Zichang He

Anuj Apte, Shree Hari Sureshbabu, Ruslan Shaydulin et al.

Quantum Approximate Optimization Algorithm (QAOA) is a promising quantum heuristic with empirical evidence of speedup over classical state-of-the-art for some problems. QAOA uses a parameterized circuit with $p$ layers, where higher $p$ yields better solutions, but requires optimizing $2p$ independent parameters, which is challenging at large $p$. We present an iterative interpolation method that exploits the smoothness of optimal parameter schedules by expressing them in a basis of orthogonal functions, generalizing the work of Zhou et al. By optimizing a small number of basis coefficients and iteratively increasing both circuit depth and coefficient count until convergence, our method constructs high-quality schedules for large $p$. We provide theoretical justification using Jackson's theorem and Lipschitz continuity to bound the required number of basis coefficients for a given accuracy. Our approach achieves better performance with fewer optimization steps than existing methods across three benchmark problems: the Sherrington-Kirkpatrick (SK) model, portfolio optimization, and Low Autocorrelation Binary Sequences (LABS). For the largest LABS instance, we achieve near-optimal merit factors with schedules exceeding 1000 layers, an order of magnitude beyond previous methods. Additionally, we observe that a mild growth in QAOA depth suffices to solve the SK model exactly, a result of independent theoretical interest.

Yuwei Jin, Zichang He, Tianyi Hao et al.

The rapid progress in quantum hardware is expected to make them viable tools for the study of quantum algorithms in the near term. The timeline to useful algorithmic experimentation can be accelerated by techniques that use many noisy shots to produce an accurate estimate of the observable of interest. One such technique is to encode the quantum circuit using an error detection code and discard the samples for which an error has been detected. An underexplored property of error-detecting codes is the flexibility in the circuit encoding and fault-tolerant gadgets, which enables their co-optimization with the algorthmic circuit. However, standard circuit optimization tools cannot be used to exploit this flexibility as optimization must preserve the fault-tolerance of the gadget. In this work, we focus on the $[[k+2, k, 2]]$ Iceberg quantum error detection code, which is tailored to trapped-ion quantum processors. We design new flexible fault-tolerant gadgets for the Iceberg code, which we then co-optimize with the algorithmic circuit for the quantum approximate optimization algorithm (QAOA) using tree search. By co-optimizing the QAOA circuit and the Iceberg gadgets, we achieve an improvement in QAOA success probability from $44\%$ to $65\%$ and an increase in post-selection rate from $4\%$ to $33\%$ at 22 algorithmic qubits, utilizing 330 algorithmic two-qubit gates and 744 physical two-qubit gates on the Quantinuum H2-1 quantum computer, compared to the previous state-of-the-art hardware demonstration. Furthermore, we demonstrate better-than-unencoded performance for up to 34 algorithmic qubits, employing 510 algorithmic two-qubit gates and 1140 physical two-qubit gates.

Ryan Solgi, Zichang He, William Jiahua Liang et al.

Various tensor decomposition methods have been proposed for data compression. In real world applications of the tensor decomposition, selecting the tensor shape for the given data poses a challenge and the shape of the tensor may affect the error and the compression ratio. In this work, we study the effect of the tensor shape on the tensor decomposition and propose an optimization model to find an optimum shape for the tensor train (TT) decomposition. The proposed optimization model maximizes the compression ratio of the TT decomposition given an error bound. We implement a genetic algorithm (GA) linked with the TT-SVD algorithm to solve the optimization model. We apply the proposed method for the compression of RGB images. The results demonstrate the effectiveness of the proposed evolutionary tensor shape search for the TT decomposition.

Hsiang Hsu, Pradeep Niroula, Zichang He et al.

Machine unlearning offers a practical alternative to avoid full model re-training by approximately removing the influence of specific user data. While existing methods certify unlearning via statistical indistinguishability from re-trained models, these guarantees do not naturally extend to model outputs when inputs are adversarially perturbed. In particular, slight perturbations of forget samples may still be correctly recognized by the unlearned model - even when a re-trained model fails to do so - revealing a novel privacy risk: information about the forget samples may persist in their local neighborhood. In this work, we formalize this vulnerability as residual knowledge and show that it is inevitable in high-dimensional settings. To mitigate this risk, we propose a fine-tuning strategy, named RURK, that penalizes the model's ability to re-recognize perturbed forget samples. Experiments on vision benchmarks with deep neural networks demonstrate that residual knowledge is prevalent across existing unlearning methods and that our approach effectively prevents residual knowledge.

Zichang He, Zheng Zhang

Fabrication process variations can significantly influence the performance and yield of nano-scale electronic and photonic circuits. Stochastic spectral methods have achieved great success in quantifying the impact of process variations, but they suffer from the curse of dimensionality. Recently, low-rank tensor methods have been developed to mitigate this issue, but two fundamental challenges remain open: how to automatically determine the tensor rank and how to adaptively pick the informative simulation samples. This paper proposes a novel tensor regression method to address these two challenges. We use a $\ell_{q}/ \ell_{2}$ group-sparsity regularization to determine the tensor rank. The resulting optimization problem can be efficiently solved via an alternating minimization solver. We also propose a two-stage adaptive sampling method to reduce the simulation cost. Our method considers both exploration and exploitation via the estimated Voronoi cell volume and nonlinearity measurement respectively. The proposed model is verified with synthetic and some realistic circuit benchmarks, on which our method can well capture the uncertainty caused by 19 to 100 random variables with only 100 to 600 simulation samples.

