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arXiv · 2007.05469

Efficient ancilla-free reversible and quantum circuits for the Hidden Weighted Bit function

Sergey Bravyi·Theodore J. Yoder·Dmitri Maslov
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Abstract

The Hidden Weighted Bit function plays an important role in the study of classical models of computation. A common belief is that this function is exponentially hard for the implementation by reversible ancilla-free circuits, even though introducing a small number of ancillae allows a very efficient implementation. In this paper, we refute the exponential hardness conjecture by developing a polynomial-size reversible ancilla-free circuit computing the Hidden Weighted Bit function. Our circuit has size $O(n^{6.42})$, where $n$ is the number of input bits. We also show that the Hidden Weighted Bit function can be computed by a quantum ancilla-free circuit of size $O(n^2)$. The technical tools employed come from a combination of Theoretical Computer Science (Barrington's theorem) and Physics (simulation of fermionic Hamiltonians) techniques.

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Sergey Bravyi, Theodore J. Yoder, Dmitri Maslov. 2020-07-10. Efficient ancilla-free reversible and quantum circuits for the Hidden Weighted Bit function. https://doi.org/10.1109/tc.2021.3076435

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