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Researcher profile

Pan Zhang

Pan Zhang contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Computer Visioncond-mat.stat-mechquant-phMachine Learningmath.DGphysics.comp-pheess.IVGraphicsArtificial Intelligencecond-mat.mtrl-scicond-mat.str-elSocial and Information NetworksComputationcond-mat.dis-nneess.SYhep-thmath.SPphysics.soc-phSystems and Control

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Published work

23 published item(s)

preprint2026arXiv

Inverse Knowledge Search over Verifiable Reasoning: Synthesizing a Scientific Encyclopedia from a Long Chains-of-Thought Knowledge Base

Most scientific materials compress reasoning, presenting conclusions while omitting the derivational chains that justify them. This compression hinders verification by lacking explicit, step-wise justifications and inhibits cross-domain links by collapsing the very pathways that establish the logical and causal connections between concepts. We introduce a scalable framework that decompresses scientific reasoning, constructing a verifiable Long Chain-of-Thought (LCoT) knowledge base and projecting it into an emergent encyclopedia, SciencePedia. Our pipeline operationalizes an endpoint-driven, reductionist strategy: a Socratic agent, guided by a curriculum of around 200 courses, generates approximately 3 million first-principles questions. To ensure high fidelity, multiple independent solver models generate LCoTs, which are then rigorously filtered by prompt sanitization and cross-model answer consensus, retaining only those with verifiable endpoints. This verified corpus powers the Brainstorm Search Engine, which performs inverse knowledge search -- retrieving diverse, first-principles derivations that culminate in a target concept. This engine, in turn, feeds the Plato synthesizer, which narrates these verified chains into coherent articles. The initial SciencePedia comprises approximately 200,000 fine-grained entries spanning mathematics, physics, chemistry, biology, engineering, and computation. In evaluations across six disciplines, Plato-synthesized articles (conditioned on retrieved LCoTs) exhibit substantially higher knowledge-point density and significantly lower factual error rates than an equally-prompted baseline without retrieval (as judged by an external LLM). Built on this verifiable LCoT knowledge base, this reasoning-centric approach enables trustworthy, cross-domain scientific synthesis at scale and establishes the foundation for an ever-expanding encyclopedia.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Schrödinger Operators, Integral Curvature, and the Euler Characteristic of Riemannian Manifolds

We establish new connections between integral curvature bounds and the Euler characteristic of closed Riemannian manifolds through the perspective of Schrödinger-type operators. Central to our approach is the twisted Dirac operator \(\mathcal{D}_θ\), whose index equals \(χ(M)\). Under integral smallness conditions on the negative part of a potential \(V\) and a Sobolev--Poincaré inequality, we show that a suitable scaling of \(θ\) forces the kernel of \(\mathcal{D}_{tθ}\) to vanish, thereby implying \(χ(M)=0\). Applying this framework to geometrically natural potentials yields several topological consequences. In even dimensions, sufficiently small integral bounds on partial sums of curvature operator eigenvalues force \(χ(M)\) either to vanish or to have a sign determined by the middle dimension. For four-manifolds, a small \(L^{p}\)-norm of the negative Ricci curvature relative to the diameter guarantees \(χ(M)\ge 0\). Moreover, when \(χ(M)\neq 0\) we obtain a Li--Yau type lower bound for the first eigenvalue of the rough Laplacian on \(1\)-forms in terms of the diameter and an integral curvature quantity. Subsequently, we provide an explicit lower bound for the first eigenvalue of the Laplacian on $1$-forms under almost nonnegative curvature conditions, thereby giving an affirmative answer to Yau's Problem 79.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Strategic Over-Parameterization for Generalizable Low-Rank Adaptation

