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• W3041326991 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." @default.
• W3041326991 created "2020-07-16" @default.
• W3041326991 creator A5002718143 @default.
• W3041326991 creator A5021754799 @default.
• W3041326991 creator A5082889085 @default.
• W3041326991 date "2020-07-10" @default.
• W3041326991 modified "2023-09-30" @default.
• W3041326991 title "Efficient ancilla-free reversible and quantum circuits for the Hidden Weighted Bit function" @default.
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• W3041326991 hasPublicationYear "2020" @default.
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