674 lines
23 KiB
Plaintext
674 lines
23 KiB
Plaintext
---
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title: Statevector (v0.31)
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description: API reference for qiskit.quantum_info.Statevector in qiskit v0.31
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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.Statevector
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---
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# Statevector
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<Class id="qiskit.quantum_info.Statevector" isDedicatedPage={true} github="https://github.com/qiskit/qiskit/tree/stable/0.18/qiskit/quantum_info/states/statevector.py" signature="Statevector(data, dims=None)" modifiers="class">
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Bases: `qiskit.quantum_info.states.quantum_state.QuantumState`, `qiskit.quantum_info.operators.mixins.tolerances.TolerancesMixin`
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Statevector class
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Initialize a statevector object.
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**Parameters**
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* \*\*(****np.array**** or ****list**** or ****Statevector**** or ****Operator**** or \*\***QuantumCircuit or** (*data*) – qiskit.circuit.Instruction): Data from which the statevector can be constructed. This can be either a complex vector, another statevector, a ```Operator` with only one column or a ``QuantumCircuit``` or `Instruction`. If the data is a circuit or instruction, the statevector is constructed by assuming that all qubits are initialized to the zero state.
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* **dims** (*int or tuple or list*) – Optional. The subsystem dimension of the state (See additional information).
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**Raises**
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**QiskitError** – if input data is not valid.
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**Additional Information:**
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The `dims` kwarg can be None, an integer, or an iterable of integers.
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* `Iterable` – the subsystem dimensions are the values in the list with the total number of subsystems given by the length of the list.
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* `Int` or `None` – the length of the input vector specifies the total dimension of the density matrix. If it is a power of two the state will be initialized as an N-qubit state. If it is not a power of two the state will have a single d-dimensional subsystem.
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## Methods
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<span id="qiskit-quantum-info-statevector-conjugate" />
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### conjugate
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<Function id="qiskit.quantum_info.Statevector.conjugate" signature="Statevector.conjugate()">
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Return the conjugate of the operator.
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</Function>
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<span id="qiskit-quantum-info-statevector-copy" />
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### copy
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<Function id="qiskit.quantum_info.Statevector.copy" signature="Statevector.copy()">
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Make a copy of current operator.
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</Function>
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<span id="qiskit-quantum-info-statevector-dims" />
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### dims
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<Function id="qiskit.quantum_info.Statevector.dims" signature="Statevector.dims(qargs=None)">
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Return tuple of input dimension for specified subsystems.
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</Function>
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<span id="qiskit-quantum-info-statevector-draw" />
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### draw
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<Function id="qiskit.quantum_info.Statevector.draw" signature="Statevector.draw(output=None, **drawer_args)">
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Return a visualization of the Statevector.
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**repr**: ASCII TextMatrix of the state’s `__repr__`.
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**text**: ASCII TextMatrix that can be printed in the console.
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**latex**: An IPython Latex object for displaying in Jupyter Notebooks.
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**latex\_source**: Raw, uncompiled ASCII source to generate array using LaTeX.
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**qsphere**: Matplotlib figure, rendering of statevector using plot\_state\_qsphere().
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**hinton**: Matplotlib figure, rendering of statevector using plot\_state\_hinton().
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**bloch**: Matplotlib figure, rendering of statevector using plot\_bloch\_multivector().
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**city**: Matplotlib figure, rendering of statevector using plot\_state\_city().
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**paulivec**: Matplotlib figure, rendering of statevector using plot\_state\_paulivec().
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**Parameters**
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* **output** (*str*) – Select the output method to use for drawing the state. Valid choices are repr, text, latex, latex\_source, qsphere, hinton, bloch, city, or paulivec. Default is repr. Default can be changed by adding the line `state_drawer = <default>` to `~/.qiskit/settings.conf` under `[default]`.
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* **drawer\_args** – Arguments to be passed directly to the relevant drawing function or constructor (TextMatrix(), array\_to\_latex(), plot\_state\_qsphere(), plot\_state\_hinton() or plot\_bloch\_multivector()). See the relevant function under qiskit.visualization for that function’s documentation.
