242 lines
14 KiB
Plaintext
242 lines
14 KiB
Plaintext
---
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title: FermionicOperator
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description: API reference for qiskit.chemistry.FermionicOperator
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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.chemistry.FermionicOperator
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---
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<span id="qiskit-chemistry-fermionicoperator" />
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# qiskit.chemistry.FermionicOperator
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<Class id="qiskit.chemistry.FermionicOperator" isDedicatedPage={true} github="https://github.com/qiskit-community/qiskit-aqua/tree/stable/0.8/qiskit/chemistry/fermionic_operator.py" signature="FermionicOperator(h1, h2=None, ph_trans_shift=None)" modifiers="class">
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A set of functions to map fermionic Hamiltonians to qubit Hamiltonians.
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References:
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* *E. Wigner and P. Jordan., Über das Paulische Äquivalenzverbot, Z. Phys., 47:631 (1928).*
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* *S. Bravyi and A. Kitaev. Fermionic quantum computation, Ann. of Phys., 298(1):210–226 (2002).*
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* *A. Tranter, S. Sofia, J. Seeley, M. Kaicher, J. McClean, R. Babbush, P. Coveney, F. Mintert, F. Wilhelm, and P. Love. The Bravyi–Kitaev transformation: Properties and applications. Int. Journal of Quantum Chemistry, 115(19):1431–1441 (2015).*
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* *S. Bravyi, J. M. Gambetta, A. Mezzacapo, and K. Temme, arXiv e-print arXiv:1701.08213 (2017).*
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* *K. Setia, J. D. Whitfield, arXiv:1712.00446 (2017)*
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This class requires the integrals stored in the ‘*chemist*’ notation
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> h2(i,j,k,l) –> adag\_i adag\_k a\_l a\_j
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and the integral values are used for the coefficients of the second-quantized Hamiltonian that is built. The integrals input here should be in block spin format and also have indexes reordered as follows ‘ijkl->ljik’
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There is another popular notation, the ‘*physicist*’ notation
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> h2(i,j,k,l) –> adag\_i adag\_j a\_k a\_l
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If you are using the ‘*physicist*’ notation, you need to convert it to the ‘*chemist*’ notation. E.g. h2=numpy.einsum(‘ikmj->ijkm’, h2)
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The [`QMolecule`](qiskit.chemistry.QMolecule "qiskit.chemistry.QMolecule") class has [`one_body_integrals`](qiskit.chemistry.QMolecule#one_body_integrals "qiskit.chemistry.QMolecule.one_body_integrals") and [`two_body_integrals`](qiskit.chemistry.QMolecule#two_body_integrals "qiskit.chemistry.QMolecule.two_body_integrals") properties that can be directly supplied to the h1 and h2 parameters here respectively.
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**Parameters**
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* **h1** (*numpy.ndarray*) – second-quantized fermionic one-body operator, a 2-D (NxN) tensor
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* **h2** (*numpy.ndarray*) – second-quantized fermionic two-body operator, a 4-D (NxNxNxN) tensor
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* **ph\_trans\_shift** (*float*) – energy shift caused by particle hole transformation
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### \_\_init\_\_
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<Function id="qiskit.chemistry.FermionicOperator.__init__" signature="__init__(h1, h2=None, ph_trans_shift=None)">
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This class requires the integrals stored in the ‘*chemist*’ notation
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> h2(i,j,k,l) –> adag\_i adag\_k a\_l a\_j
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and the integral values are used for the coefficients of the second-quantized Hamiltonian that is built. The integrals input here should be in block spin format and also have indexes reordered as follows ‘ijkl->ljik’
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There is another popular notation, the ‘*physicist*’ notation
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> h2(i,j,k,l) –> adag\_i adag\_j a\_k a\_l
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If you are using the ‘*physicist*’ notation, you need to convert it to the ‘*chemist*’ notation. E.g. h2=numpy.einsum(‘ikmj->ijkm’, h2)
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The [`QMolecule`](qiskit.chemistry.QMolecule "qiskit.chemistry.QMolecule") class has [`one_body_integrals`](qiskit.chemistry.QMolecule#one_body_integrals "qiskit.chemistry.QMolecule.one_body_integrals") and [`two_body_integrals`](qiskit.chemistry.QMolecule#two_body_integrals "qiskit.chemistry.QMolecule.two_body_integrals") properties that can be directly supplied to the h1 and h2 parameters here respectively.
