quantum_walk

Discrete-Time Quantum Walk

Quantum walk operator for a path graph with 16 nodes ($P_{16}$).

Implementation

Diffuser part of the $C$ operator is deployed using zero_diffuzer(x: QNum). For the full $C$, one needs to control the operation of the zero diffuzer using the first register and also to iterate through all vertices. This is done in W_iteration(i: int, vertices: QNum, adjacent_vertices: QNum).

For $S$, one needs to check if two vertices are connected using edge_oracle(res: Output[QBit], vertices: QNum, adjacent_vertices: QNum) and then to apply a bit-wise swap in S_operator(vertices: QNum, adjacent_vertices: QNum) on all connected vertices.

Software Requirements

The following Python packages are required to run this notebook:

• numpy
• classiq

Note: These packages are included in the top-level requirements.txt. If you have set up the base environment as described in the main README, no additional installation is needed.

GNU GPL v3+

Copyright (C) 2024 Mohammadreza Khellat GNU GPL v3+

This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.

See also https://www.gnu.org/licenses/gpl.html