MQT YAQS — Scalable simulation and characterization for open systems, noisy circuits, and realistic hardware

MQT YAQS (pronounced "yaks" like the animals) is a Python library designed for scalable, computationally efficient simulation and characterization of open quantum dynamics, noisy quantum circuits, and hardware-realistic device models. MQT YAQS uses state-of-the-art techniques in these areas such as parallelized trajectories, tensor network compression, and problem-size-appropriate backends wherever possible (see Cite This). It is part of the Munich Quantum Toolkit (MQT).

Key Features

• Analog simulation: Large-scale open-system and unitary time evolution using parallelized quantum trajectories when a noise model is attached [1] (trajectory guidance [4]).
• Digital circuit simulation: Noisy circuits at scale, final and mid-circuit observables, shot-based readout, and OpenQASM 2 inputs [3] (uv pip install mqt-yaqs[qasm3] for OpenQASM 3).
• Digital–analog simulation: Compose analog evolution and digital operations in one ordered program with automatic state handoff, program-wide observable traces, and continuous stochastic trajectories across segment boundaries (guide).
• Equivalence checking: Scalable comparison of quantum circuits [2].
• Process characterization: Quantify non-Markovian memory in multi-time quantum processes, how much temporal history a process retains, with exact reference checks where needed (guide).
• Process tensor surrogates: Train a causal Transformer surrogate for fast prediction of non-Markovian response to local interventions and measurement over time (guide).
• Noise model characterization: Fit Markovian Lindblad jump rates from observable dynamics (guide).
• Hardware-oriented modeling: Realistic noise models including Gaussian and other strength distributions, plus hardware dynamics such as transmon–resonator systems, and heterogeneous site dimensions (examples).
• Multiple backends: Monte Carlo wavefunction and master equation evolution are available for analog simulation on smaller systems, alongside the scalable MPS trajectory path.

If you have any questions, feel free to create a discussion or an issue on GitHub.

Contributors and Supporters

The Munich Quantum Toolkit (MQT) is developed by the Chair for Design Automation at the Technical University of Munich and supported by MQSC. Among others, it is part of the Munich Quantum Software Stack (MQSS) ecosystem, which is being developed as part of the Munich Quantum Valley (MQV) initiative.

Thank you to all the contributors who have helped make MQT YAQS a reality!

The MQT will remain free, open-source, and permissively licensed—now and in the future. We are firmly committed to keeping it open and actively maintained for the quantum computing community.

To support this endeavor, please consider:

• Starring and sharing our repositories: https://github.com/munich-quantum-toolkit
• Contributing code, documentation, tests, or examples via issues and pull requests
• Citing the MQT in your publications (see Cite This)
• Citing our research in your publications (see References)
• Using the MQT in research and teaching, and sharing feedback and use cases
• Sponsoring us on GitHub: https://github.com/sponsors/munich-quantum-toolkit

Getting Started

mqt.yaqs is available via PyPI.

uv pip install mqt.yaqs

Simulation

Analog simulation guide

Noisy analog Hamiltonian simulation

from mqt.yaqs import AnalogSimParams, Hamiltonian, NoiseModel, Observable, Simulator, State

sim = Simulator(show_progress=False)
state = State(length=3, initial="zeros")
H = Hamiltonian.ising(length=3, J=1.0, g=0.5)
noise = NoiseModel([{"name": "lowering", "sites": [i], "strength": 0.05} for i in range(3)])
params = AnalogSimParams(
    observables=[Observable("z", sites=0)],
    elapsed_time=0.5,
    dt=0.1,
    preset="fast",
    num_traj=8,
)
print(sim.run(state, H, params, noise).expectation_values[0][-1])

Circuit simulation guide

Noisy digital circuit simulation (observables)

from qiskit.circuit import QuantumCircuit

from mqt.yaqs import NoiseModel, Observable, Simulator, State, DigitalSimParams

circuit = QuantumCircuit(3)
circuit.h(0)
circuit.cx(0, 1)
circuit.cx(1, 2)
noise = NoiseModel([{"name": "lowering", "sites": [i], "strength": 0.05} for i in range(3)])
params = DigitalSimParams(observables=[Observable("z", sites=0)], preset="fast", num_traj=8)
result = Simulator(show_progress=False).run(State(3, initial="zeros"), circuit, params, noise)
print(result.expectation_values[0])

