460 lines
21 KiB
Plaintext
460 lines
21 KiB
Plaintext
---
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title: SparsePauliOp
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description: API reference for qiskit.quantum_info.SparsePauliOp
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in_page_toc_min_heading_level: 1
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python_api_type: class
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python_api_name: qiskit.quantum_info.SparsePauliOp
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---
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# qiskit.quantum\_info.SparsePauliOp
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<Class id="qiskit.quantum_info.SparsePauliOp" isDedicatedPage={true} github="https://github.com/qiskit/qiskit/tree/stable/0.17/qiskit/quantum_info/operators/symplectic/sparse_pauli_op.py" signature="SparsePauliOp(data, coeffs=None)" modifiers="class">
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Sparse N-qubit operator in a Pauli basis representation.
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This is a sparse representation of an N-qubit matrix [`Operator`](qiskit.quantum_info.Operator "qiskit.quantum_info.Operator") in terms of N-qubit [`PauliTable`](qiskit.quantum_info.PauliTable "qiskit.quantum_info.PauliTable") and complex coefficients.
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It can be used for performing operator arithmetic for hundred of qubits if the number of non-zero Pauli basis terms is sufficiently small.
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The Pauli basis components are stored as a [`PauliTable`](qiskit.quantum_info.PauliTable "qiskit.quantum_info.PauliTable") object and can be accessed using the [`table`](#qiskit.quantum_info.SparsePauliOp.table "qiskit.quantum_info.SparsePauliOp.table") attribute. The coefficients are stored as a complex Numpy array vector and can be accessed using the [`coeffs`](#qiskit.quantum_info.SparsePauliOp.coeffs "qiskit.quantum_info.SparsePauliOp.coeffs") attribute.
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Initialize an operator object.
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**Parameters**
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* **data** ([*PauliTable*](qiskit.quantum_info.PauliTable "qiskit.quantum_info.PauliTable")) – Pauli table of terms.
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* **coeffs** (*np.ndarray*) – complex coefficients for Pauli terms.
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**Raises**
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**QiskitError** – If the input data or coeffs are invalid.
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### \_\_init\_\_
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<Function id="qiskit.quantum_info.SparsePauliOp.__init__" signature="__init__(data, coeffs=None)">
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Initialize an operator object.
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**Parameters**
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* **data** ([*PauliTable*](qiskit.quantum_info.PauliTable "qiskit.quantum_info.PauliTable")) – Pauli table of terms.
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* **coeffs** (*np.ndarray*) – complex coefficients for Pauli terms.
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**Raises**
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**QiskitError** – If the input data or coeffs are invalid.
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</Function>
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## Methods
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| ---------------------------------------------------------------------------------------------------------------------------------------------- | -------------------------------------------------------------------------- |
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| [`__init__`](#qiskit.quantum_info.SparsePauliOp.__init__ "qiskit.quantum_info.SparsePauliOp.__init__")(data\[, coeffs]) | Initialize an operator object. |
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| [`adjoint`](#qiskit.quantum_info.SparsePauliOp.adjoint "qiskit.quantum_info.SparsePauliOp.adjoint")() | Return the adjoint of the Operator. |
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| [`compose`](#qiskit.quantum_info.SparsePauliOp.compose "qiskit.quantum_info.SparsePauliOp.compose")(other\[, qargs, front]) | Return the operator composition with another SparsePauliOp. |
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| [`conjugate`](#qiskit.quantum_info.SparsePauliOp.conjugate "qiskit.quantum_info.SparsePauliOp.conjugate")() | Return the conjugate of the SparsePauliOp. |
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| [`copy`](#qiskit.quantum_info.SparsePauliOp.copy "qiskit.quantum_info.SparsePauliOp.copy")() | Make a deep copy of current operator. |
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| [`dot`](#qiskit.quantum_info.SparsePauliOp.dot "qiskit.quantum_info.SparsePauliOp.dot")(other\[, qargs]) | Return the right multiplied operator self \* other. |
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| [`expand`](#qiskit.quantum_info.SparsePauliOp.expand "qiskit.quantum_info.SparsePauliOp.expand")(other) | Return the reverse-order tensor product with another SparsePauliOp. |
