MPOState

class MPOState(*args, **kwargs)[source]

Bases: MatrixProductOperator, State

An MPO enforcing the Vidal gauge.

This specialization of quimb’s existing quimb.tensor.MatrixProductOperator enforces the Vidal gauge throughout its existence. This ensures a stable behavior of the DynamicMPF algorithm when using the TEBDEvolver.

Initialize a MPOState instance.

Hint

All arguments (positional and keyword) are simply forwarded to the quimb.tensor.MatrixProductOperator constructor. Additionally, the vidal_singular_values attribute gets initialized to a list of empty lists of length equal to the number of sites in this MPO.

Parameters:

Attributes

vidal_singular_values: list[list[float]]

A nested list of singular values. The outer list is of equal length as this MPO itself (quimb.tensor.TensorNetwork1D.L). Every item is another list of all the singular values for determining the Vidal gauge at that site.

Methods

gate_split(gate, where, inplace=False, conj=False, **split_opts)[source]

Apply a two-site gate and contract it back into the MPO.

The basic principle of this method is the same as that of quimb.tensor.MatrixProductState.gate_split(). However, the implementation ensures that the Vidal gauge is conserved.

Parameters:

  • gate (ndarray) – the gate to be applied to the MPO. Its shape should be either (d**2, d**2) for a physical dimension of d, or a reshaped version thereof.

  • where (tuple[int, int]) – the indices of the sites where the gate should be applied.

  • inplace (bool) – whether to perform the gate application in-place or return a new MPOState with the gate applied to it.

  • conj (bool) –

    whether the gate should be applied to the lower (conj=False, the default, lower_ind()) or upper (conj=True, upper_ind()) indices of the underlying MPO.

    Note

    This is essentially how the LHS and RHS of the DynamicMPF are differentiated, by passing their Evolver.conjugate property to this argument.

  • split_opts – additional keyword arguments that will be forwarded to the quimb.tensor.tensor_split() function. These can be used to affect the truncation of the tensor before it gets contracted back into the MPO.

Returns:

The MPOState with the gate applied and contracted.

Return type:

MPOState

gate_split_(gate, where, *, inplace=True, conj=False, **split_opts)
Parameters:
Return type:

MPOState

overlap(initial_state)[source]

Compute the overlap of this state with the provided initial state.

Warning

This implementation only supports instances of quimb.tensor.MatrixProductState for initial_state.

Parameters:

initial_state (Any) – the initial state with which to compute the overlap.

Raises:

TypeError – if the provided initial state has an incompatible type.

Returns:

The overlap of this state with the provided one.

Return type:

complex