or have respective eigenvalues with magnitudes above an eigenvalue magnitude threshold;
• generating an estimated solution to a Schrödinger equation that includes the transformed Hamiltonian matrix;
• and
• outputting the estimated solution to one or more additional computing processes.

A computing device comprising:

• a processor configured to simulate a quantum device at least in part by:
• at a Hamiltonian estimation module, receiving a single-particle Hamiltonian matrix that describes an initial Hamiltonian operator, wherein the initial Hamiltonian operator models a plurality of parts of the quantum device;
• at a Hamiltonian transformation module:
• based at least in part on the single-particle Hamiltonian matrix, estimating a many-body ground state for the plurality of parts, wherein estimating the many-body ground state includes estimating a plurality of single-particle eigenstates of the single-particle Hamiltonian matrix;
• based at least in part on the many-body ground state, computing a reduced density matrix for the first part;
• estimating a plurality of eigenvalues and a corresponding plurality of eigenvectors of the reduced density matrix;
• generating a part-specific down-folding matrix for the first part, wherein the part-specific down-folding matrix encodes a transformation into a natural-orbital vector space of the first part spanned by the subset of the plurality of eigenvectors of the reduced density matrix;
• generating, from the part-specific down-folding matrix, a global down-folding matrix associated with one or more parts of the plurality of parts including the first part;
• and
• transforming the single-particle Hamiltonian matrix into the natural-orbital basis by multiplying a conjugate transpose of the global down-folding matrix by the single-particle Hamiltonian matrix and by the global down-folding matrix to obtain the transformed Hamiltonian matrix;
• and
• at a solver:
• generating an estimated solution to a Schrödinger equation that includes the transformed Hamiltonian matrix;
• and
• outputting the estimated solution to one or more additional computing processes.