Variational quantum Eigensolver (VQE) is a leading candidate for harnessing quantum computers to advance quantum chemistry and materials simulations, yet its training efficiency deteriorates rapidly for large Hamiltonians. Two issues underlie this bottleneck: (i) the no-cloning theorem imposes a linear growth in circuit evaluations with the number of parameters per gradient step; and (ii) deeper circuits encounter barren plateaus (BPs), leading to exponentially increasing measurement overheads. To address these challenges, here we propose a deep learning framework, dubbed Titan, which identifies and freezes inactive parameters of a given ansatze at initialization for a specific class of Hamiltonians, reducing the optimization overhead without sacrificing accuracy. The motivation of Titan starts with our empirical findings that a subset of parameters consistently has a negligible influence on training dynamics. Its design combines a theoretically grounded data construction strategy, ensuring each training example is informative and BP-resilient, with an adaptive neural architecture that generalizes across ansatze of varying sizes. Across benchmark transverse-field Ising models, Heisenberg models, and multiple molecule systems up to 30 qubits, Titan achieves up to 3 times faster convergence and 40% to 60% fewer circuit evaluations than state-of-the-art baselines, while matching or surpassing their estimation accuracy. By proactively trimming parameter space, Titan lowers hardware demands and offers a scalable path toward utilizing VQE to advance practical quantum chemistry and materials science.

Variational quantum algorithms (VQAs) promise near-term quantum advantage, yet parametrized quantum states commonly built from the digital gate-based approach often suffer from scalability issues such as barren plateaus, where the loss landscape becomes flat. We study an analog VQA ansätze composed of $M$ quenches of a disordered Ising chain, whose dynamics is native to several quantum simulation platforms. By tuning the disorder strength we place each quench in either a thermalized phase or a many-body-localized (MBL) phase and analyse (i) the ansätze's expressivity and (ii) the scaling of loss variance. Numerics shows that both phases reach maximal expressivity at large $M$, but barren plateaus emerge at far smaller $M$ in the thermalized phase than in the MBL phase. Exploiting this gap, we propose an MBL initialisation strategy: initialise the ansätze in the MBL regime at intermediate quench $M$, enabling an initial trainability while retaining sufficient expressivity for subsequent optimization. The results link quantum phases of matter and VQA trainability, and provide practical guidelines for scaling analog-hardware VQAs.

We propose SnCQA, a set of hardware-efficient variational circuits of equivariant quantum convolutional circuits respective to permutation symmetries and spatial lattice symmetries with the number of qubits $n$. By exploiting permutation symmetries of the system, such as lattice Hamiltonians common to many quantum many-body and quantum chemistry problems, Our quantum neural networks are suitable for solving machine learning problems where permutation symmetries are present, which could lead to significant savings of computational costs. Aside from its theoretical novelty, we find our simulations perform well in practical instances of learning ground states in quantum computational chemistry, where we could achieve comparable performances to traditional methods with few tens of parameters. Compared to other traditional variational quantum circuits, such as the pure hardware-efficient ansatz (pHEA), we show that SnCQA is more scalable, accurate, and noise resilient (with $20\times$ better performance on $3 \times 4$ square lattice and $200\% - 1000\%$ resource savings in various lattice sizes and key criterions such as the number of layers, parameters, and times to converge in our cases), suggesting a potentially favorable experiment on near-time quantum devices.

Multilingual pretrained language models (MPLMs) have demonstrated substantial performance improvements in zero-shot cross-lingual transfer across various natural language understanding tasks by finetuning MPLMs on task-specific labelled data of a source language (e.g. English) and evaluating on a wide range of target languages. Recent studies show that prompt-based finetuning surpasses regular finetuning in few-shot scenarios. However, the exploration of prompt-based learning in multilingual tasks remains limited. In this study, we propose the ProFiT pipeline to investigate the cross-lingual capabilities of Prompt-based Finetuning. We conduct comprehensive experiments on diverse cross-lingual language understanding tasks (sentiment classification, paraphrase identification, and natural language inference) and empirically analyze the variation trends of prompt-based finetuning performance in cross-lingual transfer across different few-shot and full-data settings. Our results reveal the effectiveness and versatility of prompt-based finetuning in cross-lingual language understanding. Our findings indicate that prompt-based finetuning outperforms vanilla finetuning in full-data scenarios and exhibits greater advantages in few-shot scenarios, with different performance patterns dependent on task types. Additionally, we analyze underlying factors such as language similarity and pretraining data size that impact the cross-lingual performance of prompt-based finetuning. Overall, our work provides valuable insights into the cross-lingual prowess of prompt-based finetuning.

Considering the relation between neural networks (NN) and TN, the first works focused on the restricted Boltzmann machines (RBM), which are one of the simplest Tensor networks (TN) have been extensively used to classes of NN. It is impossible to efficiently map an represent the states of quantum many-body physical systems RBM onto a TN, as they correspond to string-bond states [1-3]. Matrix product states (MPS) are possibly with an arbitrary nonlocal geometry [28]. This result was the simplest family of TN, and are suitable to capture later refined to show that an RBM may correspond to an the ground state of 1D gapped Hamiltonians [4, 5]. They MPS with an exponentially large bond dimension, and can be contracted in polynomial time to compute physical only short-range RBM can be mapped onto efficiently quantities exactly, and optimized by density matrix computable entangled plaquette states [31]. Similar results renormalization group (DMRG) [6] when used as variational have been obtained that deep Boltzmann machines ansätze. More powerful TN architectures that with proper constraints can be mapped onto TN that cannot be efficiently contracted in general have been are efficiently computable through transfer matrix methods proposed later, notably projected entangled pair states [32].