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**Returns**
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`matplotlib.Figure` or `str` or `TextMatrix` or `IPython.display.Latex`: Drawing of the Statevector.
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**Raises**
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**ValueError** – when an invalid output method is selected.
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</Function>
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<span id="qiskit-quantum-info-statevector-equiv" />
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### equiv
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<Function id="qiskit.quantum_info.Statevector.equiv" signature="Statevector.equiv(other, rtol=None, atol=None)">
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Return True if other is equivalent as a statevector up to global phase.
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<Admonition title="Note" type="note">
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If other is not a Statevector, but can be used to initialize a statevector object, this will check that Statevector(other) is equivalent to the current statevector up to global phase.
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</Admonition>
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**Parameters**
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* **other** ([*Statevector*](qiskit.quantum_info.Statevector "qiskit.quantum_info.Statevector")) – an object from which a `Statevector` can be constructed.
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* **rtol** (*float*) – relative tolerance value for comparison.
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* **atol** (*float*) – absolute tolerance value for comparison.
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**Returns**
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True if statevectors are equivalent up to global phase.
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**Return type**
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bool
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</Function>
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<span id="qiskit-quantum-info-statevector-evolve" />
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### evolve
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<Function id="qiskit.quantum_info.Statevector.evolve" signature="Statevector.evolve(other, qargs=None)">
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Evolve a quantum state by the operator.
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**Parameters**
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* **other** ([*Operator*](qiskit.quantum_info.Operator "qiskit.quantum_info.Operator")) – The operator to evolve by.
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* **qargs** (*list*) – a list of Statevector subsystem positions to apply the operator on.
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**Returns**
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the output quantum state.
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**Return type**
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[Statevector](qiskit.quantum_info.Statevector "qiskit.quantum_info.Statevector")
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**Raises**
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**QiskitError** – if the operator dimension does not match the specified Statevector subsystem dimensions.
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</Function>
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<span id="qiskit-quantum-info-statevector-expand" />
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### expand
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<Function id="qiskit.quantum_info.Statevector.expand" signature="Statevector.expand(other)">
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Return the tensor product state other ⊗ self.
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**Parameters**
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**other** ([*Statevector*](qiskit.quantum_info.Statevector "qiskit.quantum_info.Statevector")) – a quantum state object.
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**Returns**
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the tensor product state other ⊗ self.
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**Return type**
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[Statevector](qiskit.quantum_info.Statevector "qiskit.quantum_info.Statevector")
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**Raises**
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**QiskitError** – if other is not a quantum state.
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</Function>
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<span id="qiskit-quantum-info-statevector-expectation-value" />
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### expectation\_value
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<Function id="qiskit.quantum_info.Statevector.expectation_value" signature="Statevector.expectation_value(oper, qargs=None)">
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Compute the expectation value of an operator.
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**Parameters**
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* **oper** ([*Operator*](qiskit.quantum_info.Operator "qiskit.quantum_info.Operator")) – an operator to evaluate expval of.
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* **qargs** (*None or list*) – subsystems to apply operator on.
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**Returns**
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the expectation value.
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**Return type**
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complex
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</Function>
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<span id="qiskit-quantum-info-statevector-from-instruction" />
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### from\_instruction
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<Function id="qiskit.quantum_info.Statevector.from_instruction" signature="Statevector.from_instruction(instruction)" modifiers="classmethod">
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Return the output statevector of an instruction.
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The statevector is initialized in the state $|{0,\ldots,0}\rangle$ of the same number of qubits as the input instruction or circuit, evolved by the input instruction, and the output statevector returned.
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**Parameters**
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**instruction** ([*qiskit.circuit.Instruction*](qiskit.circuit.Instruction "qiskit.circuit.Instruction") *or*[*QuantumCircuit*](qiskit.circuit.QuantumCircuit "qiskit.circuit.QuantumCircuit")) – instruction or circuit
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**Returns**
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The final statevector.
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**Return type**
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[Statevector](qiskit.quantum_info.Statevector "qiskit.quantum_info.Statevector")
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**Raises**
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**QiskitError** – if the instruction contains invalid instructions for the statevector simulation.
