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.

公开(公告)号：US20220067567A1

公开(公告)日：2022-03-03

申请号：US17464278

申请日：2021-09-01

Applicant: Google LLC

Inventor： Thomas Eugene O`Brien ,  Ryan Babbush ,  Nicholas Charles Rubin ,  Jarrod Ryan McClean

IPC: G06N10/00 ,  G06F5/01 ,  G06F17/16

Abstract: Methods, systems, and apparatus for verified quantum phase estimation. In one aspect, a method includes repeatedly performing a experiment. Performing one repetition of the experiment includes: applying a second unitary to a system register of N qubits prepared in a target computational basis state; applying, conditioned on a state of a control qubit, a first unitary to the system register; applying an inverse of the second unitary to the system register and measuring each qubit to determine an output state of the system register; measuring the control qubit to obtain a corresponding measurement result m; and post-selecting on the target computational basis state by, in response to determining that the output state indicates that each qubit was in the target computational basis state prior to measurement, incrementing a first or second classical variable by (−1)m. Phases or expectation values of the first unitary are estimated based on the classical variables.

公开(公告)号：US20230030423A1

公开(公告)日：2023-02-02

申请号：US17867182

申请日：2022-07-18

Applicant: Google LLC

Inventor： Nicholas Charles Rubin ,  Ryan Babbush

IPC: G06N10/20

Abstract: Methods, systems and apparatus for preparing a target quantum state of a quantum system, where the target quantum state is stationary with respect to a parameterized many-body qubit operator. In one aspect a method includes preparing an initial quantum state as an input state for a first iteration; iteratively evolving the initial quantum state and subsequent input quantum states as inputs for subsequent iterations until an approximation of the target stationary quantum state is obtained, comprising, for each iteration: computing, by quantum computation, parameter values of the many-body qubit operator for the iteration; computing, by quantum computation, an evolution time for the iteration, comprising evaluating changes in elements of a 2-RDM for the iteration; and evolving the initial quantum state or the subsequent input quantum state for the iteration using the computed parameter values and evolution time to generate a subsequent input quantum state for the subsequent iteration.

公开(公告)号：US20220019931A1

公开(公告)日：2022-01-20

申请号：US17428189

申请日：2020-02-14

Applicant: Google LLC

Inventor： Zhang Jiang ,  Ryan Babbush ,  Jarrod Ryan McClean ,  Nicholas Charles Rubin

IPC: G06N10/00 ,  G06F17/16 ,  G06F9/455

Abstract: Methods, systems and apparatus for simulating physical systems. In one aspect, a method includes the actions of selecting a first set of basis functions for the simulation, wherein the first set of basis functions comprises an active and a virtual set of orbitals; defining a set of expansion operators for the simulation, wherein expansion operators in the set of expansion operators approximate fermionic excitations in an active space spanned by the active set of orbitals and a virtual space spanned by the virtual set of orbitals; performing multiple quantum computations to determine a matrix representation of a Hamiltonian characterizing the system in a second set of basis functions, computing, using the determined matrix representation of the Hamiltonian, eigenvalues and eigenvectors of the Hamiltonian; and determining properties of the physical system using the computed eigenvalues and eigenvectors.