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| [`from_list`](#qiskit.quantum_info.SparsePauliOp.from_list "qiskit.quantum_info.SparsePauliOp.from_list")(obj) | Construct from a list \[(pauli\_str, coeffs)] |
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| [`from_operator`](#qiskit.quantum_info.SparsePauliOp.from_operator "qiskit.quantum_info.SparsePauliOp.from_operator")(obj\[, atol, rtol]) | Construct from an Operator objector. |
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| [`input_dims`](#qiskit.quantum_info.SparsePauliOp.input_dims "qiskit.quantum_info.SparsePauliOp.input_dims")(\[qargs]) | Return tuple of input dimension for specified subsystems. |
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| [`is_unitary`](#qiskit.quantum_info.SparsePauliOp.is_unitary "qiskit.quantum_info.SparsePauliOp.is_unitary")(\[atol, rtol]) | Return True if operator is a unitary matrix. |
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| [`label_iter`](#qiskit.quantum_info.SparsePauliOp.label_iter "qiskit.quantum_info.SparsePauliOp.label_iter")() | Return a label representation iterator. |
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| [`matrix_iter`](#qiskit.quantum_info.SparsePauliOp.matrix_iter "qiskit.quantum_info.SparsePauliOp.matrix_iter")(\[sparse]) | Return a matrix representation iterator. |
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| [`output_dims`](#qiskit.quantum_info.SparsePauliOp.output_dims "qiskit.quantum_info.SparsePauliOp.output_dims")(\[qargs]) | Return tuple of output dimension for specified subsystems. |
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| [`power`](#qiskit.quantum_info.SparsePauliOp.power "qiskit.quantum_info.SparsePauliOp.power")(n) | Return the compose of a operator with itself n times. |
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| [`reshape`](#qiskit.quantum_info.SparsePauliOp.reshape "qiskit.quantum_info.SparsePauliOp.reshape")(\[input\_dims, output\_dims, num\_qubits]) | Return a shallow copy with reshaped input and output subsystem dimensions. |
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| [`simplify`](#qiskit.quantum_info.SparsePauliOp.simplify "qiskit.quantum_info.SparsePauliOp.simplify")(\[atol, rtol]) | Simplify PauliTable by combining duplicates and removing zeros. |
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| [`tensor`](#qiskit.quantum_info.SparsePauliOp.tensor "qiskit.quantum_info.SparsePauliOp.tensor")(other) | Return the tensor product with another SparsePauliOp. |
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| [`to_list`](#qiskit.quantum_info.SparsePauliOp.to_list "qiskit.quantum_info.SparsePauliOp.to_list")(\[array]) | Convert to a list Pauli string labels and coefficients. |
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| [`to_matrix`](#qiskit.quantum_info.SparsePauliOp.to_matrix "qiskit.quantum_info.SparsePauliOp.to_matrix")(\[sparse]) | Convert to a dense or sparse matrix. |
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| [`to_operator`](#qiskit.quantum_info.SparsePauliOp.to_operator "qiskit.quantum_info.SparsePauliOp.to_operator")() | Convert to a matrix Operator object |
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| [`transpose`](#qiskit.quantum_info.SparsePauliOp.transpose "qiskit.quantum_info.SparsePauliOp.transpose")() | Return the transpose of the SparsePauliOp. |
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## Attributes
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| ------------------------------------------------------------------------------------------------------------ | -------------------------------------------------------------------- |
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| [`atol`](#qiskit.quantum_info.SparsePauliOp.atol "qiskit.quantum_info.SparsePauliOp.atol") | Default absolute tolerance parameter for float comparisons. |
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| [`coeffs`](#qiskit.quantum_info.SparsePauliOp.coeffs "qiskit.quantum_info.SparsePauliOp.coeffs") | Return the Pauli coefficients. |
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| [`dim`](#qiskit.quantum_info.SparsePauliOp.dim "qiskit.quantum_info.SparsePauliOp.dim") | Return tuple (input\_shape, output\_shape). |
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| [`num_qubits`](#qiskit.quantum_info.SparsePauliOp.num_qubits "qiskit.quantum_info.SparsePauliOp.num_qubits") | Return the number of qubits if a N-qubit operator or None otherwise. |
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| [`qargs`](#qiskit.quantum_info.SparsePauliOp.qargs "qiskit.quantum_info.SparsePauliOp.qargs") | Return the qargs for the operator. |
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| [`rtol`](#qiskit.quantum_info.SparsePauliOp.rtol "qiskit.quantum_info.SparsePauliOp.rtol") | Default relative tolerance parameter for float comparisons. |
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| [`size`](#qiskit.quantum_info.SparsePauliOp.size "qiskit.quantum_info.SparsePauliOp.size") | The number of Pauli of Pauli terms in the operator. |
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| [`table`](#qiskit.quantum_info.SparsePauliOp.table "qiskit.quantum_info.SparsePauliOp.table") | Return the the PauliTable. |
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### adjoint
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<Function id="qiskit.quantum_info.SparsePauliOp.adjoint" signature="adjoint()">
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Return the adjoint of the Operator.