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</Function>
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<span id="qiskit-quantum-info-statevector-from-int" />
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### from\_int
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<Function id="qiskit.quantum_info.Statevector.from_int" signature="Statevector.from_int(i, dims)" modifiers="static">
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Return a computational basis statevector.
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**Parameters**
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* **i** (*int*) – the basis state element.
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* **dims** (*int or tuple or list*) – The subsystem dimensions of the statevector (See additional information).
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**Returns**
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The computational basis state $|i\rangle$.
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**Return type**
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[Statevector](qiskit.quantum_info.Statevector "qiskit.quantum_info.Statevector")
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#### Additional Information:
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The `dims` kwarg can be an integer or an iterable of integers.
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* `Iterable` – the subsystem dimensions are the values in the list with the total number of subsystems given by the length of the list.
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* `Int` – the integer specifies the total dimension of the state. If it is a power of two the state will be initialized as an N-qubit state. If it is not a power of two the state will have a single d-dimensional subsystem.
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</Function>
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<span id="qiskit-quantum-info-statevector-from-label" />
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### from\_label
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<Function id="qiskit.quantum_info.Statevector.from_label" signature="Statevector.from_label(label)" modifiers="classmethod">
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Return a tensor product of Pauli X,Y,Z eigenstates.
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| Label | Statevector |
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| ----- | ------------------------------- |
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| `"0"` | $[1, 0]$ |
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| `"1"` | $[0, 1]$ |
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| `"+"` | $[1 / \sqrt{2}, 1 / \sqrt{2}]$ |
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| `"-"` | $[1 / \sqrt{2}, -1 / \sqrt{2}]$ |
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| `"r"` | $[1 / \sqrt{2}, i / \sqrt{2}]$ |
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| `"l"` | $[1 / \sqrt{2}, -i / \sqrt{2}]$ |
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**Parameters**
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**label** (*string*) – a eigenstate string ket label (see table for allowed values).
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**Returns**
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The N-qubit basis state density matrix.
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**Return type**
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[Statevector](qiskit.quantum_info.Statevector "qiskit.quantum_info.Statevector")
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**Raises**
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**QiskitError** – if the label contains invalid characters, or the length of the label is larger than an explicitly specified num\_qubits.
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</Function>
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<span id="qiskit-quantum-info-statevector-is-valid" />
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### is\_valid
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<Function id="qiskit.quantum_info.Statevector.is_valid" signature="Statevector.is_valid(atol=None, rtol=None)">
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Return True if a Statevector has norm 1.
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</Function>
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<span id="qiskit-quantum-info-statevector-measure" />
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### measure
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<Function id="qiskit.quantum_info.Statevector.measure" signature="Statevector.measure(qargs=None)">
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Measure subsystems and return outcome and post-measure state.
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Note that this function uses the QuantumStates internal random number generator for sampling the measurement outcome. The RNG seed can be set using the [`seed()`](qiskit.quantum_info.Statevector#seed "qiskit.quantum_info.Statevector.seed") method.
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**Parameters**
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**qargs** (*list or None*) – subsystems to sample measurements for, if None sample measurement of all subsystems (Default: None).
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**Returns**
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**the pair `(outcome, state)` where `outcome` is the**
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measurement outcome string label, and `state` is the collapsed post-measurement state for the corresponding outcome.
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**Return type**
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tuple
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</Function>
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<span id="qiskit-quantum-info-statevector-probabilities" />
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### probabilities
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<Function id="qiskit.quantum_info.Statevector.probabilities" signature="Statevector.probabilities(qargs=None, decimals=None)">
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Return the subsystem measurement probability vector.
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Measurement probabilities are with respect to measurement in the computation (diagonal) basis.
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**Parameters**
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* **qargs** (*None or list*) – subsystems to return probabilities for, if None return for all subsystems (Default: None).
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* **decimals** (*None or int*) – the number of decimal places to round values. If None no rounding is done (Default: None).
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**Returns**
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The Numpy vector array of probabilities.
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**Return type**
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np.array
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**Examples**
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Consider a 2-qubit product state $|\psi\rangle=|+\rangle\otimes|0\rangle$.