Adapting large language models (LLMs) to downstream tasks via full fine-tuning is increasingly impractical due to its computational and memory demands. Parameter-efficient fine-tuning (PEFT) approaches such as Low-Rank Adaptation (LoRA) mitigate this by confining updates to a compact set of trainable parameters, but this aggressive reduction often sacrifices generalization, especially under transfer across heterogeneous tasks and domains. We revisit the tension between parameter efficiency and adaptation capacity, and ask whether the two are truly at odds. We answer in the negative by introducing LoRA-Over, a framework grounded in a simple principle: enrich the optimization landscape during training, then collapse the enrichment at inference. LoRA-Over injects auxiliary parameters into the low-rank adapters during training to broaden the effective hypothesis space, and through a decomposition-based reformulation folds them back into a standard low-rank structure with negligible reconstruction error, keeping inference cost identical to vanilla LoRA. Since not all weight matrices benefit equally from added capacity, we further propose two scheduling strategies, one statically predefined and one dynamically determined at runtime, that direct extra capacity where most needed. We evaluate LoRA-Over on language understanding (GLUE, T5-Base), dialogue (MT-Bench), arithmetic reasoning (GSM8K), and code generation (HumanEval), using LLaMA 2-7B and LLaMA 3.1-8B. Across all benchmarks and scales, LoRA-Over consistently outperforms vanilla LoRA, showing that principled over-parameterization designed to vanish at inference is an effective lever for improving PEFT generalization. Code will be released upon acceptance.

0 citations0 reviewsNo code linkedOpen access
preprint2023arXiv

The Limit of the Yang-Mills-Higgs Flow for twisted Higgs pairs

In this paper, we consider the Yang-Mills-Higgs flow for twisted Higgs pairs over Kähler manifolds. We prove that this flow converges to a reflexive twisted Higgs sheaf outside a closed subset of codimension $4$, and the limiting twisted Higgs sheaf is isomorphic to the double dual of the graded twisted Higgs sheaves associated to the Harder-Narasimhan--eshadri filtration of the initial twisted Higgs bundle.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

A new higher order Yang--Mills--Higgs flow in Riemannian $4$-manifold

Let $(M,g)$ be a closed Riemannian $4$-manifold and let $E$ be a vector bundle over $M$ with structure group $G$, where $G$ is a compact Lie group. In this paper, we consider a new higher order Yang--Mills--Higgs functional, in which the Higgs field is a section of $Ω^0(\textmd{ad}E)$. We show that, under suitable conditions, solutions to the gradient flow do not hit any finite time singularities. In the case that $E$ is a line bundle, we are able to use a different blow up procedure and obtain an improvement of the long time result in \cite{Z1}. The proof is rather relevant to the properties of the Green function, which is very different from the previous techniques in \cite{Ke,Sa,Z1}.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Origin of performance degradation in high-delithiation Li$_x$CoO$_2$: insights from direct atomic simulations using global neural network potentials

Li$_x$CoO$_2$ based batteries have serious capacity degradation and safety issues when cycling at high-delithiation states but full and consistent mechanisms are still poorly understood. Herein, a global neural network potential (GNNP) is developed to provide direct theoretical understandings by performing long-time and large-size atomic simulations. We propose a self-consistent picture as follows: (i) CoO$_2$ layers are easier to glide with longer distances at more highly delithiated states, resulting in structural transitions and structural inhomogeneity; (ii) at regions between different phases with different Li distributions due to gliding, local strains are induced and accumulate during cycling processes; (3) accumulated strains cause the rupture of Li diffusion channels and result in formation of oxygen dimers during cycling especially when Li has inhomogeneous distributions, leading to capacity degradations and safety issues. We find that large tensile strains combined with inhomogeneous distributions of Li ions play critical roles in the formation processes of blocked Li diffusion channels and the oxygen dimers at high-delithiation states, which could be the fundamental origins of capacity degradations and safety issues. Correspondingly, suppressing accumulations of strains by controlling charge and discharge conditions as well as suppressing the gliding will be helpful for improving the performance of lithium-ion batteries (LIBs).