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</Function>
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### atol
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<Attribute id="qiskit.quantum_info.SparsePauliOp.atol">
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Default absolute tolerance parameter for float comparisons.
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</Attribute>
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### coeffs
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<Attribute id="qiskit.quantum_info.SparsePauliOp.coeffs">
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Return the Pauli coefficients.
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</Attribute>
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### compose
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<Function id="qiskit.quantum_info.SparsePauliOp.compose" signature="compose(other, qargs=None, front=False)">
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Return the operator composition with another SparsePauliOp.
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**Parameters**
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* **other** ([*SparsePauliOp*](#qiskit.quantum_info.SparsePauliOp "qiskit.quantum_info.SparsePauliOp")) – a SparsePauliOp object.
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* **qargs** (*list or None*) – Optional, a list of subsystem positions to apply other on. If None apply on all subsystems (default: None).
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* **front** (*bool*) – If True compose using right operator multiplication, instead of left multiplication \[default: False].
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**Returns**
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The composed SparsePauliOp.
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**Return type**
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[SparsePauliOp](#qiskit.quantum_info.SparsePauliOp "qiskit.quantum_info.SparsePauliOp")
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**Raises**
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**QiskitError** – if other cannot be converted to an operator, or has incompatible dimensions for specified subsystems.
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<Admonition title="Note" type="note">
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Composition (`&`) by default is defined as left matrix multiplication for matrix operators, while [`dot()`](#qiskit.quantum_info.SparsePauliOp.dot "qiskit.quantum_info.SparsePauliOp.dot") is defined as right matrix multiplication. That is that `A & B == A.compose(B)` is equivalent to `B.dot(A)` when `A` and `B` are of the same type.
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Setting the `front=True` kwarg changes this to right matrix multiplication and is equivalent to the [`dot()`](#qiskit.quantum_info.SparsePauliOp.dot "qiskit.quantum_info.SparsePauliOp.dot") method `A.dot(B) == A.compose(B, front=True)`.
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</Admonition>
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</Function>
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### conjugate
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<Function id="qiskit.quantum_info.SparsePauliOp.conjugate" signature="conjugate()">
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Return the conjugate of the SparsePauliOp.
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</Function>
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### copy
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<Function id="qiskit.quantum_info.SparsePauliOp.copy" signature="copy()">
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Make a deep copy of current operator.
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</Function>
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### dim
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<Attribute id="qiskit.quantum_info.SparsePauliOp.dim">
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Return tuple (input\_shape, output\_shape).
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</Attribute>
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### dot
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<Function id="qiskit.quantum_info.SparsePauliOp.dot" signature="dot(other, qargs=None)">
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Return the right multiplied operator self \* other.
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**Parameters**
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* **other** ([*Operator*](qiskit.quantum_info.Operator "qiskit.quantum_info.Operator")) – an operator object.
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* **qargs** (*list or None*) – Optional, a list of subsystem positions to apply other on. If None apply on all subsystems (default: None).
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**Returns**
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The right matrix multiplied Operator.
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**Return type**
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[Operator](qiskit.quantum_info.Operator "qiskit.quantum_info.Operator")
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</Function>
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### expand
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<Function id="qiskit.quantum_info.SparsePauliOp.expand" signature="expand(other)">
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Return the reverse-order tensor product with another SparsePauliOp.
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**Parameters**
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**other** ([*SparsePauliOp*](#qiskit.quantum_info.SparsePauliOp "qiskit.quantum_info.SparsePauliOp")) – a SparsePauliOp object.
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**Returns**
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**the tensor product $b \otimes a$, where $a$**
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is the current SparsePauliOp, and $b$ is the other SparsePauliOp.
