qecGPT: decoding Quantum Error-correcting Codes with Generative Pre-trained Transformers

We propose a general framework for decoding quantum error-correcting codes with generative modeling. The model utilizes autoregressive neural networks, specifically Transformers, to learn the joint probability of logical operators and syndromes. This training is in an unsupervised way, without the need for labeled training data, and is thus referred to as pre-training. After the pre-training, the model can efficiently compute the likelihood of logical operators for any given syndrome, using maximum likelihood decoding. It can directly generate the most-likely logical operators with computational complexity $\mathcal O(2k)$ in the number of logical qubits $k$, which is significantly better than the conventional maximum likelihood decoding algorithms that require $\mathcal O(4^k)$ computation. Based on the pre-trained model, we further propose refinement to achieve more accurately the likelihood of logical operators for a given syndrome by directly sampling the stabilizer operators. We perform numerical experiments on stabilizer codes with small code distances, using both depolarizing error models and error models with correlated noise. The results show that our approach provides significantly better decoding accuracy than the minimum weight perfect matching and belief-propagation-based algorithms. Our framework is general and can be applied to any error model and quantum codes with different topologies such as surface codes and quantum LDPC codes. Furthermore, it leverages the parallelization capabilities of GPUs, enabling simultaneous decoding of a large number of syndromes. Our approach sheds light on the efficient and accurate decoding of quantum error-correcting codes using generative artificial intelligence and modern computational power.Comment: Comments are welcom

An Improved Repetitive Control for Circulating Current Restraining in MMC-MTDC

The modular multilevel converter (MMC) is widely used in many important application fields such as high voltage DC transmission system. And the multi-terminal architecture of it attracts many attentions. However, the circulating current of MMC is an inherent problem which is mainly caused by the voltage mismatch between arms and DC bus. In this paper, an advanced repetitive control method is proposed. This method is based on the even-harmonic characteristic of the circulating current and the potential feature of repetitive control that it has an internal integration part. The pole diagram of the closed loop transform function of the proposed control system proves the stability of the proposed method. And according to the simulation results of a three-terminal MMC-MTDC model in PSCAD/EMTDC, the improved repetitive control presents better circulation repression ability and superior anti-interference capability by comparing with traditional PI control method. Additionally, the simulation results also indicate that the proposed repetitive controller can restrain the fluctuation of SM voltage more effectively than PI control

Thermodynamics of Strained Vanadium Dioxide Single Crystals

Vanadium dioxide undergoes a metal-insulator transition, in which the strain condition plays an important role. To investigate the strain contribution, a phenomenological thermodynamic potential for the vanadium dioxide single crystal was constructed. The transformations under the uniaxial stress, wire, and thin film boundary conditions were analyzed, and the corresponding phase diagrams were constructed. The calculated phase diagrams agree well with existing experimental data, and show that the transformation temperature (and Curie temperature) strongly depends on the strain condition

Nonprofit contracting and partnership in elderly care : a comparison between China and the Netherlands

This paper offers an empirical account of the engagement and success of nonprofits in contracting for elderly care in China and the Netherlands as two contrasting contexts. While contracting as an innovation demonstrates a state-centered approach in China, its Dutch counterpart has sought a balance between state and professional influences. The paper argues that public sector reforms, civil society development and social regulation support schemes contextualize the engagement and success of nonprofits in contracting for elderly care. Surveys among the managers of 176 elderly care organizations in Shanghai and 70 elderly care organizations in the Netherlands shows that the fundamental elements of nonprofit contracting in elderly care are strikingly similar between both contexts, although their manifestation is shaped by each specific institutional context.Peer reviewe