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Real-Time Neural Character Rendering with Pose-Guided Multiplane Images

We propose pose-guided multiplane image (MPI) synthesis which can render an animatable character in real scenes with photorealistic quality. We use a portable camera rig to capture the multi-view images along with the driving signal for the moving subject. Our method generalizes the image-to-image translation paradigm, which translates the human pose to a 3D scene representation -- MPIs that can be rendered in free viewpoints, using the multi-views captures as supervision. To fully cultivate the potential of MPI, we propose depth-adaptive MPI which can be learned using variable exposure images while being robust to inaccurate camera registration. Our method demonstrates advantageous novel-view synthesis quality over the state-of-the-art approaches for characters with challenging motions. Moreover, the proposed method is generalizable to novel combinations of training poses and can be explicitly controlled. Our method achieves such expressive and animatable character rendering all in real time, serving as a promising solution for practical applications.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Semi-Supervised Image-to-Image Translation using Latent Space Mapping

Recent image-to-image translation works have been transferred from supervised to unsupervised settings due to the expensive cost of capturing or labeling large amounts of paired data. However, current unsupervised methods using the cycle-consistency constraint may not find the desired mapping, especially for difficult translation tasks. On the other hand, a small number of paired data are usually accessible. We therefore introduce a general framework for semi-supervised image translation. Unlike previous works, our main idea is to learn the translation over the latent feature space instead of the image space. Thanks to the low dimensional feature space, it is easier to find the desired mapping function, resulting in improved quality of translation results as well as the stability of the translation model. Empirically we show that using feature translation generates better results, even using a few bits of paired data. Experimental comparisons with state-of-the-art approaches demonstrate the effectiveness of the proposed framework on a variety of challenging image-to-image translation tasks

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Solving the sampling problem of the Sycamore quantum circuits

We study the problem of generating independent samples from the output distribution of Google's Sycamore quantum circuits with a target fidelity, which is believed to be beyond the reach of classical supercomputers and has been used to demonstrate quantum supremacy. We propose a new method to classically solve this problem by contracting the corresponding tensor network just once, and is massively more efficient than existing methods in obtaining a large number of uncorrelated samples with a target fidelity. For the Sycamore quantum supremacy circuit with $53$ qubits and $20$ cycles, we have generated one million uncorrelated bitstrings $\{\mathbf s\}$ which are sampled from a distribution $\hat P(\mathbf s)=|\hat ψ(\mathbf s)|^2$, where the approximate state $\hat ψ$ has fidelity $F\approx 0.0037$. The whole computation has cost about $15$ hours on a computational cluster with $512$ GPUs. The obtained one million samples, the contraction code and contraction order is made public. If our algorithm could be implemented with high efficiency on a modern supercomputer with ExaFLOPS performance, we estimate that ideally, the simulation would cost a few dozens of seconds, which is faster than Google's quantum hardware.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Prototypical Pseudo Label Denoising and Target Structure Learning for Domain Adaptive Semantic Segmentation

Self-training is a competitive approach in domain adaptive segmentation, which trains the network with the pseudo labels on the target domain. However inevitably, the pseudo labels are noisy and the target features are dispersed due to the discrepancy between source and target domains. In this paper, we rely on representative prototypes, the feature centroids of classes, to address the two issues for unsupervised domain adaptation. In particular, we take one step further and exploit the feature distances from prototypes that provide richer information than mere prototypes. Specifically, we use it to estimate the likelihood of pseudo labels to facilitate online correction in the course of training. Meanwhile, we align the prototypical assignments based on relative feature distances for two different views of the same target, producing a more compact target feature space. Moreover, we find that distilling the already learned knowledge to a self-supervised pretrained model further boosts the performance. Our method shows tremendous performance advantage over state-of-the-art methods. We will make the code publicly available.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Simulating the Sycamore quantum supremacy circuits

We propose a general tensor network method for simulating quantum circuits. The method is massively more efficient in computing a large number of correlated bitstring amplitudes and probabilities than existing methods. As an application, we study the sampling problem of Google's Sycamore circuits, which are believed to be beyond the reach of classical supercomputers and have been used to demonstrate quantum supremacy. Using our method, employing a small computational cluster containing 60 graphical processing units (GPUs), we have generated one million correlated bitstrings with some entries fixed, from the Sycamore circuit with 53 qubits and 20 cycles, with linear cross-entropy benchmark (XEB) fidelity equals 0.739, which is much higher than those in Google's quantum supremacy experiments.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Tropical Tensor Network for Ground States of Spin Glasses

