|
|
@@ -1,9 +1,43 @@ |
|
|
|
# -*- coding: utf-8 -*- |
|
|
|
|
|
|
|
""" |
|
|
|
This program generates and caches lookup tables, and handles the Clifford group. |
|
|
|
It provides tables for Clifford group multiplication and conjugation, |
|
|
|
as well as CZ and decompositions of the 2x2 Cliffords. |
|
|
|
This module handles operations on the Clifford group. It makes extensive use of the lookup tables in ``abp.tables``. |
|
|
|
The code to generate those tables is included in this distribution as ``abp/build_tables.py`` |
|
|
|
This package emumerates and labels the single-qubit Clifford group, and provides methods for matrix multiplication and conjugation. |
|
|
|
It also includes the look-up table for the CZ gate. |
|
|
|
|
|
|
|
There are 24 members of the single-qubit Clifford group. You can refer to some of them by multiple names. |
|
|
|
The complete set of aliases for single-qubit Cliffords is as follows: |
|
|
|
|
|
|
|
======= ========================= |
|
|
|
Index Aliases |
|
|
|
======= ========================= |
|
|
|
0 ``IA, identity, identity_h`` |
|
|
|
1 ``px, XA, px_h`` |
|
|
|
2 ``py, YA, py_h`` |
|
|
|
3 ``pz, ZA, pz_h`` |
|
|
|
4 ``IB`` |
|
|
|
5 ``XB, sqz, msqz_h, phase_h`` |
|
|
|
6 ``YB, msqz, sqz_h, phase`` |
|
|
|
7 ``ZB`` |
|
|
|
8 ``IC`` |
|
|
|
9 ``XC, msqy, sqy_h`` |
|
|
|
10 ``YC, hadamard, hadamard_h`` |
|
|
|
11 ``ZC, sqy, msqy_h`` |
|
|
|
12 ``ID`` |
|
|
|
13 ``XD`` |
|
|
|
14 ``YD, sqx, msqx_h`` |
|
|
|
15 ``ZD, msqx, sqx_h`` |
|
|
|
16 ``IE`` |
|
|
|
17 ``XE`` |
|
|
|
18 ``YE`` |
|
|
|
19 ``ZE`` |
|
|
|
20 ``IF`` |
|
|
|
21 ``XF`` |
|
|
|
22 ``YF`` |
|
|
|
23 ``ZF`` |
|
|
|
======= ========================= |
|
|
|
|
|
|
|
""" |
|
|
|
|
|
|
|
from tables import * |
|
|
@@ -26,9 +60,18 @@ def human_name(i): |
|
|
|
choices = sorted((key for key, value in by_name.items() if value == i), key=len) |
|
|
|
return choices[-1] |
|
|
|
|
|
|
|
|
|
|
|
def is_diagonal(v): |
|
|
|
""" TODO: remove this. Checks if a VOP is diagonal or not """ |
|
|
|
return v in {0, 3, 5, 6} |
|
|
|
|
|
|
|
|
|
|
|
if __name__ == '__main__': |
|
|
|
from itertools import groupby |
|
|
|
|
|
|
|
for i in range(24): |
|
|
|
members = [key for key, value in by_name.items() if value == i and str(key)!=str(i)] |
|
|
|
members = sorted(members, key=len) |
|
|
|
print "* {}: {}".format(i, ", ".join(members)) |
|
|
|
|
|
|
|
|
|
|
|
|