Quantum Circuits with Unbounded Fan-out
Abstract
We demonstrate that the unbounded fan-out gate is very powerful. Constant-depth polynomial-size quantum circuits with bounded fan-in and unbounded fan-out over a fixed basis (denoted by QNCf^0) can approximate with polynomially small error the following gates: parity, mod[q], And, Or, majority, threshold[t], exact[q], and Counting. Classically, we need logarithmic depth even if we can use unbounded fan-in gates. If we allow arbitrary one-qubit gates instead of a fixed basis, then these circuits can also be made exact in log-star depth. Sorting, arithmetical operations, phase estimation, and the quantum Fourier transform with arbitrary moduli can also be approximated in constant depth.
Cite
@article{arxiv.quant-ph/0208043,
title = {Quantum Circuits with Unbounded Fan-out},
author = {Peter Hoyer and Robert Spalek},
journal= {arXiv preprint arXiv:quant-ph/0208043},
year = {2017}
}
Comments
20 pages, 9 figures, STACS'2003. v3: rewritten from scratch, new co-author, everything put into constant depth (including quantum Fourier transform). v4: polished a lot