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```python
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from qiskit.quantum_info import Statevector
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psi = Statevector.from_label('+0')
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# Probabilities for measuring both qubits
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probs = psi.probabilities()
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print('probs: {}'.format(probs))
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# Probabilities for measuring only qubit-0
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probs_qubit_0 = psi.probabilities([0])
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print('Qubit-0 probs: {}'.format(probs_qubit_0))
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# Probabilities for measuring only qubit-1
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probs_qubit_1 = psi.probabilities([1])
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print('Qubit-1 probs: {}'.format(probs_qubit_1))
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```
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```
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probs: [0.5 0. 0.5 0. ]
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Qubit-0 probs: [1. 0.]
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Qubit-1 probs: [0.5 0.5]
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```
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We can also permute the order of qubits in the `qargs` list to change the qubit position in the probabilities output
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```python
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from qiskit.quantum_info import Statevector
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psi = Statevector.from_label('+0')
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# Probabilities for measuring both qubits
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probs = psi.probabilities([0, 1])
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print('probs: {}'.format(probs))
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# Probabilities for measuring both qubits
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# but swapping qubits 0 and 1 in output
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probs_swapped = psi.probabilities([1, 0])
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print('Swapped probs: {}'.format(probs_swapped))
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```
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```
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probs: [0.5 0. 0.5 0. ]
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Swapped probs: [0.5 0.5 0. 0. ]
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```
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</Function>
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<span id="qiskit-quantum-info-statevector-probabilities-dict" />
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### probabilities\_dict
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<Function id="qiskit.quantum_info.Statevector.probabilities_dict" signature="Statevector.probabilities_dict(qargs=None, decimals=None)">
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Return the subsystem measurement probability dictionary.
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Measurement probabilities are with respect to measurement in the computation (diagonal) basis.
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This dictionary representation uses a Ket-like notation where the dictionary keys are qudit strings for the subsystem basis vectors. If any subsystem has a dimension greater than 10 comma delimiters are inserted between integers so that subsystems can be distinguished.
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**Parameters**
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* **qargs** (*None or list*) – subsystems to return probabilities for, if None return for all subsystems (Default: None).
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* **decimals** (*None or int*) – the number of decimal places to round values. If None no rounding is done (Default: None).
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**Returns**
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The measurement probabilities in dict (ket) form.
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**Return type**
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dict
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</Function>
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<span id="qiskit-quantum-info-statevector-purity" />
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### purity
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<Function id="qiskit.quantum_info.Statevector.purity" signature="Statevector.purity()">
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Return the purity of the quantum state.
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</Function>
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<span id="qiskit-quantum-info-statevector-reset" />
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### reset
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<Function id="qiskit.quantum_info.Statevector.reset" signature="Statevector.reset(qargs=None)">
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Reset state or subsystems to the 0-state.
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**Parameters**
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**qargs** (*list or None*) – subsystems to reset, if None all subsystems will be reset to their 0-state (Default: None).
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**Returns**
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the reset state.
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**Return type**
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[Statevector](qiskit.quantum_info.Statevector "qiskit.quantum_info.Statevector")
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#### Additional Information:
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If all subsystems are reset this will return the ground state on all subsystems. If only a some subsystems are reset this function will perform a measurement on those subsystems and evolve the subsystems so that the collapsed post-measurement states are rotated to the 0-state. The RNG seed for this sampling can be set using the [`seed()`](qiskit.quantum_info.Statevector#seed "qiskit.quantum_info.Statevector.seed") method.
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</Function>
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<span id="qiskit-quantum-info-statevector-reverse-qargs" />
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### reverse\_qargs
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<Function id="qiskit.quantum_info.Statevector.reverse_qargs" signature="Statevector.reverse_qargs()">
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Return a Statevector with reversed subsystem ordering.
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For a tensor product state this is equivalent to reversing the order of tensor product subsystems. For a statevector $|\psi \rangle = |\psi_{n-1} \rangle \otimes ... \otimes |\psi_0 \rangle$ the returned statevector will be $|\psi_{0} \rangle \otimes ... \otimes |\psi_{n-1} \rangle$.
