Quantum function computation using sublogarithmic space (abstract & poster)

TL;DR

This paper demonstrates that quantum Turing machines can compute functions more efficiently than probabilistic Turing machines when using less than logarithmic space, highlighting quantum advantage in space-bounded computation.

Contribution

It proves that quantum Turing machines outperform probabilistic ones in function computation within sublogarithmic space bounds, a novel result in quantum computational complexity.

Findings

Quantum Turing machines are strictly superior to probabilistic Turing machines in sublogarithmic space.

Quantum advantage is established for any space bound o(log(n)).

The result advances understanding of quantum computational power in space-limited settings.

Abstract

We prove that quantum Turing machines are strictly superior to probabilistic Turing machines in function computation for any space bound $ o(\log(n)) $.