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**Return type**
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[SparsePauliOp](#qiskit.quantum_info.SparsePauliOp "qiskit.quantum_info.SparsePauliOp")
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</Function>
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### from\_list
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<Function id="qiskit.quantum_info.SparsePauliOp.from_list" signature="from_list(obj)" modifiers="static">
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Construct from a list \[(pauli\_str, coeffs)]
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</Function>
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### from\_operator
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<Function id="qiskit.quantum_info.SparsePauliOp.from_operator" signature="from_operator(obj, atol=None, rtol=None)" modifiers="static">
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Construct from an Operator objector.
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Note that the cost of this construction is exponential as it involves taking inner products with every element of the N-qubit Pauli basis.
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**Parameters**
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* **obj** ([*Operator*](qiskit.quantum_info.Operator "qiskit.quantum_info.Operator")) – an N-qubit operator.
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* **atol** (*float*) – Optional. Absolute tolerance for checking if coefficients are zero (Default: 1e-8).
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* **rtol** (*float*) – Optional. relative tolerance for checking if coefficients are zero (Default: 1e-5).
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**Returns**
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the SparsePauliOp representation of the operator.
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**Return type**
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[SparsePauliOp](#qiskit.quantum_info.SparsePauliOp "qiskit.quantum_info.SparsePauliOp")
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**Raises**
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**QiskitError** – if the input operator is not an N-qubit operator.
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</Function>
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### input\_dims
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<Function id="qiskit.quantum_info.SparsePauliOp.input_dims" signature="input_dims(qargs=None)">
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Return tuple of input dimension for specified subsystems.
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</Function>
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### is\_unitary
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<Function id="qiskit.quantum_info.SparsePauliOp.is_unitary" signature="is_unitary(atol=None, rtol=None)">
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Return True if operator is a unitary matrix.
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**Parameters**
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* **atol** (*float*) – Optional. Absolute tolerance for checking if coefficients are zero (Default: 1e-8).
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* **rtol** (*float*) – Optional. relative tolerance for checking if coefficients are zero (Default: 1e-5).
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**Returns**
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True if the operator is unitary, False otherwise.
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**Return type**
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bool
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</Function>
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### label\_iter
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<Function id="qiskit.quantum_info.SparsePauliOp.label_iter" signature="label_iter()">
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Return a label representation iterator.
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This is a lazy iterator that converts each term in the SparsePauliOp into a tuple (label, coeff). To convert the entire table to labels use the `to_labels()` method.
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**Returns**
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label iterator object for the PauliTable.
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**Return type**
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LabelIterator
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</Function>
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### matrix\_iter
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<Function id="qiskit.quantum_info.SparsePauliOp.matrix_iter" signature="matrix_iter(sparse=False)">
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Return a matrix representation iterator.
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This is a lazy iterator that converts each term in the SparsePauliOp into a matrix as it is used. To convert to a single matrix use the [`to_matrix()`](#qiskit.quantum_info.SparsePauliOp.to_matrix "qiskit.quantum_info.SparsePauliOp.to_matrix") method.
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**Parameters**
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**sparse** (*bool*) – optionally return sparse CSR matrices if True, otherwise return Numpy array matrices (Default: False)
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**Returns**
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matrix iterator object for the PauliTable.
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**Return type**
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MatrixIterator
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</Function>
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### num\_qubits
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<Attribute id="qiskit.quantum_info.SparsePauliOp.num_qubits">
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Return the number of qubits if a N-qubit operator or None otherwise.
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</Attribute>
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### output\_dims
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<Function id="qiskit.quantum_info.SparsePauliOp.output_dims" signature="output_dims(qargs=None)">
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Return tuple of output dimension for specified subsystems.
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</Function>
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### power
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<Function id="qiskit.quantum_info.SparsePauliOp.power" signature="power(n)">
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Return the compose of a operator with itself n times.
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**Parameters**
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**n** (*int*) – the number of times to compose with self (n>0).
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**Returns**
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the n-times composed operator.
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**Return type**
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[Pauli](qiskit.quantum_info.Pauli "qiskit.quantum_info.Pauli")
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**Raises**
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**QiskitError** – if the input and output dimensions of the operator are not equal, or the power is not a positive integer.
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</Function>
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### qargs
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<Attribute id="qiskit.quantum_info.SparsePauliOp.qargs">
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Return the qargs for the operator.
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</Attribute>
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### reshape
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<Function id="qiskit.quantum_info.SparsePauliOp.reshape" signature="reshape(input_dims=None, output_dims=None, num_qubits=None)">
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Return a shallow copy with reshaped input and output subsystem dimensions.
