import sys
sys.path.insert(0, '..')
import numpy as np
import qutip as qt
import src
from src import (utils, paulialg, stabilizer, circuit)

2.5. Methods for Clifford maps

2.5.1. Embedding small Clifford map into larger map

.embed(small_map, mask) provides the method to embed a smaller Clifford map on a subset of qubits to the current Clifford map. This is a in-place operation. The Clifford map object that provide this method will get modified under the embedding.

Parameters:

• small_map is a CliffordMap object supported on a subset of qubits.

• mask is a boolean array specifying the subset of qubits.

cmap = stabilizer.identity_map(6)
cmap

CliffordMap(
  X0-> +XIIIII
  Z0-> +ZIIIII
  X1-> +IXIIII
  Z1-> +IZIIII
  X2-> +IIXIII
  Z2-> +IIZIII
  X3-> +IIIXII
  Z3-> +IIIZII
  X4-> +IIIIXI
  Z4-> +IIIIZI
  X5-> +IIIIIX
  Z5-> +IIIIIZ)

cmap.embed(stabilizer.random_clifford_map(3), np.array([True,False,False,True,True,False]))

CliffordMap(
  X0-> +IIIZYI
  Z0-> -XIIXYI
  X1-> +IXIIII
  Z1-> +IZIIII
  X2-> +IIXIII
  Z2-> +IIZIII
  X3-> -YIIZYI
  Z3-> +ZIIZYI
  X4-> -IIIIYI
  Z4-> +IIIYXI
  X5-> +IIIIIX
  Z5-> +IIIIIZ)

2.5.2. Map Composition

.compose(other) returns the composition of the current Clifford map with another Clifford map. This will return a new Clifford map without modifying either of the input maps. The Clifford map object which initiates this method will be the preceeding map in the composition.

Parameters:

• other - another CliffordMap.

cmap.compose(stabilizer.random_clifford_map(6))

CliffordMap(
  X0-> -YZZYYZ
  Z0-> -ZIXIZI
  X1-> -ZYXXZY
  Z1-> -ZZIXII
  X2-> -YIZZZZ
  Z2-> +YIIZXZ
  X3-> -YZIYYI
  Z3-> +ZIYXXI
  X4-> -ZZYIXX
  Z4-> -ZZIXIZ
  X5-> -YXIXYZ
  Z5-> +ZIIXII)

2.5.3. Map Inversion

.inverse() returns the inverse of the current Clifford map. This will return a new Clifford map withoutt modifying the original map. The inverse map is such that its composition with the original map must be identity

cmap = stabilizer.clifford_rotation_map('Y')
cmap

CliffordMap(
  X0-> -Z
  Z0-> +X)

cmap.inverse()

CliffordMap(
  X0-> +Z
  Z0-> -X)