225 lines
10 KiB
Plaintext
225 lines
10 KiB
Plaintext
---
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title: PVQD
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description: API reference for qiskit.algorithms.PVQD
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in_page_toc_min_heading_level: 1
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python_api_type: class
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python_api_name: qiskit.algorithms.PVQD
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---
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# PVQD
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<Class id="qiskit.algorithms.PVQD" isDedicatedPage={true} github="https://github.com/qiskit/qiskit/tree/stable/0.23/qiskit/algorithms/time_evolvers/pvqd/pvqd.py" signature="PVQD(fidelity, ansatz, initial_parameters, estimator=None, optimizer=None, num_timesteps=None, evolution=None, use_parameter_shift=True, initial_guess=None)" modifiers="class">
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Bases: [`qiskit.algorithms.time_evolvers.real_time_evolver.RealTimeEvolver`](qiskit.algorithms.RealTimeEvolver "qiskit.algorithms.time_evolvers.real_time_evolver.RealTimeEvolver")
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The projected Variational Quantum Dynamics (p-VQD) Algorithm.
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In each timestep, this algorithm computes the next state with a Trotter formula (specified by the `evolution` argument) and projects the timestep onto a variational form (`ansatz`). The projection is determined by maximizing the fidelity of the Trotter-evolved state and the ansatz, using a classical optimization routine. See Ref. \[1] for details.
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The following attributes can be set via the initializer but can also be read and updated once the PVQD object has been constructed.
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### ansatz
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<Attribute id="qiskit.algorithms.PVQD.ansatz">
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The parameterized circuit representing the time-evolved state.
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**Type**
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[QuantumCircuit](qiskit.circuit.QuantumCircuit "qiskit.circuit.QuantumCircuit")
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</Attribute>
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### initial\_parameters
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<Attribute id="qiskit.algorithms.PVQD.initial_parameters">
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The parameters of the ansatz at time 0.
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**Type**
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np.ndarray
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</Attribute>
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### optimizer
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<Attribute id="qiskit.algorithms.PVQD.optimizer">
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The classical optimization routine used to maximize the fidelity of the Trotter step and ansatz.
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**Type**
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Optional\[Union\[[Optimizer](qiskit.algorithms.optimizers.Optimizer "qiskit.algorithms.optimizers.Optimizer"), [Minimizer](qiskit.algorithms.optimizers.Minimizer "qiskit.algorithms.optimizers.Minimizer")]]
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</Attribute>
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### num\_timesteps
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<Attribute id="qiskit.algorithms.PVQD.num_timesteps">
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The number of timesteps to take. If None, it is automatically selected to achieve a timestep of approximately 0.01.
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**Type**
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Optional\[int]
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</Attribute>
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### evolution
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<Attribute id="qiskit.algorithms.PVQD.evolution">
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The method to perform the Trotter step. Defaults to first-order Lie-Trotter evolution.
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**Type**
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Optional\[[EvolutionSynthesis](qiskit.synthesis.EvolutionSynthesis "qiskit.synthesis.EvolutionSynthesis")]
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</Attribute>
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### use\_parameter\_shift
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<Attribute id="qiskit.algorithms.PVQD.use_parameter_shift">
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If True, use the parameter shift rule for loss function gradients (if the ansatz supports).
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**Type**
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bool
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</Attribute>
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### initial\_guess
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<Attribute id="qiskit.algorithms.PVQD.initial_guess">
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The starting point for the first classical optimization run, at time 0. Defaults to random values in $[-0.01, 0.01]$.
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**Type**
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Optional\[np.ndarray]
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</Attribute>
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**Example**
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This snippet computes the real time evolution of a quantum Ising model on two neighboring sites and keeps track of the magnetization.
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```python
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import numpy as np
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from qiskit.algorithms.state_fidelities import ComputeUncompute
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from qiskit.algorithms.time_evolvers import TimeEvolutionProblem, PVQD
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from qiskit.primitives import Estimator, Sampler
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from qiskit.circuit.library import EfficientSU2
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from qiskit.quantum_info import SparsePauliOp, Pauli
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from qiskit.algorithms.optimizers import L_BFGS_B
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sampler = Sampler()
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fidelity = ComputeUncompute(sampler)
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estimator = Estimator()
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hamiltonian = 0.1 * SparsePauliOp(["ZZ", "IX", "XI"])
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observable = Pauli("ZZ")
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ansatz = EfficientSU2(2, reps=1)
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initial_parameters = np.zeros(ansatz.num_parameters)
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time = 1
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optimizer = L_BFGS_B()
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# setup the algorithm
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pvqd = PVQD(
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fidelity,
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ansatz,
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initial_parameters,
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estimator,
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num_timesteps=100,
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optimizer=optimizer,
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)
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# specify the evolution problem
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problem = TimeEvolutionProblem(
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hamiltonian, time, aux_operators=[hamiltonian, observable]
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)
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# and evolve!
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result = pvqd.evolve(problem)
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```
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**References**
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**\[1] Stefano Barison, Filippo Vicentini, and Giuseppe Carleo (2021), An efficient**
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quantum algorithm for the time evolution of parameterized circuits, [Quantum 5, 512](https://quantum-journal.org/papers/q-2021-07-28-512/).
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**Parameters**
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* **fidelity** ([*BaseStateFidelity*](qiskit.algorithms.state_fidelities.BaseStateFidelity "qiskit.algorithms.state_fidelities.BaseStateFidelity")) – A fidelity primitive used by the algorithm.
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* **ansatz** ([*QuantumCircuit*](qiskit.circuit.QuantumCircuit "qiskit.circuit.QuantumCircuit")) – A parameterized circuit preparing the variational ansatz to model the time evolved quantum state.
