Quart-DB uses the Quart startup functionality to connect to the database and create the connection pool. Therefore the test_app will need to be used to ensure that the connection is setup for testing as well, see the docs. To do so I recommend the following fixture be used with pytest,

@pytest.fixture(name="app", scope="function")
async def _app():
    app = create_app()  # Initialize app
    async with app.test_app() as test_app:
        yield test_app

If you would like only a connection for usage in tests I recommend the following fixture note the DATABASE_URL is being supplied as a environment variable,

async def _connection():
    db = QuartDB(Quart(__name__), url=os.environ["DATABASE_URL"])
    connection = Connection(asyncpg_connection)
    async with db.connection() as connection:
        yield connection