qiskit-documentation/docs/api/qiskit-addon-mpf/backends-quimb-tebd-mpo-state.mdx

---
title: MPOState (latest version)
description: API reference for qiskit_addon_mpf.backends.quimb_tebd.MPOState in the latest version of qiskit-addon-mpf
in_page_toc_min_heading_level: 1
python_api_type: class
python_api_name: qiskit_addon_mpf.backends.quimb_tebd.MPOState
---

# MPOState

<Class id="qiskit_addon_mpf.backends.quimb_tebd.MPOState" isDedicatedPage={true} github="https://github.com/Qiskit/qiskit-addon-mpf/tree/stable/0.3/qiskit_addon_mpf/backends/quimb_tebd/state.py#L39-L234" signature="MPOState(*args, **kwargs)" modifiers="class">
  Bases: [`MatrixProductOperator`](https://quimb.readthedocs.io/en/latest/autoapi/quimb/tensor/tensor_1d/index.html#quimb.tensor.tensor_1d.MatrixProductOperator "(in quimb v1.10)"), [`State`](backends#state "qiskit_addon_mpf.backends.interface.State")

  An MPO enforcing the Vidal gauge.

  This specialization of quimb’s existing [`quimb.tensor.MatrixProductOperator`](https://quimb.readthedocs.io/en/latest/autoapi/quimb/tensor/index.html#quimb.tensor.MatrixProductOperator "(in quimb v1.10)") enforces the Vidal gauge throughout its existence. This ensures a stable behavior of the [`DynamicMPF`](dynamic#dynamicmpf "qiskit_addon_mpf.dynamic.DynamicMPF") algorithm when using the [`TEBDEvolver`](backends-quimb-tebd-tebd-evolver "qiskit_addon_mpf.backends.quimb_tebd.TEBDEvolver").

  Initialize a [`MPOState`](#qiskit_addon_mpf.backends.quimb_tebd.MPOState "qiskit_addon_mpf.backends.quimb_tebd.MPOState") instance.

  <Admonition title="Hint" type="note">
    All arguments (positional and keyword) are simply forwarded to the [`quimb.tensor.MatrixProductOperator`](https://quimb.readthedocs.io/en/latest/autoapi/quimb/tensor/index.html#quimb.tensor.MatrixProductOperator "(in quimb v1.10)") constructor. Additionally, the [`vidal_singular_values`](#qiskit_addon_mpf.backends.quimb_tebd.MPOState.vidal_singular_values "qiskit_addon_mpf.backends.quimb_tebd.MPOState.vidal_singular_values") attribute gets initialized to a list of empty lists of length equal to the number of sites in this MPO.
  </Admonition>

  **Parameters**

  *   **args** – all positional arguments will be forwarded to the [`quimb.tensor.MatrixProductState`](https://quimb.readthedocs.io/en/latest/autoapi/quimb/tensor/index.html#quimb.tensor.MatrixProductState "(in quimb v1.10)") constructor.
  *   **kwargs** – all keyword arguments will be forwarded to the [`quimb.tensor.MatrixProductState`](https://quimb.readthedocs.io/en/latest/autoapi/quimb/tensor/index.html#quimb.tensor.MatrixProductState "(in quimb v1.10)") constructor.

  ## Attributes

  ### vidal\_singular\_values

  <Attribute id="qiskit_addon_mpf.backends.quimb_tebd.MPOState.vidal_singular_values" attributeTypeHint="list[list[float]]">
    A nested list of singular values. The outer list is of equal length as this MPO itself ([`quimb.tensor.TensorNetwork1D.L`](https://quimb.readthedocs.io/en/latest/autoapi/quimb/tensor/index.html#quimb.tensor.TensorNetwork1D.L "(in quimb v1.10)")). Every item is another list of all the singular values for determining the Vidal gauge at that site.
  </Attribute>

  ## Methods

  ### gate\_split

  <Function id="qiskit_addon_mpf.backends.quimb_tebd.MPOState.gate_split" github="https://github.com/Qiskit/qiskit-addon-mpf/tree/stable/0.3/qiskit_addon_mpf/backends/quimb_tebd/state.py#L72-L196" signature="gate_split(gate, where, inplace=False, conj=False, **split_opts)">
    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()`](https://quimb.readthedocs.io/en/latest/autoapi/quimb/tensor/index.html#quimb.tensor.MatrixProductState.gate_split "(in quimb v1.10)"). However, the implementation ensures that the Vidal gauge is conserved.

    **Parameters**

    *   **gate** ([*ndarray*](https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray "(in NumPy v2.2)")) – 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*](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.13)")*\[*[*int*](https://docs.python.org/3/library/functions.html#int "(in Python v3.13)")*,* [*int*](https://docs.python.org/3/library/functions.html#int "(in Python v3.13)")*]*) – the indices of the sites where the gate should be applied.