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* **initial\_parameters** (*np.ndarray*) – The initial parameters for the ansatz. Together with the ansatz, these define the initial state of the time evolution.
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* **estimator** ([*BaseEstimator*](qiskit.primitives.BaseEstimator "qiskit.primitives.BaseEstimator") *| None*) – An estimator primitive used for calculating expected values of auxiliary operators (if provided via the problem).
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* **optimizer** ([*Optimizer*](qiskit.algorithms.optimizers.Optimizer "qiskit.algorithms.optimizers.Optimizer") *|*[*Minimizer*](qiskit.algorithms.optimizers.Minimizer "qiskit.algorithms.optimizers.Minimizer") *| None*) – The classical optimizers used to minimize the overlap between Trotterization and ansatz. Can be either a [`Optimizer`](qiskit.algorithms.optimizers.Optimizer "qiskit.algorithms.optimizers.Optimizer") or a callable using the [`Minimizer`](qiskit.algorithms.optimizers.Minimizer "qiskit.algorithms.optimizers.Minimizer") protocol. This argument is optional since it is not required for [`get_loss()`](qiskit.algorithms.PVQD#get_loss "qiskit.algorithms.PVQD.get_loss"), but it has to be set before [`evolve()`](qiskit.algorithms.PVQD#evolve "qiskit.algorithms.PVQD.evolve") is called.
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* **num\_timesteps** (*int | None*) – The number of time steps. If `None` it will be set such that the timestep is close to 0.01.
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* **evolution** ([*EvolutionSynthesis*](qiskit.synthesis.EvolutionSynthesis "qiskit.synthesis.EvolutionSynthesis") *| None*) – The evolution synthesis to use for the construction of the Trotter step. Defaults to first-order Lie-Trotter decomposition, see also `evolution` for different options.
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* **use\_parameter\_shift** (*bool*) – If True, use the parameter shift rule to compute gradients. If False, the optimizer will not be passed a gradient callable. In that case, Qiskit optimizers will use a finite difference rule to approximate the gradients.
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* **initial\_guess** (*np.ndarray | None*) – The initial guess for the first VQE optimization. Afterwards the previous iteration result is used as initial guess. If None, this is set to a random vector with elements in the interval $[-0.01, 0.01]$.
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## Methods
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### evolve
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<Function id="qiskit.algorithms.PVQD.evolve" signature="PVQD.evolve(evolution_problem)">
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Perform real time evolution $\exp(-i t H)|\Psi\rangle$.
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Evolves an initial state $|\Psi\rangle$ for a time $t$ under a Hamiltonian $H$, as provided in the `evolution_problem`.
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**Parameters**
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**evolution\_problem** ([`TimeEvolutionProblem`](qiskit.algorithms.TimeEvolutionProblem "qiskit.algorithms.time_evolvers.time_evolution_problem.TimeEvolutionProblem")) – The evolution problem containing the hamiltonian, total evolution time and observables to evaluate.
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**Return type**
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[`TimeEvolutionResult`](qiskit.algorithms.TimeEvolutionResult "qiskit.algorithms.time_evolvers.time_evolution_result.TimeEvolutionResult")
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**Returns**
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A result object containing the evolution information and evaluated observables.
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**Raises**
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* **ValueError** – If `aux_operators` provided in the time evolution problem but no estimator provided to the algorithm.
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* **NotImplementedError** – If the evolution problem contains an initial state.
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</Function>
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### get\_loss
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<Function id="qiskit.algorithms.PVQD.get_loss" signature="PVQD.get_loss(hamiltonian, ansatz, dt, current_parameters)">
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Get a function to evaluate the infidelity between Trotter step and ansatz.
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**Parameters**
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* **hamiltonian** (*BaseOperator |* [*PauliSumOp*](qiskit.opflow.primitive_ops.PauliSumOp "qiskit.opflow.primitive_ops.PauliSumOp")) – The Hamiltonian under which to evolve.
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* **ansatz** ([*QuantumCircuit*](qiskit.circuit.QuantumCircuit "qiskit.circuit.QuantumCircuit")) – The parameterized quantum circuit which attempts to approximate the time-evolved state.
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* **dt** (*float*) – The time step.
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* **current\_parameters** (*np.ndarray*) – The current parameters.
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**Return type**
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tuple\[Callable\[\[np.ndarray], float], Callable\[\[np.ndarray], np.ndarray]] | None
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**Returns**
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**A callable to evaluate the infidelity and, if gradients are supported and required,**
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a second callable to evaluate the gradient of the infidelity.
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</Function>
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### step
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<Function id="qiskit.algorithms.PVQD.step" signature="PVQD.step(hamiltonian, ansatz, theta, dt, initial_guess)">
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Perform a single time step.
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**Parameters**
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* **hamiltonian** (*BaseOperator |* [*PauliSumOp*](qiskit.opflow.primitive_ops.PauliSumOp "qiskit.opflow.primitive_ops.PauliSumOp")) – The Hamiltonian under which to evolve.
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* **ansatz** ([*QuantumCircuit*](qiskit.circuit.QuantumCircuit "qiskit.circuit.QuantumCircuit")) – The parameterized quantum circuit which attempts to approximate the time-evolved state.
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* **theta** (*np.ndarray*) – The current parameters.
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* **dt** (*float*) – The time step.
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* **initial\_guess** (*np.ndarray*) – The initial guess for the classical optimization of the fidelity between the next variational state and the Trotter-evolved last state. If None, this is set to a random vector with elements in the interval $[-0.01, 0.01]$.
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**Return type**
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tuple\[np.ndarray, float]
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**Returns**
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A tuple consisting of the next parameters and the fidelity of the optimization.
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</Function>
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</Class>
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