magic
Accessible in numqi.magic
numqi.magic.get_Weyl_H(dim)
get the Weyl-Heisenberg operator H, same as same as numqi.gate.get_quditH
Weyl-Heisenberg matrices wiki-link
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
dim
|
int
|
the dimension |
required |
Returns:
| Name | Type | Description |
|---|---|---|
ret |
ndarray
|
the Weyl-Heisenberg operator H of shape (dim,dim) |
numqi.magic.get_Weyl_Z(dim)
get the Weyl-Heisenberg operator Z, same as same as numqi.gate.get_quditZ
Weyl-Heisenberg matrices wiki-link
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
dim
|
int
|
the dimension |
required |
Returns:
| Name | Type | Description |
|---|---|---|
ret |
ndarray
|
the Weyl-Heisenberg operator Z of shape (dim,dim) |
numqi.magic.get_Weyl_X(dim)
get the Weyl-Heisenberg operator X
Weyl-Heisenberg matrices wiki-link
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
dim
|
int
|
the dimension |
required |
Returns:
| Name | Type | Description |
|---|---|---|
ret |
ndarray
|
the Weyl-Heisenberg operator X of shape (dim,dim) |
numqi.magic.get_Heisenberg_Weyl_operator(dim)
get the Heisenberg-Weyl operator of prime dimension
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
dim
|
int
|
the prime dimension |
required |
Returns:
| Name | Type | Description |
|---|---|---|
T_list |
ndarray
|
the list of Heisenberg-Weyl operator \(T_u\) of shape (dim,dim,dim,dim) |
A_list |
ndarray
|
the list of Heisenberg-Weyl operator \(A_u\) in matrix form of shape (dim,dim,dim,dim) |
numqi.magic.get_qutrit_nonstabilizer_state(key)
get the non-stabilizer state of qutrit
reference: The resource theory of stabilizer quantum computation doi-link
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
key
|
str
|
the key of the non-stabilizer state, can be {'Hplus', 'Hminus', 'Hi', 'T', 'Strange', 'Norrell'} |
required |
Returns:
| Name | Type | Description |
|---|---|---|
ret |
ndarray
|
the non-stabilizer state of shape (3,) |
numqi.magic.plot_qubit_magic_state_3d()
plot the magic state set (octahedron) of qubit
Parameters:
Returns:
| Name | Type | Description |
|---|---|---|
fig |
Figure
|
the figure object |
ax |
Axes3D
|
the axis object |
numqi.magic.matrix_to_wigner_basis(np0, is_hermitian=False)
convert the matrix to Wigner basis
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
np0
|
ndarray
|
the matrix of shape (...,dim,dim) |
required |
is_hermitian
|
bool
|
whether the matrix is hermitian |
False
|
Returns:
| Name | Type | Description |
|---|---|---|
ret |
ndarray
|
the Wigner basis of shape (...,dim*dim) |
numqi.magic.wigner_basis_to_matrix(np0)
convert the Wigner basis to matrix
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
np0
|
ndarray
|
the Wigner basis of shape (...,dim*dim) |
required |
Returns:
| Name | Type | Description |
|---|---|---|
ret |
ndarray
|
the matrix of shape (...,dim,dim) |
numqi.magic.get_wigner_trace_norm(np0)
get the Wigner trace norm of matrix
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
np0
|
ndarray
|
the matrix of shape (...,dim,dim) |
required |
Returns:
| Name | Type | Description |
|---|---|---|
ret |
ndarray
|
the Wigner trace norm of shape (...) |
numqi.magic.get_magic_state_boundary_qubit(rho)
get the magic state boundary of qubit
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
rho
|
ndarray
|
density matrix of shape (2,2) or (batch_size, 2, 2) |
required |
Returns:
| Name | Type | Description |
|---|---|---|
ret |
ndarray
|
the magic state boundary of shape (batch_size,) |
numqi.magic.get_thauma_sdp(rho, kind, use_tqdm=False, sqrt_order=3, pade_order=3)
get the thauma of quantum state using semi-definite programming (SDP)
reference: Efficiently Computable Bounds for Magic State Distillation doi-link
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
rho
|
ndarray
|
the quantum state(s) of shape (dim, dim) or (batch_size, dim, dim) |
required |
kind
|
str
|
the kind of thauma, can be {'min', 'max', 'entropy'} |
required |
use_tqdm
|
bool
|
whether to use tqdm for progress bar |
False
|
sqrt_order
|
int
|
the order of square root approximation |
3
|
pade_order
|
int
|
the order of Pade approximation |
3
|
Returns:
| Name | Type | Description |
|---|---|---|
ret |
ndarray
|
the thauma of quantum state(s) |
numqi.magic.get_thauma_boundary(rho, use_tqdm=False)
get the thauma boundary of quantum state using semi-definite programming (SDP)
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
rho
|
ndarray
|
the quantum state(s) of shape (dim, dim) or (batch_size, dim, dim) |
required |
use_tqdm
|
bool
|
whether to use tqdm for progress bar |
False
|
Returns:
| Name | Type | Description |
|---|---|---|
ret |
ndarray
|
the thauma boundary of quantum state(s) |