  It has been shown that the apparent advantage of some quantum machine
learning algorithms may be efficiently replicated using classical algorithms
with suitable data access -- a process known as dequantization. Existing works
on dequantization compare quantum algorithms which take copies of an n-qubit
quantum state $|x\rangle = \sum_{i} x_i |i\rangle$ as input to classical
algorithms which have sample and query (SQ) access to the vector $x$. In this
note, we prove that classical algorithms with SQ access can accomplish some
learning tasks exponentially faster than quantum algorithms with quantum state
inputs. Because classical algorithms are a subset of quantum algorithms, this
demonstrates that SQ access can sometimes be significantly more powerful than
quantum state inputs. Our findings suggest that the absence of exponential
quantum advantage in some learning tasks may be due to SQ access being too
powerful relative to quantum state inputs. If we compare quantum algorithms
with quantum state inputs to classical algorithms with access to measurement
data on quantum states, the landscape of quantum advantage can be dramatically
different. We remark that when the quantum states are constructed from
exponential-size classical data, comparing SQ access and quantum state inputs
is appropriate since both require exponential time to prepare.
