Functions:
| Name | Description |
|---|
single_pauli_exponent | [Qmod core-library function]. |
commuting_paulis_exponent | [Qmod core-library function]. |
suzuki_trotter | [Qmod core-library function]. |
multi_suzuki_trotter | [Qmod core-library function]. |
sequential_suzuki_trotter | [Qmod core-library function]. |
qdrift | [Qmod core-library function]. |
exponentiate | [Qmod core-library function]. |
single_pauli_exponent
single_pauli_exponent(
pauli_string: CArray[Pauli],
coefficient: CReal,
qbv: QArray[QBit, Literal[‘pauli_string.len’]]
) -> None
[Qmod core-library function]
Exponentiates the specified single Pauli operator multiplied by some coefficient.
Parameters:
| Name | Type | Description | Default |
|---|
pauli_string | CArray[Pauli] | The Pauli operator to be exponentiated. | required |
coefficient | CReal | A coefficient multiplying the Pauli operator. | required |
qbv | QArray[QBit, Literal['pauli_string.len']] | The target quantum variable of the exponentiation. | required |
commuting_paulis_exponent
commuting_paulis_exponent(
pauli_operator: CArray[PauliTerm],
evolution_coefficient: CReal,
qbv: QArray[QBit, Literal[‘pauli_operator[0].pauli.len’]]
) -> None
[Qmod core-library function]
Exponentiates the specified commutative Pauli operator.
As all the Pauli operator’s terms commute, the exponential of the whole operator
is exactly the product of exponentials of each term.
Calling this funciton with a non-commutative Pauli operator will issue an error.
Parameters:
| Name | Type | Description | Default |
|---|
pauli_operator | CArray[PauliTerm] | The Pauli operator to be exponentiated. | required |
evolution_coefficient | CReal | A global evolution coefficient multiplying the Pauli operator. | required |
qbv | QArray[QBit, Literal['pauli_operator[0].pauli.len']] | The target quantum variable of the exponentiation. | required |
suzuki_trotter
suzuki_trotter(
pauli_operator: SparsePauliOp,
evolution_coefficient: CReal,
order: CInt,
repetitions: CInt,
qbv: QArray[QBit]
) -> None
[Qmod core-library function]
Applies the Suzuki-Trotter decomposition to a Pauli operator.
The Suzuki-Trotter decomposition is a method for approximating the exponential of a sum of operators by a product of exponentials of each operator.
The Suzuki-Trotter decomposition of a given order nullifies the error of the Taylor series expansion of the product of exponentials up to that order.
The error of a Suzuki-Trotter decomposition decreases as the order and number of repetitions increase.
Parameters:
| Name | Type | Description | Default |
|---|
pauli_operator | SparsePauliOp | The Pauli operator to be exponentiated. | required |
evolution_coefficient | CReal | A global evolution coefficient multiplying the Pauli operator. | required |
order | CInt | The order of the Suzuki-Trotter decomposition. | required |
repetitions | CInt | The number of repetitions of the Suzuki-Trotter decomposition. | required |
qbv | QArray[QBit] | The target quantum variable of the exponentiation. | required |
multi_suzuki_trotter
multi_suzuki_trotter(
hamiltonians: CArray[SparsePauliOp],
evolution_coefficients: CArray[CReal],
order: CInt,
repetitions: CInt,
qbv: QArray
) -> None
[Qmod core-library function]
Applies the Suzuki-Trotter decomposition jointly to a sum of Hamiltonians
(represented as Pauli operators), each with its separate evolution coefficient,
approximating exp{−i(H1t1+H2t2+…)} with a specified order and number of
repetitions.
The Suzuki-Trotter decomposition is a method for approximating the exponential of a sum of operators by a product of exponentials of each operator.
The Suzuki-Trotter decomposition of a given order nullifies the error of the Taylor series expansion of the product of exponentials up to that order.
The error of a Suzuki-Trotter decomposition decreases as the order and number of repetitions increase.
Parameters:
| Name | Type | Description | Default |
|---|
hamiltonians | CArray[SparsePauliOp] | The hamiltonians to be exponentiated, in sparse representation. | required |
evolution_coefficients | CArray[CReal] | The hamiltonian coefficients (can be link-time). | required |
order | CInt | The order of the Suzuki-Trotter decomposition. | required |
repetitions | CInt | The number of repetitions of the Suzuki-Trotter decomposition. | required |
qbv | QArray | The target quantum variable of the exponentiation. | required |
sequential_suzuki_trotter
sequential_suzuki_trotter(
hamiltonians: CArray[SparsePauliOp],
evolution_coefficients: CArray[CReal],
order: CInt,
repetitions: CInt,
qbv: QArray
) -> None
[Qmod core-library function]
Applies the Suzuki-Trotter decomposition jointly to a sum of Hamiltonians
(represented as Pauli operators), each with its separate evolution coefficient,
approximating exp{−i(H1t1+H2t2+…)} with a specified order and number of
repetitions. Does not reorder the Pauli terms.
The Suzuki-Trotter decomposition is a method for approximating the exponential of a sum of operators by a product of exponentials of each operator.
The Suzuki-Trotter decomposition of a given order nullifies the error of the Taylor series expansion of the product of exponentials up to that order.
The error of a Suzuki-Trotter decomposition decreases as the order and number of repetitions increase.
Parameters:
| Name | Type | Description | Default |
|---|
hamiltonians | CArray[SparsePauliOp] | The hamiltonians to be exponentiated, in sparse representation. | required |
evolution_coefficients | CArray[CReal] | The hamiltonian coefficients (can be link-time). | required |
order | CInt | The order of the Suzuki-Trotter decomposition. | required |
repetitions | CInt | The number of repetitions of the Suzuki-Trotter decomposition. | required |
qbv | QArray | The target quantum variable of the exponentiation. | required |
qdrift
qdrift(
pauli_operator: SparsePauliOp,
evolution_coefficient: CReal,
num_qdrift: CInt,
qbv: QArray[QBit, Literal[‘pauli_operator.num_qubits’]]
) -> None
[Qmod core-library function]
Exponentiates a Pauli operator using the QDrift method. The QDrift method is a stochastic method based on the Trotter decomposition for approximating the exponential of a sum of operators by a product of exponentials of each operator.
The QDrift method randomizes the order of the operators in the product of exponentials to stochastically reduce the error of the approximation.
The error of the QDrift method decreases as the number of QDrift steps increases.
Parameters:
| Name | Type | Description | Default |
|---|
pauli_operator | SparsePauliOp | The Pauli operator to be exponentiated. | required |
evolution_coefficient | CReal | A global evolution coefficient multiplying the Pauli operator. | required |
num_qdrift | CInt | | required |
qbv | QArray[QBit, Literal['pauli_operator.num_qubits']] | The target quantum variable of the exponentiation. | required |
exponentiate
exponentiate(
hamiltonian: SparsePauliOp,
evolution_coefficient: CReal,
qbv: QArray[QBit]
) -> None
[Qmod core-library function]
Exponentiates a Pauli operator.
Parameters:
| Name | Type | Description | Default |
|---|
hamiltonian | SparsePauliOp | The Pauli operator to be exponentiated. | required |
evolution_coefficient | CReal | A global coefficient multiplying the Pauli operator. | required |
qbv | QArray[QBit] | The target quantum variable of the exponentiation. | required |
