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- W4313531985 abstract "Recent work by Bravyi, Gosset, and Koenig showed that there exists a search problem that a constant-depth quantum circuit can solve, but that any constant-depth classical circuit with bounded fan-in cannot. They also pose the question: can we achieve a similar proof of separation for an input-independent sampling task? In this paper, we show that the answer to this question is yes. We introduce a distribution $D_{n}$ and give a constant-depth, $n$ qubit, quantum circuit that samples from a distribution close to $D_{n}$ in total variation distance. For any $delta < 1$ we also prove, unconditionally, that any classical circuit with bounded fan-in gates that takes as input $n + n^delta$ uniformly random bits and produces output close to $D_{n}$ in total variation distance has depth $Omega(log log n)$. This gives an unconditional proof that constant-depth quantum circuits can sample from distributions which can't be reproduced by constant-depth bounded fan-in classical circuits, even up to additive error. The distribution $D_n$ and classical circuit lower bounds are based on work of Viola, in which he shows a different (but related) distribution cannot be sampled from approximately by constant-depth bounded fan-in classical circuits." @default.
- W4313531985 created "2023-01-06" @default.
- W4313531985 creator A5031527222 @default.
- W4313531985 creator A5042095445 @default.
- W4313531985 date "2023-01-03" @default.
- W4313531985 modified "2023-10-14" @default.
- W4313531985 title "Unconditional Quantum Advantage for Sampling with Shallow Circuits" @default.
- W4313531985 doi "https://doi.org/10.48550/arxiv.2301.00995" @default.
- W4313531985 hasPublicationYear "2023" @default.
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