# Losses¶

Module name: qmlt.tf.losses

A collection of loss functions for tensorflow that are specific to quantum machine learning and optimization.

## Summary¶

 trace_distance(rho, sigma) Trace distance $$\frac{1}{2}\tr \{ \sqrt{ (\rho - \sigma})^2 \}$$ between quantum states $$\rho$$ and $$\sigma$$. expectation(rho, operator) Expectation value $$\tr\{ \rho O\}$$ of operator $$O$$ with respect to the quantum state $$\rho$$.

## Code details¶

qmlt.tf.losses.trace_distance(rho, sigma)[source]

Trace distance $$\frac{1}{2}\tr \{ \sqrt{ (\rho - \sigma})^2 \}$$ between quantum states $$\rho$$ and $$\sigma$$.

The inputs and outputs are tensors of dtype float, and all computations support automatic differentiation.

Parameters: rho (tf.Tensor) – 2-dimensional Hermitian matrix representing state $$\rho$$. sigma (tf.Tensor) – 2-dimensional Hermitian matrix of the same dimensions and dtype as rho, representing state $$\sigma$$. Returns the scalar trace distance. tf.Tensor
qmlt.tf.losses.expectation(rho, operator)[source]

Expectation value $$\tr\{ \rho O\}$$ of operator $$O$$ with respect to the quantum state $$\rho$$.

The inputs and outputs are tensors of dtype float, and all computations support automatic differentiation.

Parameters: rho (tf.Tensor) – 2-dimensional Hermitian tensor representing state $$\rho$$. operator (tf.Tensor) – 2-dimensional Hermitian tensor of the same dimensions and dtype as rho. Returns the scalar expectation value. tf.Tensor