SHADOW HAMILTONIAN SIMULATION USING A QUANTUM COMPUTER

    公开(公告)号:US20250053849A1

    公开(公告)日:2025-02-13

    申请号:US18785890

    申请日:2024-07-26

    Applicant: Google LLC

    Abstract: Methods, systems, and apparatus for quantum simulation of a quantum system. In one aspect, a method includes, for an observable generated from a set of observables, wherein a commutator of each observable in the set of observables with the first Hamiltonian is equal to a combination of observables in the set of observables: encoding, by a quantum computer, a vector of coefficients of a time-dependent representation of the observable in a quantum state of a register of qubits; simulating, by the quantum computer, time evolution of the quantum state under a second Hamiltonian to obtain an evolved quantum state, wherein the second Hamiltonian comprises a matrix of complex weights in the linear combination of observables; measuring, by the quantum computer, the evolved quantum state; and post-processing, by a classical processor, obtained measurement results to obtain an expectation value of the observable.

    Plane wave dual basis for quantum simulation

    公开(公告)号:US12153645B2

    公开(公告)日:2024-11-26

    申请号:US18313051

    申请日:2023-05-05

    Applicant: Google LLC

    Inventor: Ryan Babbush

    Abstract: Methods, systems and apparatus for simulating quantum systems. In one aspect, a method includes the actions of obtaining a first Hamiltonian describing the quantum system, wherein the Hamiltonian is written in a plane wave basis comprising N plane wave basis vectors; applying a discrete Fourier transform to the first Hamiltonian to generate a second Hamiltonian written in a plane wave dual basis, wherein the second Hamiltonian comprises a number of terms that scales at most quadratically with N; and simulating the quantum system using the second Hamiltonian.

    Operator averaging within quantum computing systems

    公开(公告)号:US12147492B2

    公开(公告)日:2024-11-19

    申请号:US18049207

    申请日:2022-10-24

    Applicant: Google LLC

    Inventor: Ryan Babbush

    Abstract: Methods, systems and apparatus for estimating an expectation value of a quantum mechanical observable. In one aspect, a method includes identifying a first operator associated with the observable, wherein the first operator comprises a linear combination of terms. One or more constraints on expectation values of one or more of the terms in the linear combination are determined. A second operator is defined, wherein the second operator comprises a combination of the first operator and one or more of the determined constraints. The expectation value of the quantum mechanical observable is estimated using the second operator.

    Majorana loop stabilizer codes for error correction of fermionic quantum simulations

    公开(公告)号:US12086685B2

    公开(公告)日:2024-09-10

    申请号:US17296160

    申请日:2019-12-17

    Applicant: Google LLC

    CPC classification number: G06N10/00 G06F15/16

    Abstract: Methods, systems and apparatus for error correction of fermionic quantum simulation. In one aspect, a method includes representing a fermionic system as a graph of vertices and edges, where each vertex represents a fermionic system fermionic mode and each edge represents an interaction between two respective fermionic modes; allocating a qubit to each edge in the graph to form a qubit system; determining qubit operators that satisfy a set of fermionic commutation and dependence relations, where the qubit operators are non-uniform with respect to the graph vertices; determining stabilizer operators corresponding to products of quadratic Majorana operators on respective loops in the graph, where a common eigenspace of the defined stabilizer operators defines a code subspace that encodes states of the fermionic system to be simulated; and simulating the fermionic system by evolving the qubit system under a qubit Hamiltonian that includes the determined qubit operators and stabilizer operators.

