quantlop

High-performance quantum simulator for matrix-free Hamiltonian evolution

Introduction

quantlop is a Python package, backed by a native C++ core, for simulating the evolution of quantum states under Hamiltonians expressed as weighted sums of Pauli words $P_k$. For an $n$-qubit Hamiltonian

quantlop computes the action

without constructing either the full Hamiltonian matrix or its exponential. Each Pauli word is applied directly to the dense state vector, while either an adaptively scaled Taylor series or a Lanczos-Krylov subspace projection evaluates the matrix-exponential action.

A dense Hamiltonian for $n$ qubits requires $O(4^n)$ storage, whereas the matrix-free evolution works only with its compact Pauli representation. The dense state vector still grows exponentially with the number of qubits, but avoiding the dense operator substantially lowers the memory requirement for Hamiltonians with Pauli decompositions.

Installation

Install the latest release of the package directly from PyPI with:

pip install quantlop

Quick example

Here is a simple code example using quantlop native data structures:

import numpy as np
import quantlop as ql

num_qubits = 3

# define Hamiltonian in Pauli basis
pwords = [
    ql.PauliWord(coeff=0.5, string="ZZI"),
    ql.PauliWord(coeff=0.2, string="YIX"),
]
ham = ql.Hamiltonian(pwords=pwords)

# set initial state vector
psi = np.zeros(2**num_qubits, dtype=complex)
psi[0] = 1.0

# evolve state vector
evolved_psi = ql.evolve_higham(ham, psi)
# or
evolved_psi = ql.evolve_krylov(ham, psi)

Both algorithms select their Taylor truncation or Krylov dimension automatically. The default relative tolerance is 1e-9. Smaller values generally improve accuracy at the cost of more computation. The tolerance guides the internal approximation rather than measuring the final error directly.

The library also provides class methods to import Hamiltonians directly from other quantum computing frameworks:

• ql.Hamiltonian.from_pennylane to build from PennyLane Hamiltonian objects
• ql.Hamiltonian.from_qiskit to build from Qiskit SparsePauliOp objects

Multi-threading

By default, evolution is serial. To enable multi-threading, pass a non-zero positive integer as num_threads to request that many OpenMP threads. Passing "auto" selects the thread count reported by the operating system.

evolved_psi = ql.evolve_higham(ham, psi, num_threads=4)

Development

The Python package is built with scikit-build-core, while the numerical C++ code is kept in the standalone quantlop_core CMake target. See the Development section in the documentation for more details.

Build the project from source in editable mode and run Python tests with:

pip install -e .[dev,docs]
pytest -v