We present a unified exact tensor network approach to compute the ground state energy, identify the optimal configuration, and count the number of solutions for spin glasses. The method is based on tensor networks with the Tropical Algebra defined on the semiring. Contracting the tropical tensor network gives the ground state energy; differentiating through the tensor network contraction gives the ground state configuration; mixing the tropical algebra and the ordinary algebra counts the ground state degeneracy. The approach brings together the concepts from graphical models, tensor networks, differentiable programming, and quantum circuit simulation, and easily utilizes the computational power of graphical processing units (GPUs). For applications, we compute the exact ground state energy of Ising spin glasses on square lattice up to 1024 spins, on cubic lattice up to 216 spins, and on 3 regular random graphs up to 220 spins, on a single GPU; We obtain exact ground state energy of (+/-)J Ising spin glass on the chimera graph of D-Wave quantum annealer of 512 qubits in less than 100 seconds and investigate the exact value of the residual entropy of (+/-)J spin glasses on the chimera graph; Finally, we investigate ground-state energy and entropy of 3-state Potts glasses on square lattices up to size 18 x 18. Our approach provides baselines and benchmarks for exact algorithms for spin glasses and combinatorial optimization problems, and for evaluating heuristic algorithms and mean-field theories.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Bringing Old Photos Back to Life

We propose to restore old photos that suffer from severe degradation through a deep learning approach. Unlike conventional restoration tasks that can be solved through supervised learning, the degradation in real photos is complex and the domain gap between synthetic images and real old photos makes the network fail to generalize. Therefore, we propose a novel triplet domain translation network by leveraging real photos along with massive synthetic image pairs. Specifically, we train two variational autoencoders (VAEs) to respectively transform old photos and clean photos into two latent spaces. And the translation between these two latent spaces is learned with synthetic paired data. This translation generalizes well to real photos because the domain gap is closed in the compact latent space. Besides, to address multiple degradations mixed in one old photo, we design a global branch with a partial nonlocal block targeting to the structured defects, such as scratches and dust spots, and a local branch targeting to the unstructured defects, such as noises and blurriness. Two branches are fused in the latent space, leading to improved capability to restore old photos from multiple defects. The proposed method outperforms state-of-the-art methods in terms of visual quality for old photos restoration.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Contact Area Detector using Cross View Projection Consistency for COVID-19 Projects

The ability to determine what parts of objects and surfaces people touch as they go about their daily lives would be useful in understanding how the COVID-19 virus spreads. To determine whether a person has touched an object or surface using visual data, images, or videos, is a hard problem. Computer vision 3D reconstruction approaches project objects and the human body from the 2D image domain to 3D and perform 3D space intersection directly. However, this solution would not meet the accuracy requirement in applications due to projection error. Another standard approach is to train a neural network to infer touch actions from the collected visual data. This strategy would require significant amounts of training data to generalize over scale and viewpoint variations. A different approach to this problem is to identify whether a person has touched a defined object. In this work, we show that the solution to this problem can be straightforward. Specifically, we show that the contact between an object and a static surface can be identified by projecting the object onto the static surface through two different viewpoints and analyzing their 2D intersection. The object contacts the surface when the projected points are close to each other; we call this cross view projection consistency. Instead of doing 3D scene reconstruction or transfer learning from deep networks, a mapping from the surface in the two camera views to the surface space is the only requirement. For planar space, this mapping is the Homography transformation. This simple method can be easily adapted to real-life applications. In this paper, we apply our method to do office occupancy detection for studying the COVID-19 transmission pattern from an office desk in a meeting room using the contact information.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Contracting Arbitrary Tensor Networks: General Approximate Algorithm and Applications in Graphical Models and Quantum Circuit Simulations