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**Parameters**
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* **h1** (*numpy.ndarray*) – second-quantized fermionic one-body operator, a 2-D (NxN) tensor
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* **h2** (*numpy.ndarray*) – second-quantized fermionic two-body operator, a 4-D (NxNxNxN) tensor
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* **ph\_trans\_shift** (*float*) – energy shift caused by particle hole transformation
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</Function>
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## Methods
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| ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ |
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| [`__init__`](#qiskit.chemistry.FermionicOperator.__init__ "qiskit.chemistry.FermionicOperator.__init__")(h1\[, h2, ph\_trans\_shift]) | This class requires the integrals stored in the ‘*chemist*’ notation |
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| [`fermion_mode_elimination`](#qiskit.chemistry.FermionicOperator.fermion_mode_elimination "qiskit.chemistry.FermionicOperator.fermion_mode_elimination")(fermion\_mode\_array) | Eliminate modes. |
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| [`fermion_mode_freezing`](#qiskit.chemistry.FermionicOperator.fermion_mode_freezing "qiskit.chemistry.FermionicOperator.fermion_mode_freezing")(fermion\_mode\_array) | Freezing modes and extracting its energy. |
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| [`mapping`](#qiskit.chemistry.FermionicOperator.mapping "qiskit.chemistry.FermionicOperator.mapping")(map\_type\[, threshold]) | Map fermionic operator to qubit operator. |
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| [`particle_hole_transformation`](#qiskit.chemistry.FermionicOperator.particle_hole_transformation "qiskit.chemistry.FermionicOperator.particle_hole_transformation")(num\_particles) | The ‘standard’ second quantized Hamiltonian can be transformed in the particle-hole (p/h) picture, which makes the expansion of the trail wavefunction from the HF reference state more natural. |
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| [`total_angular_momentum`](#qiskit.chemistry.FermionicOperator.total_angular_momentum "qiskit.chemistry.FermionicOperator.total_angular_momentum")() | Total angular momentum. |
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| [`total_magnetization`](#qiskit.chemistry.FermionicOperator.total_magnetization "qiskit.chemistry.FermionicOperator.total_magnetization")() | A data\_preprocess\_helper fermionic operator which can be used to evaluate the magnetization of the given eigenstate. |
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| [`total_particle_number`](#qiskit.chemistry.FermionicOperator.total_particle_number "qiskit.chemistry.FermionicOperator.total_particle_number")() | A data\_preprocess\_helper fermionic operator which can be used to evaluate the number of particle of the given eigenstate. |
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| [`transform`](#qiskit.chemistry.FermionicOperator.transform "qiskit.chemistry.FermionicOperator.transform")(unitary\_matrix) | Transform the one and two body term based on unitary\_matrix. |
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## Attributes
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| ----------------------------------------------------------------------------------------------- | ----------------------------------- |
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| [`h1`](#qiskit.chemistry.FermionicOperator.h1 "qiskit.chemistry.FermionicOperator.h1") | Getter of one body integral tensor. |
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| [`h2`](#qiskit.chemistry.FermionicOperator.h2 "qiskit.chemistry.FermionicOperator.h2") | Getter of two body integral tensor. |
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| [`modes`](#qiskit.chemistry.FermionicOperator.modes "qiskit.chemistry.FermionicOperator.modes") | Getter of modes. |
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### fermion\_mode\_elimination
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<Function id="qiskit.chemistry.FermionicOperator.fermion_mode_elimination" signature="fermion_mode_elimination(fermion_mode_array)">
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Eliminate modes.
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Generate a new fermionic operator with the modes in fermion\_mode\_array deleted
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**Parameters**
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**fermion\_mode\_array** (*list*) – orbital index for elimination
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**Returns**
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Fermionic Hamiltonian
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**Return type**
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[FermionicOperator](#qiskit.chemistry.FermionicOperator "qiskit.chemistry.FermionicOperator")
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</Function>
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### fermion\_mode\_freezing
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<Function id="qiskit.chemistry.FermionicOperator.fermion_mode_freezing" signature="fermion_mode_freezing(fermion_mode_array)">
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Freezing modes and extracting its energy.
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Generate a fermionic operator with the modes in fermion\_mode\_array deleted and provide the shifted energy after freezing.