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**Parameters**
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* **input\_dims** (*None or tuple*) – new subsystem input dimensions. If None the original input dims will be preserved \[Default: None].
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* **output\_dims** (*None or tuple*) – new subsystem output dimensions. If None the original output dims will be preserved \[Default: None].
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* **num\_qubits** (*None or int*) – reshape to an N-qubit operator \[Default: None].
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**Returns**
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returns self with reshaped input and output dimensions.
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**Return type**
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BaseOperator
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**Raises**
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**QiskitError** – if combined size of all subsystem input dimension or subsystem output dimensions is not constant.
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</Function>
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### rtol
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<Attribute id="qiskit.quantum_info.SparsePauliOp.rtol">
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Default relative tolerance parameter for float comparisons.
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</Attribute>
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### simplify
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<Function id="qiskit.quantum_info.SparsePauliOp.simplify" signature="simplify(atol=None, rtol=None)">
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Simplify PauliTable by combining duplicates and removing zeros.
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**Parameters**
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* **atol** (*float*) – Optional. Absolute tolerance for checking if coefficients are zero (Default: 1e-8).
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* **rtol** (*float*) – Optional. relative tolerance for checking if coefficients are zero (Default: 1e-5).
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**Returns**
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the simplified SparsePauliOp operator.
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**Return type**
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[SparsePauliOp](#qiskit.quantum_info.SparsePauliOp "qiskit.quantum_info.SparsePauliOp")
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</Function>
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### size
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<Attribute id="qiskit.quantum_info.SparsePauliOp.size">
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The number of Pauli of Pauli terms in the operator.
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</Attribute>
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### table
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<Attribute id="qiskit.quantum_info.SparsePauliOp.table">
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Return the the PauliTable.
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</Attribute>
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### tensor
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<Function id="qiskit.quantum_info.SparsePauliOp.tensor" signature="tensor(other)">
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Return the tensor product with another SparsePauliOp.
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**Parameters**
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**other** ([*SparsePauliOp*](#qiskit.quantum_info.SparsePauliOp "qiskit.quantum_info.SparsePauliOp")) – a SparsePauliOp object.
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**Returns**
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**the tensor product $a \otimes b$, where $a$**
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is the current SparsePauliOp, and $b$ is the other SparsePauliOp.
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**Return type**
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[SparsePauliOp](#qiskit.quantum_info.SparsePauliOp "qiskit.quantum_info.SparsePauliOp")
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<Admonition title="Note" type="note">
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The tensor product can be obtained using the `^` binary operator. Hence `a.tensor(b)` is equivalent to `a ^ b`.
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</Admonition>
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</Function>
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### to\_list
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<Function id="qiskit.quantum_info.SparsePauliOp.to_list" signature="to_list(array=False)">
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Convert to a list Pauli string labels and coefficients.
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For operators with a lot of terms converting using the `array=True` kwarg will be more efficient since it allocates memory for the full Numpy array of labels in advance.
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||
**Parameters**
|
||
|
||
**array** (*bool*) – return a Numpy array if True, otherwise return a list (Default: False).
|
||
|
||
**Returns**
|
||
|
||
List of pairs (label, coeff) for rows of the PauliTable.
|
||
|
||
**Return type**
|
||
|
||
list or array
|
||
</Function>
|
||
|
||
### to\_matrix
|
||
|
||
<Function id="qiskit.quantum_info.SparsePauliOp.to_matrix" signature="to_matrix(sparse=False)">
|
||
Convert to a dense or sparse matrix.
|
||
|
||
**Parameters**
|
||
|
||
**sparse** (*bool*) – if True return a sparse CSR matrix, otherwise return dense Numpy array (Default: False).
|
||
|
||
**Returns**
|
||
|
||
A dense matrix if sparse=False. csr\_matrix: A sparse matrix in CSR format if sparse=True.
|
||
|
||
**Return type**
|
||
|
||
array
|
||
</Function>
|
||
|
||
### to\_operator
|
||
|
||
<Function id="qiskit.quantum_info.SparsePauliOp.to_operator" signature="to_operator()">
|
||
Convert to a matrix Operator object
|
||
</Function>
|
||
|
||
### transpose
|
||
|
||
<Function id="qiskit.quantum_info.SparsePauliOp.transpose" signature="transpose()">
|
||
Return the transpose of the SparsePauliOp.
|
||
</Function>
|
||
</Class>
|
||
|