    *   **inplace** ([*bool*](https://docs.python.org/3/library/functions.html#bool "(in Python v3.13)")) – whether to perform the gate application in-place or return a new [`MPOState`](#qiskit_addon_mpf.backends.quimb_tebd.MPOState "qiskit_addon_mpf.backends.quimb_tebd.MPOState") with the gate applied to it.

    *   **conj** ([*bool*](https://docs.python.org/3/library/functions.html#bool "(in Python v3.13)")) –

        whether the gate should be applied to the lower (`conj=False`, the default, [`lower_ind()`](https://quimb.readthedocs.io/en/latest/autoapi/quimb/tensor/tensor_arbgeom/index.html#quimb.tensor.tensor_arbgeom.TensorNetworkGenOperator.lower_ind "(in quimb v1.10)")) or upper (`conj=True`, [`upper_ind()`](https://quimb.readthedocs.io/en/latest/autoapi/quimb/tensor/tensor_arbgeom/index.html#quimb.tensor.tensor_arbgeom.TensorNetworkGenOperator.upper_ind "(in quimb v1.10)")) indices of the underlying MPO.

            <Admonition title="Note" type="note">
              This is essentially how the LHS and RHS of the [`DynamicMPF`](dynamic#dynamicmpf "qiskit_addon_mpf.dynamic.DynamicMPF") are differentiated, by passing their [`Evolver.conjugate`](backends#conjugate "qiskit_addon_mpf.backends.Evolver.conjugate") property to this argument.
            </Admonition>

    *   **split\_opts** – additional keyword arguments that will be forwarded to the [`quimb.tensor.tensor_split()`](https://quimb.readthedocs.io/en/latest/autoapi/quimb/tensor/index.html#quimb.tensor.tensor_split "(in quimb v1.10)") function. These can be used to affect the truncation of the tensor before it gets contracted back into the MPO.

    **Returns**

    The [`MPOState`](#qiskit_addon_mpf.backends.quimb_tebd.MPOState "qiskit_addon_mpf.backends.quimb_tebd.MPOState") with the `gate` applied and contracted.

    **Return type**

    [*MPOState*](#qiskit_addon_mpf.backends.quimb_tebd.MPOState "qiskit_addon_mpf.backends.quimb_tebd.state.MPOState")
  </Function>

  ### gate\_split\_

  <Function id="qiskit_addon_mpf.backends.quimb_tebd.MPOState.gate_split_" signature="gate_split_(gate, where, *, inplace=True, conj=False, **split_opts)">
    **Parameters**

    *   **gate** (*np.ndarray*)
    *   **where** ([*tuple*](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.13)")*\[*[*int*](https://docs.python.org/3/library/functions.html#int "(in Python v3.13)")*,* [*int*](https://docs.python.org/3/library/functions.html#int "(in Python v3.13)")*]*)
    *   **inplace** ([*bool*](https://docs.python.org/3/library/functions.html#bool "(in Python v3.13)"))
    *   **conj** ([*bool*](https://docs.python.org/3/library/functions.html#bool "(in Python v3.13)"))

    **Return type**

    [MPOState](#qiskit_addon_mpf.backends.quimb_tebd.MPOState "qiskit_addon_mpf.backends.quimb_tebd.MPOState")
  </Function>

  ### overlap

  <Function id="qiskit_addon_mpf.backends.quimb_tebd.MPOState.overlap" github="https://github.com/Qiskit/qiskit-addon-mpf/tree/stable/0.3/qiskit_addon_mpf/backends/quimb_tebd/state.py#L201-L234" signature="overlap(initial_state)">
    Compute the overlap of this state with the provided initial state.

    <Admonition title="Warning" type="caution">
      This implementation only supports instances of [`quimb.tensor.MatrixProductState`](https://quimb.readthedocs.io/en/latest/autoapi/quimb/tensor/index.html#quimb.tensor.MatrixProductState "(in quimb v1.10)") for `initial_state`.
    </Admonition>

    **Parameters**

    **initial\_state** ([*Any*](https://docs.python.org/3/library/typing.html#typing.Any "(in Python v3.13)")) – the initial state with which to compute the overlap.

    **Raises**

    [**TypeError**](https://docs.python.org/3/library/exceptions.html#TypeError "(in Python v3.13)") – if the provided initial state has an incompatible type.

    **Returns**

    The overlap of this state with the provided one.

    **Return type**

    [complex](https://docs.python.org/3/library/functions.html#complex "(in Python v3.13)")
  </Function>
</Class>