“Quantum supremacy” revisited: Low-complexity, deterministic solutions
of the Deutsch-Jozsa problem in classical physical systems
Abstract
The Deutsch-Jozsa problem is for a database of size N, where,
according to their claim, the deterministic solution of the problem on a
classical Turing computer requires O(N) computational complexity.
They produced the famous Deutsch-Jozsa quantum algorithm that offered an
exponential speedup over the envisioned classical computer, namely
O[log(N)] complexity in a quantum computer. In the present
paper, the Deutsch-Jozsa problem is implemented by two different
algorithms on a Turing machine. It is shown that, similarly to the
quantum algorithm, the Deutsch-Jozsa problem can deterministically be
solved with O[log(N)] complexity on a classical computer with
these algorithms.