We present a general method for approximately contracting tensor networks with an arbitrary connectivity. This enables us to release the computational power of tensor networks to wide use in inference and learning problems defined on general graphs. We show applications of our algorithm in graphical models, specifically on estimating free energy of spin glasses defined on various of graphs, where our method largely outperforms existing algorithms including the mean-field methods and the recently proposed neural-network-based methods. We further apply our method to the simulation of random quantum circuits, and demonstrate that, with a trade off of negligible truncation errors, our method is able to simulate large quantum circuits that are out of reach of the state-of-the-art simulation methods.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Cross-domain Correspondence Learning for Exemplar-based Image Translation

We present a general framework for exemplar-based image translation, which synthesizes a photo-realistic image from the input in a distinct domain (e.g., semantic segmentation mask, or edge map, or pose keypoints), given an exemplar image. The output has the style (e.g., color, texture) in consistency with the semantically corresponding objects in the exemplar. We propose to jointly learn the crossdomain correspondence and the image translation, where both tasks facilitate each other and thus can be learned with weak supervision. The images from distinct domains are first aligned to an intermediate domain where dense correspondence is established. Then, the network synthesizes images based on the appearance of semantically corresponding patches in the exemplar. We demonstrate the effectiveness of our approach in several image translation tasks. Our method is superior to state-of-the-art methods in terms of image quality significantly, with the image style faithful to the exemplar with semantic consistency. Moreover, we show the utility of our method for several applications

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Gradient Flows of Higher Order Yang-Mills-Higgs Functionals

In this paper, we define a family of functionals generalizing the Yang-Mills-Higgs functional on a closed Riemannian manifold. Then we prove the short time existence of the corresponding gradient flow by a gauge fixing technique. The lack of maximal principle for the higher order operator brings us a lot of inconvenience during the estimates for the Higgs field. We observe that the $L^2$-bound of the Higgs field is enough for energy estimates in $4$ dimension, and we show that, provided the order of derivatives, appearing in the higher order Yang-Mills-Higgs functionals, is strictly greater than 1, solutions to the gradient flow do not hit any finite time singularities. As for the Yang-Mills-Higgs $k$-functional with Higgs self-interaction, we show that, provided $\dim(M)<2(k+1)$, the associated gradient flow admits long time existence with smooth initial data. The proof depends on local $L^2$-derivative estimates, energy estimates and blow-up analysis.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Helium Incorporation Stabilized Direct-gap Silicides

The search of direct-gap Si-based semiconductors is of great interest due to the potential application in many technologically relevant fields. This work examines the incorporation of He as a possible route to form a direct band gap in Si. Structure predictions and first-principles calculations have shown that He reacts with Si at high pressure, to form the stable compounds Si2He and Si3He. Both compounds have host-guest structures consisting of a channel-like Si host framework filled with He guest atoms. The Si frameworks in two compounds could be persisted to ambient pressure after removal of He, forming two pure Si allotropes. Both Si-He compounds and both Si allotropes exhibit direct or quasi-direct band gaps of 0.84-1.34 eV, close to the optimal value (~1.3 eV) for solar cell applications. Analysis shows that Si2He with an electric-dipole-transition allowed band gap possesses higher absorption capacity than diamond cubic Si, which makes it to be a promising candidate material for thin-film solar cell.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Old Photo Restoration via Deep Latent Space Translation

We propose to restore old photos that suffer from severe degradation through a deep learning approach. Unlike conventional restoration tasks that can be solved through supervised learning, the degradation in real photos is complex and the domain gap between synthetic images and real old photos makes the network fail to generalize. Therefore, we propose a novel triplet domain translation network by leveraging real photos along with massive synthetic image pairs. Specifically, we train two variational autoencoders (VAEs) to respectively transform old photos and clean photos into two latent spaces. And the translation between these two latent spaces is learned with synthetic paired data. This translation generalizes well to real photos because the domain gap is closed in the compact latent space. Besides, to address multiple degradations mixed in one old photo, we design a global branch with apartial nonlocal block targeting to the structured defects, such as scratches and dust spots, and a local branch targeting to the unstructured defects, such as noises and blurriness. Two branches are fused in the latent space, leading to improved capability to restore old photos from multiple defects. Furthermore, we apply another face refinement network to recover fine details of faces in the old photos, thus ultimately generating photos with enhanced perceptual quality. With comprehensive experiments, the proposed pipeline demonstrates superior performance over state-of-the-art methods as well as existing commercial tools in terms of visual quality for old photos restoration.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Solving Statistical Mechanics on Sparse Graphs with Feedback Set Variational Autoregressive Networks