Many fundamental properties of a quantum system are captured by its Hamiltonian and ground state. Despite the significance of ground states preparation (GSP), this task is classically intractable for large-scale Hamiltonians. Quantum neural networks (QNNs), which exert the power of modern quantum machines, have emerged as a leading protocol to conquer this issue. As such, how to enhance the performance of QNNs becomes a crucial topic in GSP. Empirical evidence showed that QNNs with handcraft symmetric ansatzes generally experience better trainability than those with asymmetric ansatzes, while theoretical explanations have not been explored. To fill this knowledge gap, here we propose the effective quantum neural tangent kernel (EQNTK) and connect this concept with over-parameterization theory to quantify the convergence of QNNs towards the global optima. We uncover that the advance of symmetric ansatzes attributes to their large EQNTK value with low effective dimension, which requests few parameters and quantum circuit depth to reach the over-parameterization regime permitting a benign loss landscape and fast convergence. Guided by EQNTK, we further devise a symmetric pruning (SP) scheme to automatically tailor a symmetric ansatz from an over-parameterized and asymmetric one to greatly improve the performance of QNNs when the explicit symmetry information of Hamiltonian is unavailable. Extensive numerical simulations are conducted to validate the analytical results of EQNTK and the effectiveness of SP.

Prompting shows promising results in few-shot scenarios. However, its strength for multilingual/cross-lingual problems has not been fully exploited. Zhao and Sch\"utze (2021) made initial explorations in this direction by presenting that cross-lingual prompting outperforms cross-lingual finetuning. In this paper, we conduct empirical analysis on the effect of each component in cross-lingual prompting and derive Universal Prompting across languages, which helps alleviate the discrepancies between source-language training and target-language inference. Based on this, we propose a mask token augmentation framework to further improve the performance of prompt-based cross-lingual transfer. Notably, for XNLI, our method achieves 46.54% with only 16 English training examples per class, significantly better than 34.99% of finetuning.

We develop a theoretical framework for $S_n$-equivariant quantum convolutional circuits, building on and significantly generalizing Jordan's Permutational Quantum Computing (PQC) formalism. We show that quantum circuits are a natural choice for Fourier space neural architectures affording a super-exponential speedup in computing the matrix elements of $S_n$-Fourier coefficients compared to the best known classical Fast Fourier Transform (FFT) over the symmetric group. In particular, we utilize the Okounkov-Vershik approach to prove Harrow's statement (Ph.D. Thesis 2005 p.160) on the equivalence between $\operatorname{SU}(d)$- and $S_n$-irrep bases and to establish the $S_n$-equivariant Convolutional Quantum Alternating Ans{\"a}tze ($S_n$-CQA) using Young-Jucys-Murphy (YJM) elements. We prove that $S_n$-CQA are dense, thus expressible within each $S_n$-irrep block, which may serve as a universal model for potential future quantum machine learning and optimization applications. Our method provides another way to prove the universality of Quantum Approximate Optimization Algorithm (QAOA), from the representation-theoretical point of view. Our framework can be naturally applied to a wide array of problems with global $\operatorname{SU}(d)$ symmetry. We present numerical simulations to showcase the effectiveness of the ans{\"a}tze to find the sign structure of the ground state of the $J_1$--$J_2$ antiferromagnetic Heisenberg model on the rectangular and Kagome lattices. Our work identifies quantum advantage for a specific machine learning problem, and provides the first application of the celebrated Okounkov-Vershik's representation theory to machine learning and quantum physics.

Combining a pretrained language model (PLM) with textual patterns has been shown to help in both zero- and few-shot settings. For zero-shot performance, it makes sense to design patterns that closely resemble the text seen during self-supervised pretraining because the model has never seen anything else. Supervised training allows for more flexibility. If we allow for tokens outside the PLM's vocabulary, patterns can be adapted more flexibly to a PLM's idiosyncrasies. Contrasting patterns where a "token" can be any continuous vector vs. those where a discrete choice between vocabulary elements has to be made, we call our method CONtinuous pAtterNs (CONAN). We evaluate CONAN on two established benchmarks for lexical inference in context (LIiC) a.k.a. predicate entailment, a challenging natural language understanding task with relatively small training sets. In a direct comparison with discrete patterns, CONAN consistently leads to improved performance, setting a new state of the art. Our experiments give valuable insights into the kind of pattern that enhances a PLM's performance on LIiC and raise important questions regarding our understanding of PLMs using text patterns.

Recently, pre-trained language models (LMs) have achieved strong performance when fine-tuned on difficult benchmarks like SuperGLUE. However, performance can suffer when there are very few labeled examples available for fine-tuning. Pattern Exploiting Training (PET) is a recent approach that leverages patterns for few-shot learning. However, PET uses task-specific unlabeled data. In this paper, we focus on few shot learning without any unlabeled data and introduce ADAPET, which modifies PET's objective to provide denser supervision during fine-tuning. As a result, ADAPET outperforms PET on SuperGLUE without any task-specific unlabeled data. Our code can be found at https://github.com/rrmenon10/ADAPET.