Flexible Error Mitigation of Quantum Processes with Data Augmentation Empowered Neural Model

Flexible Error Mitigation of Quantum Processes with Data Augmentation Empowered Neural Model

by Manwen Liao¹ *, Yan Zhu¹ *, Giulio Chiribella^{1, 2, 3}, Yuxiang Yang^{1 📧}

¹ QICI Quantum Information and Computation Initiative, Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong

² Department of Computer Science, Parks Road, Oxford, OX1 3QD, United Kingdom

³ Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada

(*) equal contribution, (^📧) corresponding author.

Data Augmentation Empowered Neural Model (DAEM)

The Illustration of DAEM

Highlights of Our Framework

Exemption from noise-free statistics reliance: Our proposed architecture eliminates the need for noise-free statistics acquired from the target quantum process. This feature allows the model to be potentially applicable in real-world experiments. Additionally, while our model still relies on noisy measurement data across different noise levels, it does not assume the knowledge of noise level values.
Versatility on various types of quantum processes: The proposed architecture is flexible and can accept different forms of measurement statistics as inputs, making it suitable for various quantum processes, including quantum circuits, continuous-variable quantum processes, and dynamics of large-scale spin systems.
Adaptability to diverse settings and noise models: Our data-driven model can be trained using measurement statistics without relying on rigid assumptions about noise models or requiring a specific initial state or measurement setting. Furthermore, it is capable of mitigating not only the error of observable expectations, but also the distortion of measurement probability distributions.

Error Mitigation Results

Variational Quantum Eigensolvers (VQE)

a. The variational ansatz for preparing the ground states of 4-qubit transverse Ising models. b. Mean Absolute Errors (MAE) between the mitigated measurement expectation values for phase damping noise model and ideal expectation values. c.Mean Absolute Errors (MAE) between the mitigated measurement expectation values for amplitude damping noise model and ideal expectation values. d. Schematic diagram of quantum circuits affected by Non-Markovian noise. e. Mean Absolute Errors (MAE) between the mitigated measurement expectation values for considered Non-Markovian noise model and ideal expectation values.

Swap Test

a. The swap test circuit for comparing two 5-qubit states. The gate within the green box is the controlled-SWAP gate. b. Mean Absolute Errors (MAE) between the mitigated fidelity values and the ground truth values.

Quantum Approximate Optimisation Algorithms (QAOA)

a. An instance of a graph for for the Max-cut problem. b. The variational ansatz for implementing QAOA algorithm. c. Ideal, Noisy and Mitigated frequency of measurement results.

Spin-system dynamics

a. MAE between the mitigated measurement expectation values for phase damping noise model and ideal expectation values. b. MAE between the mitigated measurement expectation values for amplitude damping noise model and ideal expectation values.

Continuous-variable process

a. Fidelity values between the noisy/mitigated state and the ideal state. b. Snapshots of the point-wise measurement results of the state at different time points.

Requirement

This codebase has been developed with python 3.7, PyTorch 1.12+:

conda install pytorch==1.12.1 cudatoolkit=10.2 -c pytorch

See requirements.txt for additional requirements.

pip install -r requirements.txt

Data

The data for training can be downloaded from here. Alternatively, you may refer to src/dataset.py, src/error_mitigation_data, and src/TensornetSimulator to generate your training data.

Training

To train neural model for error mitigation of quantum algorithms and continuous-variable process, run:

python src/train_supervise.py --train-path /path/to/train_file --test-path /path/to/validation_file

To train neural model for mitigating errors in continuous-variable process, run:

python src/train_cv.py --train-path /path/to/train_file --test-path /path/to/validation_file

Evaluate

The evaluation results can be downloaded from here. You may evaluate and compare DAEM with ZNE and CDR by running benchmark.py.

Citation

@misc{liao2023flexible,
      title={Flexible Error Mitigation of Quantum Processes with Data Augmentation Empowered Neural Model}, 
      author={Manwen Liao and Yan Zhu and Giulio Chiribella and Yuxiang Yang},
      year={2023},
      eprint={2311.01727},
      archivePrefix={arXiv},
      primaryClass={quant-ph}
}

EXPmaster / DAEM