## Commuting Quantum Circuits with Few Outputs are Unlikely to be Classically Simulatable

- Yasuhiro Takahashi, Seiichiro Tani, Takeshi Yamazaki, Kazuyuki Tanaka
- COCOON
- 2015

Highly Influenced

@article{Hyer2005QuantumFI, title={Quantum Fan-out is Powerful}, author={Peter H\oyer and Robert Spalek}, journal={Theory of Computing}, year={2005}, volume={1}, pages={81-103} }

- Published in Theory of Computing 2005
DOI:10.4086/toc.2005.v001a005

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 ) can approximate with polynomially small error the following gates: parity, mod[q], And, Or, majority, threshold[t], exact[t], 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… CONTINUE READING