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**Returns**
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the Statevector with reversed subsystem order.
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**Return type**
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[Statevector](qiskit.quantum_info.Statevector "qiskit.quantum_info.Statevector")
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</Function>
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<span id="qiskit-quantum-info-statevector-sample-counts" />
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### sample\_counts
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<Function id="qiskit.quantum_info.Statevector.sample_counts" signature="Statevector.sample_counts(shots, qargs=None)">
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Sample a dict of qubit measurement outcomes in the computational basis.
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**Parameters**
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* **shots** (*int*) – number of samples to generate.
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* **qargs** (*None or list*) – subsystems to sample measurements for, if None sample measurement of all subsystems (Default: None).
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**Returns**
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sampled counts dictionary.
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**Return type**
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[Counts](qiskit.result.Counts "qiskit.result.Counts")
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Additional Information:
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> This function *samples* measurement outcomes using the measure [`probabilities()`](qiskit.quantum_info.Statevector#probabilities "qiskit.quantum_info.Statevector.probabilities") for the current state and qargs. It does not actually implement the measurement so the current state is not modified.
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>
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> The seed for random number generator used for sampling can be set to a fixed value by using the stats [`seed()`](qiskit.quantum_info.Statevector#seed "qiskit.quantum_info.Statevector.seed") method.
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</Function>
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<span id="qiskit-quantum-info-statevector-sample-memory" />
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### sample\_memory
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<Function id="qiskit.quantum_info.Statevector.sample_memory" signature="Statevector.sample_memory(shots, qargs=None)">
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Sample a list of qubit measurement outcomes in the computational basis.
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**Parameters**
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* **shots** (*int*) – number of samples to generate.
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* **qargs** (*None or list*) – subsystems to sample measurements for, if None sample measurement of all subsystems (Default: None).
|
||
|
||
**Returns**
|
||
|
||
list of sampled counts if the order sampled.
|
||
|
||
**Return type**
|
||
|
||
np.array
|
||
|
||
Additional Information:
|
||
|
||
> This function *samples* measurement outcomes using the measure [`probabilities()`](qiskit.quantum_info.Statevector#probabilities "qiskit.quantum_info.Statevector.probabilities") for the current state and qargs. It does not actually implement the measurement so the current state is not modified.
|
||
>
|
||
> The seed for random number generator used for sampling can be set to a fixed value by using the stats [`seed()`](qiskit.quantum_info.Statevector#seed "qiskit.quantum_info.Statevector.seed") method.
|
||
</Function>
|
||
|
||
<span id="qiskit-quantum-info-statevector-seed" />
|
||
|
||
### seed
|
||
|
||
<Function id="qiskit.quantum_info.Statevector.seed" signature="Statevector.seed(value=None)">
|
||
Set the seed for the quantum state RNG.
|
||
</Function>
|
||
|
||
<span id="qiskit-quantum-info-statevector-tensor" />
|
||
|
||
### tensor
|
||
|
||
<Function id="qiskit.quantum_info.Statevector.tensor" signature="Statevector.tensor(other)">
|
||
Return the tensor product state self ⊗ other.
|
||
|
||
**Parameters**
|
||
|
||
**other** ([*Statevector*](qiskit.quantum_info.Statevector "qiskit.quantum_info.Statevector")) – a quantum state object.
|
||
|
||
**Returns**
|
||
|
||
the tensor product operator self ⊗ other.
|
||
|
||
**Return type**
|
||
|
||
[Statevector](qiskit.quantum_info.Statevector "qiskit.quantum_info.Statevector")
|
||
|
||
**Raises**
|
||
|
||
**QiskitError** – if other is not a quantum state.
|
||
</Function>
|
||
|
||
<span id="qiskit-quantum-info-statevector-to-dict" />
|
||
|
||
### to\_dict
|
||
|
||
<Function id="qiskit.quantum_info.Statevector.to_dict" signature="Statevector.to_dict(decimals=None)">
|
||
Convert the statevector to dictionary form.
