公开(公告)号：US20240296367A1

公开(公告)日：2024-09-05

申请号：US18381765

申请日：2023-10-19

Applicant: Google LLC

Inventor： Nicholas Charles Rubin ,  Andrew Zhao

IPC: G06N10/60 ,  G06F17/16

CPC classification number: G06N10/60 ,  G06F17/16

Abstract: Methods, systems, and apparatus for solving quadratic optimization problems over orthogonal groups using quantum computing. In one aspect, a method includes receiving data representing a quadratic optimization problem, wherein decision variables of the quadratic optimization problem take values in an orthogonal group or a special orthogonal group; encoding the quadratic optimization problem as a quantum Hamiltonian, the encoding comprising using a Clifford algebra representation of the group to map orthogonal matrices or special orthogonal matrices in the group to respective quantum states in a Hilbert space; determining an approximate eigenstate of the quantum Hamiltonian; computing expectation values of Pauli operators with respect to the approximate eigenstate, wherein the Pauli operators comprise operators obtained by mapping multiplication operations of the Clifford algebra into the Hilbert space; and rounding the expectation values of the Pauli operators to elements of the orthogonal group to obtain a solution to the quadratic optimization problem.