channel
shape conventions for quantum channels
- Kraus operator
(rank, dim_out, dim_in) - Choi operator
(dim_in*dim_out, dim_in*dim_out) - Super operator
(dim_out*dim_out, dim_in*dim_in)
numqi.channel.hf_dephasing_kraus_op(noise_rate)
return kraus_op for dephasing channel
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
noise_rate
|
float
|
the probability of dephasing, 0<=noise_rate<=1 |
required |
Returns:
| Name | Type | Description |
|---|---|---|
kraus_op |
ndarray
|
(2,2,2) kraus operators |
numqi.channel.hf_depolarizing_kraus_op(noise_rate)
return kraus_op for depolarizing channel
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
noise_rate
|
float
|
the probability of depolarizing, 0<=noise_rate<=4/3 |
required |
Returns:
| Name | Type | Description |
|---|---|---|
kraus_op |
ndarray
|
(4,2,2) kraus operators |
numqi.channel.hf_amplitude_damping_kraus_op(noise_rate)
return kraus_op for amplitude damping channel
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
noise_rate
|
float
|
the probability of damping, 0<=noise_rate<=1 |
required |
Returns:
| Name | Type | Description |
|---|---|---|
kraus_op |
ndarray
|
(2,2,2) kraus operators |
numqi.channel.kraus_op_to_choi_op(op)
convert kraus_op to choi_op
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
op
|
ndarray
|
(rank, dim_out, dim_in) |
required |
Returns:
| Name | Type | Description |
|---|---|---|
choi_op |
ndarray
|
(dim_indim_out, dim_indim_out), dtype=complex |
numqi.channel.choi_op_to_kraus_op(op, dim_in, zero_eps=1e-10)
convert choi_op to kraus_op
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
op
|
ndarray
|
(dim_indim_out, dim_indim_out) |
required |
dim_in
|
int
|
input dimension |
required |
zero_eps
|
float
|
threshold for zero eigenvalues |
1e-10
|
Returns:
| Name | Type | Description |
|---|---|---|
kraus_op |
ndarray
|
(rank, dim_out, dim_in) |
numqi.channel.choi_op_to_super_op(op, dim_in)
convert choi_op to super_op
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
op
|
ndarray
|
(dim_indim_out, dim_indim_out) |
required |
dim_in
|
int
|
input dimension |
required |
Returns:
| Name | Type | Description |
|---|---|---|
super_op |
ndarray
|
(dim_outdim_out, dim_indim_in) |
numqi.channel.super_op_to_choi_op(op)
convert super_op to choi_op
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
op
|
ndarray
|
(dim_outdim_out, dim_indim_in) |
required |
Returns:
| Name | Type | Description |
|---|---|---|
choi_op |
ndarray
|
(dim_indim_out, dim_indim_out) |
numqi.channel.super_op_to_kraus_op(op, zero_eps=1e-10)
convert super_op to kraus_op
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
op
|
ndarray
|
(dim_outdim_out, dim_indim_in) |
required |
zero_eps
|
float
|
threshold for zero eigenvalues |
1e-10
|
Returns:
| Name | Type | Description |
|---|---|---|
kraus_op |
ndarray
|
(rank, dim_out, dim_in) |
numqi.channel.apply_kraus_op(op, rho)
apply kraus_op to density matrix
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
op
|
ndarray
|
(rank, dim_out, dim_in) |
required |
rho
|
ndarray
|
(dim_in, dim_in) |
required |
Returns:
| Name | Type | Description |
|---|---|---|
ret |
ndarray
|
(dim_out, dim_out) |
numqi.channel.apply_choi_op(op, rho)
apply choi_op to density matrix
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
op
|
(ndarray, Tensor)
|
(dim_indim_out, dim_indim_out) |
required |
rho
|
(ndarray, Tensor)
|
(dim_in, dim_in) |
required |
Returns:
| Name | Type | Description |
|---|---|---|
ret |
(ndarray, Tensor)
|
(dim_out, dim_out) |
numqi.channel.apply_super_op(op, rho)
apply super_op to density matrix
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
op
|
ndarray
|
(dim_outdim_out, dim_indim_in) |
required |
rho
|
ndarray
|
(dim_in, dim_in) |
required |
Returns:
| Name | Type | Description |
|---|---|---|
ret |
ndarray
|
(dim_out, dim_out) |
numqi.channel.hf_channel_to_kraus_op(hf0, dim_in)
convert hf0 (linear map) to kraus_op
warning: not all linear map can be converted to kraus_op, see arxiv-link (eq16)
warning: bad performance
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
hf0
|
Callable
|
function call for applying linear map |
required |
dim_in
|
int
|
input dimension |
required |
Returns:
| Name | Type | Description |
|---|---|---|
kraus_op |
ndarray
|
(rank, dim_out, dim_in) |
numqi.channel.hf_channel_to_choi_op(hf0, dim_in)
convert hf0 (linear map) to choi_op
warning: bad performance
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
hf0
|
Callable
|
function call for applying linear map |
required |
dim_in
|
int
|
input dimension |
required |
Returns:
| Name | Type | Description |
|---|---|---|
choi_op |
ndarray
|
(dim_indim_out, dim_indim_out) |
numqi.channel.ChannelCapacity1InfModel
Bases: Module
Capacities of Quantum Channels and How to Find Them arxiv-link
__init__(dim_in, num_state)
initiate model
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
dim_in
|
int
|
input dim |
required |
num_state
|
int
|
number of states |
required |
set_channel_kraus_op(kop)
set channel kraus op
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
kop
|
ndarray
|
(rank, dim_out, dim_in) |
required |