API reference#

PauliWord#

class quantlop.PauliWord(coeff, string)#

Represent a weighted tensor product of single-qubit Pauli operators

\[P = c\,\bigotimes_i \sigma_i\]

where \(c\) is a complex coeff and each \(\sigma_i\) is a single-qubit Pauli operator applied to qubit \(i\). The leftmost character of string acts on the most-significant qubit in the computational-basis index. For example, "XII" represents \(X \otimes I \otimes I\) and maps \(|000\rangle\) to \(|100\rangle\).

Parameters:

coeffcomplex: Scalar complex coefficient of the Pauli word.
stringstr: Non-empty string of single-qubit Pauli operators. Each character should be one of "I", "X", "Y", or "Z". Its length determines the total number of qubits.

Attributes:

num_qubitsint: Number of qubits in the Pauli word.
coeffcomplex: Coefficient supplied at construction.
stringstr: Pauli string supplied at construction.

Hamiltonian#

class quantlop.Hamiltonian(pwords)#

Represent a qubit Hamiltonian expressed as a sum of PauliWord terms

\[H = \sum_k c_k P_k\]

This representation lets quantlop.evolve_higham() and quantlop.evolve_krylov() apply the unitary evolution generated by \(H\) to a state vector \(|\psi\rangle\) without materializing the Hamiltonian matrix.

Parameters:

pwordssequence of PauliWord: Non-empty collection of Pauli terms. All words must act on the same number of qubits. The evolution algorithm assumes their sum is Hermitian.

Attributes:

num_qubitsint: Number of qubits of the Hamiltonian.
num_termsint: Number of Pauli words in the sum.

Methods

`from_pennylane`(operator, num_qubits)	Construct a Hamiltonian from a PennyLane Pauli operator.
`from_qiskit`(operator)	Construct a Hamiltonian from a Qiskit `SparsePauliOp`.
`matrix`()	Return the dense matrix representation of the Hamiltonian.
`sparse_matrix`()	Return the Hamiltonian as a Compressed Sparse Row (CSR) matrix.

classmethod from_pennylane(operator, num_qubits)#

Construct a Hamiltonian from a PennyLane Pauli operator.

Parameters:

operatorpennylane.operation.Operator: PennyLane operator with a defined pauli_rep. Its wire labels must be integer indices in range(num_qubits).
num_qubitsint: Total number of qubits in the returned Hamiltonian. This can be larger than the number of wires used by the PennyLane operator.

Returns:

Hamiltonian: Native Hamiltonian with one term per entry in the PennyLane Pauli representation.

classmethod from_qiskit(operator)#

Construct a Hamiltonian from a Qiskit SparsePauliOp.

Parameters:

operatorqiskit.quantum_info.SparsePauliOp: Qiskit sparse Pauli operator. All labels are expected to have the same width.

Returns:

Hamiltonian: Native Hamiltonian with the input terms and coefficients.

matrix()#

Return the dense matrix representation of the Hamiltonian.

The matrix is assembled as a sum of tensor products. Characters are processed from left to right, so the first character in each Pauli word is the leftmost most-significant tensor factor.

Returns:

numpy.ndarray: Complex array representing the dense Hamiltonian matrix.

Notes

This method requires \(O(4^n)\) memory where \(n\) is the number of qubits. It is intended for inspection and validation on small systems only.

sparse_matrix()#

Return the Hamiltonian as a Compressed Sparse Row (CSR) matrix.

The matrix is assembled as a sum of sparse tensor products, preserving existing qubit-ordering and phase conventions.

Returns:

scipy.sparse.csr_matrix: Complex CSR matrix representing the Hamiltonian.

Evolution#

quantlop.evolve_higham(ham, psi, theta=1.0, rtol=1e-09, num_threads=None)#

Apply Hamiltonian evolution using the Higham exponential-action algorithm.

\[|\psi(\theta)\rangle = e^{-i \theta H}|\psi\rangle\]

The implementation uses adaptive scaling and a truncated Taylor series. It applies Pauli terms directly and never constructs the dense Hamiltonian or its exponential.

See Higham method for algorithm details.

Parameters:

hamHamiltonian: Pauli-sum quantlop Hamiltonian. The algorithm assumes that the operator is Hermitian.
psiarray_like: Nonzero one-dimensional input state vector.
thetafloat, optional: Finite real floating point parameter in the exponential. The default is 1.0.
rtolfloat, optional: Relative accuracy target used to select the approximation. Smaller values generally require more computation. The default is 1e-9.
num_threadsint, optional: OpenMP thread selection for Hamiltonian-vector products. If None the execution is serial, if “auto” it automatically selects the thread count reported by the operating system. The default is None.

Returns:

numpy.ndarray: Evolved dense state vector.

Examples

import numpy as np
import quantlop as ql

ham = ql.Hamiltonian([ql.PauliWord(1.0, "X")])
psi = np.array([1.0, 0.0])
out = ql.evolve_higham(ham, psi, theta=np.pi / 2)

quantlop.evolve_krylov(ham, psi, theta=1.0, rtol=1e-09, num_threads=None)#

Apply Hamiltonian evolution using the Lanczos-Krylov subspace algorithm.

\[|\psi(\theta)\rangle = e^{-i \theta H}|\psi\rangle\]

The implementation projects the Hamiltonian onto a Lanczos basis, evolves within that Krylov subspace, and reconstructs the dense state vector.

See Krylov method for algorithm details.

Parameters:

hamHamiltonian: Pauli-sum quantlop Hamiltonian. The algorithm assumes that the operator is Hermitian.
psiarray_like: Nonzero one-dimensional input state vector.
thetafloat, optional: Finite real floating point parameter in the exponential. The default is 1.0.
rtolfloat, optional: Relative accuracy target used to select the approximation. Smaller values generally require more computation. The default is 1e-9.
num_threadsint, optional: OpenMP thread selection for Hamiltonian-vector products. If None the execution is serial, if "auto" it automatically selects the thread count reported by the operating system. The default is None.

Returns:

numpy.ndarray: Evolved dense state vector.

Examples

import numpy as np
import quantlop as ql

ham = ql.Hamiltonian([ql.PauliWord(1.0, "X")])
psi = np.array([1.0, 0.0])
out = ql.evolve_krylov(ham, psi, theta=np.pi / 2)