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Realization of Quantum Oracles using Symmetries of Boolean Functions
(pp418-448)
Peng Gao, Yiwei Li, Marek Perkowski, and Xiaoyu Song
doi:
https://doi.org/10.26421/QIC20.5-6-4
Abstracts:
Designing a quantum oracle is an important step in
practical realization of Grover algorithm, therefore it is useful to
create methodologies to design oracles. Lattice diagrams are regular
two-dimensional structures that can be directly mapped onto a quantum
circuit. We present a quantum oracle design methodology based on
lattices. The oracles are designed with a proposed method using
generalized Boolean symmetric functions realized with lattice diagrams.
We also present a decomposition-based algorithm that transforms
non-symmetric functions into symmetric or partially symmetric functions.
Our method, which combines logic minimization, logic decomposition, and
mapping, has lower quantum cost with fewer ancilla qubits.
Overall, we obtain encouraging synthesis results superior to previously
published data.
Key words:
Symmetric function, Kronecker Functional Lattice,
Grovers algorithm, Reversible circuit, Quantum oracle
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