    TRAINING QUANTUM EVOLUTIONS USING SUBLOGICAL CONTROLS

    公开(公告)号:US20230134825A1

    公开(公告)日:2023-05-04

    申请号:US18147144

    申请日:2022-12-28

    Applicant: Google LLC

    Abstract: Methods, systems, and apparatus for training quantum evolutions using sub-logical controls. In one aspect, a method includes the actions of accessing quantum hardware, wherein the quantum hardware includes a quantum system comprising one or more multi-level quantum subsystems; one or more control devices that operate on the one or more multi-level quantum subsystems according to one or more respective control parameters that relate to a parameter of a physical environment in which the multi-level quantum subsystems are located; initializing the quantum system in an initial quantum state, wherein an initial set of control parameters form a parameterization that defines the initial quantum state; obtaining one or more quantum system observables and one or more target quantum states; and iteratively training until an occurrence of a completion event.

    FERMIONIC SIMULATION GATES
    17.
    发明申请

    公开(公告)号:US20220391740A1

    公开(公告)日:2022-12-08

    申请号:US17859349

    申请日:2022-07-07

    Applicant: Google LLC

    Inventor: Ryan Babbush

    Abstract: Methods, systems, and apparatus for simulating a physical system. A Hamiltonian describing the physical system is transformed into a qubit Hamiltonian describing a corresponding system of qubits, the qubit Hamiltonian comprising a transformed kinetic energy operator. The evolution of the system of qubits under the qubit Hamiltonian is simulated, including simulating the evolution of the system of qubits under the transformed kinetic energy operator by applying a fermionic swap network to the system of qubits. The simulated evolution of the system of qubits under the qubit Hamiltonian is used to determine properties of the physical system.

    PREPARING SUPERPOSITIONS OF COMPUTATIONAL BASIS STATES ON A QUANTUM COMPUTER

    公开(公告)号:US20210271477A1

    公开(公告)日:2021-09-02

    申请号:US17257895

    申请日:2019-07-03

    Applicant: Google LLC

    Abstract: Methods, systems and apparatus for preparing arbitrary superposition quantum states of a quantum register on a quantum computer, the quantum state comprising a superposition of L computational basis states. In one aspect, a register of log L qubits is prepared in a weighted sum of register basis states, where each register basis state indexes a corresponding quantum state computational basis state, and the amplitude of each register basis state in the weighted sum of register basis states is equal to the amplitude of the corresponding computational basis state in the superposition of L computational basis states. A unitary transformation that maps the register basis states to the corresponding L computational basis states is then implemented, including, for each index 1 to L, controlling, by the register of log L qubits, transformation of the quantum system register state for the index to the corresponding computational basis state for the index.

    PERFORMING UNITARY ITERATION AND INDEXED OPERATIONS

    公开(公告)号:US20210157781A1

    公开(公告)日:2021-05-27

    申请号:US16976368

    申请日:2019-04-19

    Applicant: Google LLC

    Abstract: Methods, systems and apparatus for performing indexed operations using a unary iteration quantum circuit. In one aspect, a method includes encoding an index value in an index register comprising index qubits; encoding the index value in a control register comprising multiple control qubits; and repeatedly computing and uncomputing the control qubits to perform, conditioned on the state of the control qubits, the operation on one or more target qubits corresponding to the index value, wherein during the encoding, computing and uncomputing: the multiple control qubits are made available in sequence, and the multiple control qubits correspond to a one-hot encoding of the encoded index value.

    Preparing superpositions of computational basis states on a quantum computer

    公开(公告)号:US12299538B2

    公开(公告)日:2025-05-13

    申请号:US17257895

    申请日:2019-07-03

    Applicant: Google LLC

    Abstract: Methods, systems and apparatus for preparing arbitrary superposition quantum states of a quantum register on a quantum computer, the quantum state comprising a superposition of L computational basis states. In one aspect, a register of log L qubits is prepared in a weighted sum of register basis states, where each register basis state indexes a corresponding quantum state computational basis state, and the amplitude of each register basis state in the weighted sum of register basis states is equal to the amplitude of the corresponding computational basis state in the superposition of L computational basis states. A unitary transformation that maps the register basis states to the corresponding L computational basis states is then implemented, including, for each index 1 to L, controlling, by the register of log L qubits, transformation of the quantum system register state for the index to the corresponding computational basis state for the index.

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