147 lines
5.2 KiB
Plaintext
147 lines
5.2 KiB
Plaintext
---
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title: MatrixFunctional
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description: API reference for qiskit.algorithms.linear_solvers.MatrixFunctional
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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.algorithms.linear_solvers.MatrixFunctional
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---
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# MatrixFunctional
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<Class id="qiskit.algorithms.linear_solvers.MatrixFunctional" isDedicatedPage={true} github="https://github.com/qiskit/qiskit/tree/stable/0.23/qiskit/algorithms/linear_solvers/observables/matrix_functional.py" signature="MatrixFunctional(main_diag, off_diag)" modifiers="class">
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Bases: [`qiskit.algorithms.linear_solvers.observables.linear_system_observable.LinearSystemObservable`](qiskit.algorithms.linear_solvers.LinearSystemObservable "qiskit.algorithms.linear_solvers.observables.linear_system_observable.LinearSystemObservable")
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The deprecated class for the matrix functional of the vector solution to the linear systems.
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Examples:
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```python
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import warnings
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import numpy as np
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from qiskit import QuantumCircuit
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from qiskit.algorithms.linear_solvers.observables.matrix_functional import MatrixFunctional
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from qiskit.transpiler.passes import RemoveResetInZeroState
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from qiskit.opflow import StateFn
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tpass = RemoveResetInZeroState()
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vector = [1.0, -2.1, 3.2, -4.3]
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with warnings.catch_warnings():
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warnings.simplefilter('ignore')
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observable = MatrixFunctional(1, -1 / 3)
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init_state = vector / np.linalg.norm(vector)
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num_qubits = int(np.log2(len(vector)))
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# Get observable circuits
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obs_circuits = observable.observable_circuit(num_qubits)
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qcs = []
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for obs_circ in obs_circuits:
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qc = QuantumCircuit(num_qubits)
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qc.isometry(init_state, list(range(num_qubits)), None)
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qc.append(obs_circ, list(range(num_qubits)))
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qcs.append(tpass(qc.decompose()))
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# Get observables
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observable_ops = observable.observable(num_qubits)
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state_vecs = []
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# First is the norm
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state_vecs.append((~StateFn(observable_ops[0]) @ StateFn(qcs[0])).eval())
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for i in range(1, len(observable_ops), 2):
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state_vecs += [(~StateFn(observable_ops[i]) @ StateFn(qcs[i])).eval(),
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(~StateFn(observable_ops[i + 1]) @ StateFn(qcs[i + 1])).eval()]
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# Obtain result
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result = observable.post_processing(state_vecs, num_qubits)
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# Obtain analytical evaluation
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exact = observable.evaluate_classically(init_state)
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```
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**Parameters**
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* **main\_diag** (`float`) – The main diagonal of the tridiagonal Toeplitz symmetric matrix to compute the functional.
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* **off\_diag** (`int`) – The off diagonal of the tridiagonal Toeplitz symmetric matrix to compute the functional.
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## Methods
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### evaluate\_classically
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<Function id="qiskit.algorithms.linear_solvers.MatrixFunctional.evaluate_classically" signature="MatrixFunctional.evaluate_classically(solution)">
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Evaluates the given observable on the solution to the linear system.
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**Parameters**
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**solution** (`Union`\[`array`, [`QuantumCircuit`](qiskit.circuit.QuantumCircuit "qiskit.circuit.quantumcircuit.QuantumCircuit")]) – The solution to the system as a numpy array or the circuit that prepares it.
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**Return type**
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`float`
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**Returns**
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The value of the observable.
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</Function>
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### observable
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<Function id="qiskit.algorithms.linear_solvers.MatrixFunctional.observable" signature="MatrixFunctional.observable(num_qubits)">
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The observable operators.
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**Parameters**
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**num\_qubits** (`int`) – The number of qubits on which the observable will be applied.
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**Return type**
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`Union`\[[`TensoredOp`](qiskit.opflow.list_ops.TensoredOp "qiskit.opflow.list_ops.tensored_op.TensoredOp"), `List`\[[`TensoredOp`](qiskit.opflow.list_ops.TensoredOp "qiskit.opflow.list_ops.tensored_op.TensoredOp")]]
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**Returns**
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The observable as a list of sums of Pauli strings.
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</Function>
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### observable\_circuit
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<Function id="qiskit.algorithms.linear_solvers.MatrixFunctional.observable_circuit" signature="MatrixFunctional.observable_circuit(num_qubits)">
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The circuits to implement the matrix functional observable.
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**Parameters**
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**num\_qubits** (`int`) – The number of qubits on which the observable will be applied.
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**Return type**
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`Union`\[[`QuantumCircuit`](qiskit.circuit.QuantumCircuit "qiskit.circuit.quantumcircuit.QuantumCircuit"), `List`\[[`QuantumCircuit`](qiskit.circuit.QuantumCircuit "qiskit.circuit.quantumcircuit.QuantumCircuit")]]
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**Returns**
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The observable as a list of QuantumCircuits.
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</Function>
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### post\_processing
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<Function id="qiskit.algorithms.linear_solvers.MatrixFunctional.post_processing" signature="MatrixFunctional.post_processing(solution, num_qubits, scaling=1)">
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Evaluates the matrix functional on the solution to the linear system.
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**Parameters**
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* **solution** (`Union`\[`float`, `List`\[`float`]]) – The list of probabilities calculated from the circuit and the observable.
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* **num\_qubits** (`int`) – The number of qubits where the observable was applied.
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* **scaling** (`float`) – Scaling of the solution.
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**Return type**
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`float`
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**Returns**
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The value of the absolute average.
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**Raises**
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**ValueError** – If the input is not in the correct format.
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</Function>
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</Class>
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