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arXiv · 2108.03193

On the Exponential Sample Complexity of the Quantum State Sign Estimation Problem

Arthur G. Rattew·Marco Pistoia
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Abstract

We demonstrate that the ability to estimate the relative sign of an arbitrary $n$-qubit quantum state (with real amplitudes), given only $k$ copies of that state, would yield a $kn$-query algorithm for unstructured search. Thus the quantum sample complexity of sign estimation must be exponential: $\Omega(2^{n/2}/n)$. In particular, we show that an efficient procedure for solving the sign estimation problem would allow for a polynomial time solution to the NP-complete problem 3-SAT.

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Arthur G. Rattew, Marco Pistoia. 2021-08-06. On the Exponential Sample Complexity of the Quantum State Sign Estimation Problem. https://arxiv.org/abs/2108.03193

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