Revisiting dequantization and quantum advantage in learning tasks

TL;DR

This paper shows that classical algorithms with sample and query access can outperform quantum algorithms with quantum state inputs in certain learning tasks, challenging assumptions about quantum advantage.

Contribution

It proves that classical algorithms with SQ access can be exponentially faster than quantum algorithms with quantum state inputs, highlighting the power of SQ access.

Findings

Classical SQ access algorithms can outperform quantum state input algorithms.

SQ access can be more powerful than quantum state inputs in some learning tasks.

Quantum advantage may be limited by the power of data access models.

Abstract

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.