Characterization

Environmental memory guide

Environmental memory characterization

from mqt.yaqs import AnalogSimParams, Hamiltonian, MemoryCharacterizer

ham = Hamiltonian.ising(length=3, J=1.0, g=0.5)
params = AnalogSimParams(dt=0.1)
result = MemoryCharacterizer(show_progress=False).characterize(
    ham,
    params,
    num_interventions=4,
    cut=2,
    n_pasts=4,
    n_futures=4,
)
print(result.summary())

Noise characterization guide

Noise model characterization

import numpy as np

from mqt.yaqs import AnalogSimParams, Hamiltonian, NoiseCharacterizer, NoiseModel, Observable, State

n = 2
ham = Hamiltonian.ising(length=n, J=1.0, g=2.0)
state = State(n, initial="zeros")
observables = [Observable("z", sites=s) for s in range(n)]
params = AnalogSimParams(observables=observables, elapsed_time=0.5, dt=0.1, sample_timesteps=True)
reference = NoiseModel([{"name": "pauli_z", "sites": [s], "strength": 0.1} for s in range(n)])
guess = NoiseModel([{"name": "pauli_z", "sites": [s], "strength": 0.3} for s in range(n)])
result = NoiseCharacterizer(show_progress=False).characterize(
    ham,
    params,
    init_state=state,
    init_guess=guess,
    observables=observables,
    reference_model=reference,
    x_low=np.zeros(n),
    x_up=np.full(n, 0.5),
    max_iter=30,
    popsize=6,
    seed=0,
)
print(result.optimal_model)

Documentation: Quickstart · Analog simulation · Circuit observables · Environmental memory · Noise characterization · full guide

System Requirements

MQT YAQS can be installed on all major operating systems with all officially supported Python versions. Building (and running) is continuously tested under Linux, macOS, and Windows using the latest available system versions for GitHub Actions.

Cite This

Please cite the work that best fits your use case.

Peer-Reviewed Research

When citing the underlying methods and research, please reference the most relevant peer-reviewed publications from the list below:

[1] A. Sander, M. Fröhlich, M. Eigel, J. Eisert, P. Gelß, M. Hintermüller, R. M. Milbradt, R. Wille, C. B. Mendl. Large-scale stochastic simulation of open quantum systems. Nature Communications 16, 11074 (2025).

[2] A. Sander, L. Burgholzer, and R. Wille. Equivalence checking of quantum circuits via intermediary matrix product operator. Phys. Rev. Research 7, 023261 (2025).

[3] A. Sander, M. Fröhlich, M. Ali, M. Eigel, J. Eisert, M. Hintermüller, C. B. Mendl, R. M. Milbradt, R. Wille. Quantum circuit simulation with a local time-dependent variational principle. arXiv:2508.10096 (2025).

[4] A. Sander, S. Cichy, M. Eigel, J. Eisert, M. Fröhlich, T. Peham, R. Wille. Computational regimes in matrix-product-state-based quantum trajectory simulations. arXiv:2606.13779 (2026).

The Munich Quantum Toolkit (the project)

When discussing the overall MQT project or its ecosystem, cite the MQT Handbook:

@inproceedings{mqt,
  title        = {The {{MQT}} Handbook: {{A}} Summary of Design Automation Tools and Software for Quantum Computing},
  shorttitle   = {{The MQT Handbook}},
  author       = {Wille, Robert and Berent, Lucas and Forster, Tobias and Kunasaikaran, Jagatheesan and Mato, Kevin and Peham, Tom and Quetschlich, Nils and Rovara, Damian and Sander, Aaron and Schmid, Ludwig and Schoenberger, Daniel and Stade, Yannick and Burgholzer, Lukas},
  year         = 2024,
  booktitle    = {IEEE International Conference on Quantum Software (QSW)},
  doi          = {10.1109/QSW62656.2024.00013},
  eprint       = {2405.17543},
  eprinttype   = {arxiv},
  addendum     = {A live version of this document is available at \url{https://mqt.readthedocs.io}}
}

Acknowledgements

The Munich Quantum Toolkit has been supported by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (grant agreement No. 101001318), the Bavarian State Ministry for Science and Arts through the Distinguished Professorship Program, as well as the Munich Quantum Valley, which is supported by the Bavarian state government with funds from the Hightech Agenda Bayern Plus.