|
||
|
||
This dictionary representation uses a Ket-like notation where the dictionary keys are qudit strings for the subsystem basis vectors. If any subsystem has a dimension greater than 10 comma delimiters are inserted between integers so that subsystems can be distinguished.
|
||
|
||
**Parameters**
|
||
|
||
**decimals** (*None or int*) – the number of decimal places to round values. If None no rounding is done (Default: None).
|
||
|
||
**Returns**
|
||
|
||
the dictionary form of the Statevector.
|
||
|
||
**Return type**
|
||
|
||
dict
|
||
|
||
**Example**
|
||
|
||
The ket-form of a 2-qubit statevector $|\psi\rangle = |-\rangle\otimes |0\rangle$
|
||
|
||
```python
|
||
from qiskit.quantum_info import Statevector
|
||
|
||
psi = Statevector.from_label('-0')
|
||
print(psi.to_dict())
|
||
```
|
||
|
||
```
|
||
{'00': (0.7071067811865475+0j), '10': (-0.7071067811865475+0j)}
|
||
```
|
||
|
||
For non-qubit subsystems the integer range can go from 0 to 9. For example in a qutrit system
|
||
|
||
```python
|
||
import numpy as np
|
||
from qiskit.quantum_info import Statevector
|
||
|
||
vec = np.zeros(9)
|
||
vec[0] = 1 / np.sqrt(2)
|
||
vec[-1] = 1 / np.sqrt(2)
|
||
psi = Statevector(vec, dims=(3, 3))
|
||
print(psi.to_dict())
|
||
```
|
||
|
||
```
|
||
{'00': (0.7071067811865475+0j), '22': (0.7071067811865475+0j)}
|
||
```
|
||
|
||
For large subsystem dimensions delimiters are required. The following example is for a 20-dimensional system consisting of a qubit and 10-dimensional qudit.
|
||
|
||
```python
|
||
import numpy as np
|
||
from qiskit.quantum_info import Statevector
|
||
|
||
vec = np.zeros(2 * 10)
|
||
vec[0] = 1 / np.sqrt(2)
|
||
vec[-1] = 1 / np.sqrt(2)
|
||
psi = Statevector(vec, dims=(2, 10))
|
||
print(psi.to_dict())
|
||
```
|
||
|
||
```
|
||
{'00': (0.7071067811865475+0j), '91': (0.7071067811865475+0j)}
|
||
```
|
||
</Function>
|
||
|
||
<span id="qiskit-quantum-info-statevector-to-operator" />
|
||
|
||
### to\_operator
|
||
|
||
<Function id="qiskit.quantum_info.Statevector.to_operator" signature="Statevector.to_operator()">
|
||
Convert state to a rank-1 projector operator
|
||
</Function>
|
||
|
||
<span id="qiskit-quantum-info-statevector-trace" />
|
||
|
||
### trace
|
||
|
||
<Function id="qiskit.quantum_info.Statevector.trace" signature="Statevector.trace()">
|
||
Return the trace of the quantum state as a density matrix.
|
||
</Function>
|
||
|
||
## Attributes
|
||
|
||
### atol
|
||
|
||
<Attribute id="qiskit.quantum_info.Statevector.atol" attributeValue="1e-08" />
|
||
|
||
### data
|
||
|
||
<Attribute id="qiskit.quantum_info.Statevector.data">
|
||
Return data.
|
||
</Attribute>
|
||
|
||
### dim
|
||
|
||
<Attribute id="qiskit.quantum_info.Statevector.dim">
|
||
Return total state dimension.
|
||
</Attribute>
|
||
|
||
### num\_qubits
|
||
|
||
<Attribute id="qiskit.quantum_info.Statevector.num_qubits">
|
||
Return the number of qubits if a N-qubit state or None otherwise.
|
||
</Attribute>
|
||
|
||
### rtol
|
||
|
||
<Attribute id="qiskit.quantum_info.Statevector.rtol" attributeValue="1e-05" />
|
||
|
||
### settings
|
||
|
||
<Attribute id="qiskit.quantum_info.Statevector.settings">
|
||
Return settings.
|
||
|
||
**Return type**
|
||
|
||
`Dict`
|
||
</Attribute>
|
||
</Class>
|
||
|