Zichang He, Bo Zhao, Zheng Zhang

Magnetic resonance imaging (MRI) is a powerful imaging modality that revolutionizes medicine and biology. The imaging speed of high-dimensional MRI is often limited, which constrains its practical utility. Recently, low-rank tensor models have been exploited to enable fast MR imaging with sparse sampling. Most existing methods use some pre-defined sampling design, and active sensing has not been explored for low-rank tensor imaging. In this paper, we introduce an active low-rank tensor model for fast MR imaging. We propose an active sampling method based on a Query-by-Committee model, making use of the benefits of low-rank tensor structure. Numerical experiments on a 3-D MRI data set demonstrate the effectiveness of the proposed method.

Zichang He, Wen Jiang

The sure thing principle and the law of total probability are basic laws in classic probability theory. A disjunction fallacy leads to the violation of these two classical laws. In this paper, an Evidential Markov (EM) decision making model based on Dempster-Shafer (D-S) evidence theory and Markov modelling is proposed to address this issue and model the real human decision-making process. In an evidential framework, the states are extended by introducing an uncertain state which represents the hesitance of a decision maker. The classical Markov model can not produce the disjunction effect, which assumes that a decision has to be certain at one time. However, the state is allowed to be uncertain in the EM model before the final decision is made. An extra uncertainty degree parameter is defined by a belief entropy, named Deng entropy, to assignment the basic probability assignment of the uncertain state, which is the key to predict the disjunction effect. A classical categorization decision-making experiment is used to illustrate the effectiveness and validity of EM model. The disjunction effect can be well predicted and the free parameters are less compared with the existing models.

Zichang He, Wen Jiang

Dempster-Shafer evidence theory is wildly applied in multi-sensor data fusion. However, lots of uncertainty and interference exist in practical situation, especially in the battle field. It is still an open issue to model the reliability of sensor reports. Many methods are proposed based on the relationship among collected data. In this letter, we proposed a quantum mechanical approach to evaluate the reliability of sensor reports, which is based on the properties of a sensor itself. The proposed method is used to modify the combining of evidences.

Zichang He, Wen Jiang

Supplier selection is a typical multi-criteria decision making (MCDM) problem and lots of uncertain information exist inevitably. To address this issue, a new method was proposed based on interval data fusion. Our method follows the original way to generate classical basic probability assignment(BPA) determined by the distance among the evidences. However, the weights of criteria are kept as interval numbers to generate interval BPAs and do the fusion of interval BPAs. Finally, the order is ranked and the decision is made according to the obtained interval BPAs. In this paper, a numerical example of supplier selection is applied to verify the feasibility and validity of our method. The new method is presented aiming at solving multiple-criteria decision-making problems in which the weights of criteria or experts are described in fuzzy data like linguistic terms or interval data.

Zichang He, Wen Jiang

Categorization is necessary for many decision making tasks. However, the categorization process may interfere the decision making result and the law of total probability can be violated in some situations. To predict the interference effect of categorization, some model based on quantum probability has been proposed. In this paper, a new quantum dynamic belief (QDB) model is proposed. Considering the precise decision may not be made during the process, the concept of uncertainty is introduced in our model to simulate real human thinking process. Then the interference effect categorization can be predicted by handling the uncertain information. The proposed model is applied to a categorization decision-making experiment to explain the interference effect of categorization. Compared with other models, our model is relatively more succinct and the result shows the correctness and effectiveness of our model.

Zichang He, Wen Jiang

Markov chain model is widely applied in many fields, especially the field of prediction. The classical Discrete-time Markov chain(DTMC) is a widely used method for prediction. However, the classical DTMC model has some limitation when the system is complex with uncertain information or state space is not discrete. To address it, a new belief Markov chain model is proposed by combining Dempster-Shafer evidence theory with Markov chain. In our model, the uncertain data is allowed to be handle in the form of interval number and the basic probability assignment(BPA) is generated based on the distance between interval numbers. The new belief Markov chain model overcomes the shortcomings of classical Markov chain and has an efficient ability in dealing with uncertain information. Moreover, an example of inventory prediction and the comparison between our model and classical DTMC model can show the effectiveness and rationality of our proposed model.

Zichang He, Wen Jiang

The sure thing principle and the law of total probability are basic laws in classic probability theory. A disjunction fallacy leads to the violation of these two classical probability laws. In this paper, a new quantum dynamic belief decision making model based on quantum dynamic modelling and Dempster-Shafer (D-S) evidence theory is proposed to address this issue and model the real human decision-making process. Some mathematical techniques are borrowed from quantum mathematics. Generally, belief and action are two parts in a decision making process. The uncertainty in belief part is represented by a superposition of certain states. The uncertainty in actions is represented as an extra uncertainty state. The interference effect is produced due to the entanglement between beliefs and actions. Basic probability assignment (BPA) of decisions is generated by quantum dynamic modelling. Then BPA of the extra uncertain state and an entanglement degree defined by an entropy function named Deng entropy are used to measure the interference effect. Compared the existing model, the number of free parameters is less in our model. Finally, a classical categorization decision-making experiment is illustrated to show the effectiveness of our model.