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**Parameters**
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**fermion\_mode\_array** (*list*) – orbital index for freezing
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**Returns**
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Fermionic Hamiltonian and energy of frozen modes
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**Return type**
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tuple([FermionicOperator](#qiskit.chemistry.FermionicOperator "qiskit.chemistry.FermionicOperator"), float)
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</Function>
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### h1
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<Attribute id="qiskit.chemistry.FermionicOperator.h1">
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Getter of one body integral tensor.
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</Attribute>
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### h2
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<Attribute id="qiskit.chemistry.FermionicOperator.h2">
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Getter of two body integral tensor.
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</Attribute>
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### mapping
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<Function id="qiskit.chemistry.FermionicOperator.mapping" signature="mapping(map_type, threshold=1e-08)">
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Map fermionic operator to qubit operator.
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Using multiprocess to speedup the mapping, the improvement can be observed when h2 is a non-sparse matrix.
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**Parameters**
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* **map\_type** (*str*) – case-insensitive mapping type. “jordan\_wigner”, “parity”, “bravyi\_kitaev”, “bksf”
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* **threshold** (*float*) – threshold for Pauli simplification
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**Returns**
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create an Operator object in Paulis form.
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**Return type**
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[WeightedPauliOperator](qiskit.aqua.operators.legacy.WeightedPauliOperator "qiskit.aqua.operators.legacy.WeightedPauliOperator")
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**Raises**
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[**QiskitChemistryError**](qiskit.chemistry.QiskitChemistryError "qiskit.chemistry.QiskitChemistryError") – if the map\_type can not be recognized.
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</Function>
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### modes
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<Attribute id="qiskit.chemistry.FermionicOperator.modes">
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Getter of modes.
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</Attribute>
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### particle\_hole\_transformation
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<Function id="qiskit.chemistry.FermionicOperator.particle_hole_transformation" signature="particle_hole_transformation(num_particles)">
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The ‘standard’ second quantized Hamiltonian can be transformed in the particle-hole (p/h) picture, which makes the expansion of the trail wavefunction from the HF reference state more natural. In fact, for both trail wavefunctions implemented in q-lib (‘heuristic’ hardware efficient and UCCSD) the p/h Hamiltonian improves the speed of convergence of the VQE algorithm for the calculation of the electronic ground state properties. For more information on the p/h formalism see: P. Barkoutsos, arXiv:1805.04340([https://arxiv.org/abs/1805.04340](https://arxiv.org/abs/1805.04340)).
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**Parameters**
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**num\_particles** (*list, int*) – number of particles, if it is a list, the first number is alpha and the second number is beta.
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**Returns**
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new\_fer\_op, energy\_shift
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**Return type**
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tuple
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</Function>
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### total\_angular\_momentum
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<Function id="qiskit.chemistry.FermionicOperator.total_angular_momentum" signature="total_angular_momentum()">
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Total angular momentum.
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A data\_preprocess\_helper fermionic operator which can be used to evaluate the total angular momentum of the given eigenstate.
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**Returns**
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Fermionic Hamiltonian
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**Return type**
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[FermionicOperator](#qiskit.chemistry.FermionicOperator "qiskit.chemistry.FermionicOperator")
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</Function>
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### total\_magnetization
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<Function id="qiskit.chemistry.FermionicOperator.total_magnetization" signature="total_magnetization()">
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A data\_preprocess\_helper fermionic operator which can be used to evaluate the magnetization of the given eigenstate.
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**Returns**
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Fermionic Hamiltonian
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**Return type**
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[FermionicOperator](#qiskit.chemistry.FermionicOperator "qiskit.chemistry.FermionicOperator")
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</Function>
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### total\_particle\_number
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<Function id="qiskit.chemistry.FermionicOperator.total_particle_number" signature="total_particle_number()">
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A data\_preprocess\_helper fermionic operator which can be used to evaluate the number of particle of the given eigenstate.
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**Returns**
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Fermionic Hamiltonian
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**Return type**
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[FermionicOperator](#qiskit.chemistry.FermionicOperator "qiskit.chemistry.FermionicOperator")
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</Function>
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### transform
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<Function id="qiskit.chemistry.FermionicOperator.transform" signature="transform(unitary_matrix)">
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Transform the one and two body term based on unitary\_matrix.
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</Function>
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</Class>
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