Revisiting dequantization and quantum advantage in learning tasks

• URL: http://arxiv.org/abs/2112.00811v1
• Date: Wed, 1 Dec 2021 20:05:56 GMT
• Title: Revisiting dequantization and quantum advantage in learning tasks
• Authors: Jordan Cotler, Hsin-Yuan Huang, Jarrod R. McClean
• Abstract summary: We show that classical algorithms with sample and query (SQ) access can accomplish some learning tasks exponentially faster than quantum algorithms with 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.
• Score: 3.265773263570237
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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