TensorHEOM

Authors: Kiyoto Nakamura, Dennis Herb

TensorHEOM is a Python package for simulating quantum circuits in non-Markovian environments using free-pole hierarchical equations of motion (FP-HEOM) and tensor-train (TT) compression.

The package is designed for superconducting-qubit simulations and connects circuit-level Qiskit input with microscopic open-system dynamics.

Installation

Install TensorHEOM from PyPI with

pip install ttheom

Basic usage

A typical workflow is:

1. Define a Qiskit quantum circuit.
2. Specify system, bath, and numerical parameters.
3. Run the TensorHEOM simulation.
4. Analyze the reduced density matrix, fidelity, and entanglement measures.

from qiskit import QuantumCircuit
from ttheom import *

# Set system parameters
system_kwargs = {
    "numQ": 2,
    "freqQ": [5, 5], # GHz
    "rhoIni": [
        [1, 0, 0, 0],
        [0, 0, 0, 0],
        [0, 0, 0, 0],
        [0, 0, 0, 0],
    ],
    "gateTime": [16, 16, 50], # ns
    "idlingTime": 1, # ns
} 

omegaQmax, rho = prepareSystemArgs(**system_kwargs)

# Define input circuit
qc = QuantumCircuit(2)
qc.h(0)
qc.cx(0, 1)

system_kwargs["qc"] = qc

# Set bath parameters
bath_kwargs = {    
    "T": 30, # mK
    "T1": 32, # us
    "omegaC": 20,
    "exp": 1/8,
    "tol": 1e-4,
}
bathParams = prepareBathArgs(rho, omegaQmax, **bath_kwargs)

# AAA decomposition
z, d = getBathParams(bathParams[0])

# Set simulation parameters
simulation_kwargs= {
    "dtFB": 3.0, # ps
    "depth": [1, 1],
    "bondDim": 5,
    "strideTime": 0.1, # ns
    "useRFPlus": False,
    "isRK13": False,
}

# Run the calculation 
kwargs = {**system_kwargs, **bath_kwargs, **simulation_kwargs}
kwargs["directory"] = "results"
kwargs["fileName"] = "package_test"
calcTimeEvo(**kwargs) 

Graphical interface

TensorHEOM also provides a graphical user interface:

from ttheom import TensorHeomApp

TensorHeomApp().mainloop()

Documentation and examples

Example scripts and workflows are provided in the repository and in the accompanying paper.

References

Recent papers from our group:

• K. Nakamura and J. Ankerhold, Impact of time-retarded noise on dynamical decoupling schemes for qubits. Physical Review B 111, 064503 (2025).
• K. Nakamura and J. Ankerhold, Entanglement dynamics and performance of two-qubit gates for superconducting qubits under non-Markovian effects. Physical Review Research 8, 013337 (2026).

License

TensorHEOM is distributed under the BSD 3-Clause License.

Support

For questions or support, please contact Dennis Herb at dennis.herb@uni-ulm.de.