We propose a method for solving statistical mechanics problems defined on sparse graphs. It extracts a small Feedback Vertex Set (FVS) from the sparse graph, converting the sparse system to a much smaller system with many-body and dense interactions with an effective energy on every configuration of the FVS, then learns a variational distribution parameterized using neural networks to approximate the original Boltzmann distribution. The method is able to estimate free energy, compute observables, and generate unbiased samples via direct sampling without auto-correlation. Extensive experiments show that our approach is more accurate than existing approaches for sparse spin glasses. On random graphs and real-world networks, our approach significantly outperforms the standard methods for sparse systems such as the belief-propagation algorithm; on structured sparse systems such as two-dimensional lattices our approach is significantly faster and more accurate than recently proposed variational autoregressive networks using convolution neural networks.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

Phase transitions and optimal algorithms for semi-supervised classifications on graphs: from belief propagation to graph convolution network

We perform theoretical and algorithmic studies for the problem of clustering and semi-supervised classification on graphs with both pairwise relational information and single-point feature information, upon a joint stochastic block model for generating synthetic graphs with both edges and node features. Asymptotically exact analysis based on the Bayesian inference of the underlying model are conducted, using the cavity method in statistical physics. Theoretically, we identify a phase transition of the generative model, which puts fundamental limits on the ability of all possible algorithms in the clustering task of the underlying model. Algorithmically, we propose a belief propagation algorithm that is asymptotically optimal on the generative model, and can be further extended to a belief propagation graph convolution neural network (BPGCN) for semi-supervised classification on graphs. For the first time, well-controlled benchmark datasets with asymptotially exact properties and optimal solutions could be produced for the evaluation of graph convolution neural networks, and for the theoretical understanding of their strengths and weaknesses. In particular, on these synthetic benchmark networks we observe that existing graph convolution neural networks are subject to an sparsity issue and an ovefitting issue in practice, both of which are successfully overcome by our BPGCN. Moreover, when combined with classic neural network methods, BPGCN yields extraordinary classification performances on some real-world datasets that have never been achieved before.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

Self-falsifiable Hierarchical Detection of Overlapping Communities On Social Networks

No community detection algorithm can be optimal for all possible networks, thus it is important to identify whether the algorithm is suitable for a given network. We propose a multi-step algorithmic solution scheme for overlapping community detection based on an advanced label propagation process, which imitates the community formation process on social networks. Our algorithm is parameter-free and is able to reveal the hierarchical order of communities in the graph. The unique property of our solution scheme is self-falsifiability; an automatic quality check of the results is conducted after the detection, and the fitness of the algorithm for the specific network is reported. Extensive experiments show that our algorithm is self-consistent, reliable on networks of a wide range of size and different sorts, and is more robust than existing algorithms on both sparse and large-scale social networks. Results further suggest that our solution scheme may uncover features of networks&#39; intrinsic community structures.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

Solving Quantum Statistical Mechanics with Variational Autoregressive Networks and Quantum Circuits

We extend the ability of unitary quantum circuits by interfacing it with classical autoregressive neural networks. The combined model parametrizes a variational density matrix as a classical mixture of quantum pure states, where the autoregressive network generates bitstring samples as input states to the quantum circuit. We devise an efficient variational algorithm to jointly optimize the classical neural network and the quantum circuit for quantum statistical mechanics problems. One can obtain thermal observables such as the variational free energy, entropy, and specific heat. As a by product, the algorithm also gives access to low energy excitation states. We demonstrate applications to thermal properties and excitation spectra of the quantum Ising model with resources that are feasible on near-term quantum computers.

0 citations0 reviewsNo code linkedOpen access