quairkit.loss.distance¶

The source file of the class for the distance.

class quairkit.loss.distance.TraceDistance(target_state)¶

The class of the loss function to compute the trace distance.

This interface allows you to use the trace distance as a loss function for training quantum circuits. The trace distance is defined as \(D(\rho, \sigma) = \frac{1}{2}\text{tr}|\rho-\sigma|\).

Parameters:¶

target_state : StateSimulator¶: The target quantum state to be used to compute the trace distance. Can be a single state or a batch of states.

Note

This class supports batch operations. When both target and input states have batch dimensions, the trace distance is computed element-wise along the batch dimension.

Examples

from quairkit.database import one_state, bell_state
from quairkit.loss import TraceDistance

# Single state example
target_state = one_state(1)  # Define target
input_state = bell_state(1)  # Define input
trace_distance = TraceDistance(target_state)
result = trace_distance(input_state)
print('Single state distance:', result)

Single state distance: tensor(0.7071)

# Batched states example
from quairkit.database import random_state

target_state_batch = random_state(num_systems=1, size=2)  # Batch of 2 targets
input_state_batch = random_state(num_systems=1, size=2)   # Batch of 2 inputs
trace_distance = TraceDistance(target_state_batch)
batch_result = trace_distance(input_state_batch)
print('Batched distances:', batch_result)

Batched distances: tensor([0.7912, 0.7283])

forward(state)¶

Compute the trace distance between the input state and the target state.

The value computed by this function can be used as a loss function to optimize quantum circuits.

Parameters:¶

state : StateSimulator¶: The input quantum state which will be used to compute the trace distance with the target state. Can be a single state or a batch of states. Must have the same number of systems as the target state.

Returns:¶

The trace distance between the input state and the target state. Returns a scalar for single states, or a tensor for batched states.

Raises:¶

AssertionError – If the number of systems in the input state does not match the target state.
NotImplementedError – If the backend is wrong or not supported.

Return type:¶

Tensor

class quairkit.loss.distance.StateFidelity(target_state)¶

The class of the loss function to compute the state fidelity.

This interface allows you to use the state fidelity as a loss function for training quantum circuits. The state fidelity is defined as \(F(\rho, \sigma) = \text{tr}(\sqrt{\sqrt{\rho}\sigma\sqrt{\rho}})\).

Parameters:¶

target_state : StateSimulator¶: The target quantum state to be used to compute the state fidelity. Can be a single state or a batch of states.

Note

This class supports batch operations. When both target and input states have batch dimensions, the fidelity is computed element-wise along the batch dimension.

Examples

from quairkit.database import one_state, bell_state
from quairkit.loss import StateFidelity

# Single state example
target_state = one_state(1)  # Define target
input_state = bell_state(1)  # Define input
fidelity_calculator = StateFidelity(target_state)
result = fidelity_calculator(input_state)
print('Single state fidelity:', result)

Single state fidelity: tensor(0.7071)

# Batched states example
from quairkit.database import random_state

target_batch = random_state(num_systems=1, size=2)  # Batch of 2 targets
input_batch = random_state(num_systems=1, size=2)   # Batch of 2 inputs
fidelity_calculator = StateFidelity(target_batch)
batch_result = fidelity_calculator(input_batch)
print('Batched fidelities:', batch_result)

Batched fidelities: tensor([0.5658, 0.7090])

forward(state)¶

Compute the state fidelity between the input state and the target state.

The value computed by this function can be used as a loss function to optimize quantum circuits.

Parameters:¶

state : StateSimulator¶: The input quantum state which will be used to compute the state fidelity with the target state. Can be a single state or a batch of states. Must have the same number of systems as the target state.

Returns:¶

The state fidelity between the input state and the target state. Returns a scalar for single states, or a tensor for batched states. The fidelity ranges from 0 to 1.

Raises:¶

AssertionError – If the number of systems in the input state does not match the target state.
NotImplementedError – If the backend is wrong or not supported.

Return type:¶

Tensor