Related papers: What if you have only one copy? Low-depth quantum circuits have no advantage in decision problems!

What if you have only one copy? Low-depth quantum circuits have no advantage in decision problems!

URL: http://arxiv.org/abs/2404.05714v1
Date: Mon, 8 Apr 2024 17:52:03 GMT
Title: What if you have only one copy? Low-depth quantum circuits have no advantage in decision problems!
Authors: Nengkun Yu,
Abstract summary: We show that gleaning insights into specific properties is feasible even with a single-state sample. Our results apply to quantum states with low circuit complexity, including noise-affected ones. We reveal no quantum advantage in decision problems involving low-depth quantum circuits.
Score: 14.322753787990036
License: http://creativecommons.org/publicdomain/zero/1.0/
Abstract: The conventional approach to understanding the characteristics of an unknown quantum state involves having numerous identical independent copies of the system in that state. However, we demonstrate that gleaning insights into specific properties is feasible even with a single-state sample. Perhaps surprisingly, the confidence level of our findings increases proportionally with the number of qubits. Our conclusions apply to quantum states with low circuit complexity, including noise-affected ones. Additionally, this extends to learning from a solitary sample of probability distributions. Our results establish a strong lower bound for discriminating quantum states with low complexity. Furthermore, we reveal no quantum advantage in decision problems involving low-depth quantum circuits. Our results can be used to verify NISQ devices.

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