qml.math

This package contains unified functions for framework-agnostic tensor and array manipulation. Given the input tensor-like object, the call is dispatched to the corresponding array manipulation framework, allowing for end-to-end differentiation to be preserved.

Warning

These functions are experimental, and only a subset of common functionality is supported. Furthermore, the names and behaviour of these functions may differ from similar functions in common frameworks; please refer to the function docstrings for more details.

The following frameworks are currently supported:

• NumPy

• Autograd

• TensorFlow

• PyTorch

• JAX

Functions

add(*args[, like])	Add arguments element-wise.
allclose(a, b[, rtol, atol])	Returns True if two arrays are element-wise equal within a tolerance.
allequal(tensor1, tensor2, **kwargs)	Returns True if two tensors are element-wise equal along a given axis.
array(*args[, like])	Creates an array or tensor object of the target framework.
block_diag(values[, like])	Combine a sequence of 2D tensors to form a block diagonal tensor.
cast(tensor, dtype)	Casts the given tensor to a new type.
cast_like(tensor1, tensor2)	Casts a tensor to the same dtype as another.
concatenate(values[, axis, like])	Concatenate a sequence of tensors along the specified axis.
convert_like(tensor1, tensor2)	Convert a tensor to the same type as another.
cov_matrix(prob, obs[, wires, diag_approx])	Calculate the covariance matrix of a list of commuting observables, given the joint probability distribution of the system in the shared eigenbasis.
detach(tensor[, like])	Detach a tensor from its trace and return just its numerical values.
diag(values[, k, like])	Construct a diagonal tensor from a list of scalars.
dm_from_state_vector(state[, check_state, ...])	Convenience function to compute a (full) density matrix from a state vector.
dot(tensor1, tensor2[, like])	Returns the matrix or dot product of two tensors.
einsum(indices, *operands[, like, optimize])	Evaluates the Einstein summation convention on the operands.
expand_matrix(mat, wires[, wire_order, ...])	Re-express a matrix acting on a subspace defined by a set of wire labels according to a global wire order.
expectation_value(operator_matrix, state_vector)	Compute the expectation value of an operator with respect to a pure state.
eye(*args[, like])	Creates an identity array or tensor object of the target framework.
fidelity(state0, state1[, check_state, c_dtype])	Compute the fidelity for two states (given as density matrices) acting on quantum systems with the same size.
fidelity_statevector(state0, state1[, ...])	Compute the fidelity for two states (given as state vectors) acting on quantum systems with the same size.
frobenius_inner_product(A, B[, normalize, like])	Frobenius inner product between two matrices.
get_dtype_name(x)	An interface independent way of getting the name of the datatype.
get_interface(*values)	Determines the correct framework to dispatch to given a tensor-like object or a sequence of tensor-like objects.
get_deep_interface(value)	Given a deep data structure with interface-specific scalars at the bottom, return their interface name.
get_trainable_indices(values[, like])	Returns a set containing the trainable indices of a sequence of values.
in_backprop(tensor[, interface])	Returns True if the tensor is considered to be in a backpropagation environment, it works for Autograd, TensorFlow and Jax.
is_abstract(tensor[, like])	Returns True if the tensor is considered abstract.
is_independent(func, interface, args[, ...])	Test whether a function is independent of its input arguments, both numerically and analytically.
iscomplex(tensor[, like])	Return True if the tensor has a non-zero complex component.
marginal_prob(prob, axis)	Compute the marginal probability given a joint probability distribution expressed as a tensor.
max_entropy(state, indices[, base, ...])	Compute the maximum entropy of a density matrix on a given subsystem.
min_entropy(state, indices[, base, ...])	Compute the minimum entropy from a density matrix.
multi_dispatch([argnum, tensor_list])	Decorator to dispatch arguments handled by the interface.
mutual_info(state, indices0, indices1[, ...])	Compute the mutual information between two subsystems given a state:
ones_like(tensor[, dtype])	Returns a tensor of all ones with the same shape and dtype as the input tensor.
partial_trace(matrix, indices[, c_dtype])	Compute the reduced density matrix by tracing out the provided indices.
purity(state, indices[, check_state, c_dtype])	Computes the purity of a density matrix.
reduce_dm(density_matrix, indices[, ...])	Compute the density matrix from a state represented with a density matrix.
reduce_statevector(state, indices[, ...])	Compute the density matrix from a state vector.
relative_entropy(state0, state1[, base, ...])	Compute the quantum relative entropy of one state with respect to another.
requires_grad(tensor[, interface])	Returns True if the tensor is considered trainable.
sqrt_matrix(density_matrix)	Compute the square root matrix of a density matrix where \(\rho = \sqrt{\rho} \times \sqrt{\rho}\)
scatter_element_add(tensor, index, value[, like])	In-place addition of a multidimensional value over various indices of a tensor.
stack(values[, axis, like])	Stack a sequence of tensors along the specified axis.
svd(tensor[, like])	Compute the singular value decomposition of a tensor in each interface.
tensordot(tensor1, tensor2[, axes, like])	Returns the tensor product of two tensors.
trace_distance(state0, state1[, ...])	Compute the trace distance between two quantum states.
unwrap(values[, max_depth])	Unwrap a sequence of objects to NumPy arrays.
vn_entropy(state, indices[, base, ...])	Compute the Von Neumann entropy from a density matrix on a given subsystem.
vn_entanglement_entropy(state, indices0, ...)	Compute the Von Neumann entanglement entropy between two subsystems in a given state.
where(condition[, x, y])	Returns elements chosen from x or y depending on a boolean tensor condition, or the indices of entries satisfying the condition.

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