All reports by Author Luke Schaeffer:

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TR19-089
| 21st June 2019
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Adam Bene Watts, Robin Kothari, Luke Schaeffer, Avishay Tal#### Exponential separation between shallow quantum circuits and unbounded fan-in shallow classical circuits

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TR19-061
| 16th April 2019
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Scott Aaronson, Daniel Grier, Luke Schaeffer#### A Quantum Query Complexity Trichotomy for Regular Languages

Adam Bene Watts, Robin Kothari, Luke Schaeffer, Avishay Tal

Recently, Bravyi, Gosset, and König (Science, 2018) exhibited a search problem called the 2D Hidden Linear Function (2D HLF) problem that can be solved exactly by a constant-depth quantum circuit using bounded fan-in gates (or QNC^0 circuits), but cannot be solved by any constant-depth classical circuit using bounded fan-in AND, ... more >>>

Scott Aaronson, Daniel Grier, Luke Schaeffer

We present a trichotomy theorem for the quantum query complexity of regular languages. Every regular language has quantum query complexity $\Theta(1)$, $\tilde{\Theta}(\sqrt n)$, or $\Theta(n)$. The extreme uniformity of regular languages prevents them from taking any other asymptotic complexity. This is in contrast to even the context-free languages, which we ... more >>>