What if you have only one copy? Low-depth quantum circuits have no advantage in decision problems!
arxiv(2024)
摘要
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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