Magento 2 : How to load quote by quote id

you can inject in your class an instance of \Magento\Quote\Model\QuoteFactory.

protected $quoteFactory;

public function __construct(
    ...
    \Magento\Quote\Model\QuoteFactory $quoteFactory,
    ....
) {
    ....
    $this->quoteFactory = $quoteFactory;
    ....
}

Then you can use:

$quote = $this->quoteFactory->create()->load($quoteId);

This should work for now, but soon, the load method is going to go away and you need to use a service contract.
So you can use \Magento\Quote\Api\CartRepositoryInterface.
Same as above, inject an instance of this class in your class:

protected $quoteRepository;

public function __construct(
    ...
    \Magento\Quote\Api\CartRepositoryInterface $quoteRepository,
    ....
) {
    ....
    $this->quoteRepository = $quoteRepository;
    ....
}

and use this:

$this->quoteRepository->get($quoteId);

If you want to see how the code looks like, the implementation for \Magento\Quote\Api\CartRepositoryInterface is \Magento\Quote\Model\QuoteRepository

First you need to inject a \Magento\Quote\Model\QuoteFactory in your class constructor:

protected $_quoteFactory;

public function __construct(
    ...
    \Magento\Quote\Model\QuoteFactory $quoteFactory
) {
    $this->_quoteFactory = $quoteFactory;
    parent::__construct(...);
}

Then in your class you can do:

$this->_quoteFactory->create()->loadByIdWithoutStore($quoteId);

On a side note you can also use the following methods to load a quote:

• loadActive($quoteId) where it loads corresponding active quote (where is_active = 1)
• loadByCustomerId($customerId) where it load the active quote corresponding to the customer id.

NB: you can also use the object manager directly to do it but it is not recommended:

$this->_objectManager->create('Magento\Quote\Model\Quote')->loadByIdWithoutStor‌​e($quoteId);