arXiv subjects

Haining Pan

Publications and source records attributed to Haining Pan.

At least 19 recordsLinked to original sources

arXiv2026

Avoiding Dilution: Using Diffusion and Vision Transformers to resolve Majorana Features in Nanowires at High Temperature

Identifying Majorana zero modes in semiconductor--superconductor nanowires requires ultra-low temperature transport measurements in dilution refrigerators, making device screening slow and resource-intensive. Here, we investigate whether high-temperature conductance data can be used to infer low-temperature Majorana nanowire properties before committing devices to dilution-refrigerator characterization. We generate paired high- and low-temperature conductance simulations for disordered Majorana nanowires and train neural networks to perform two related tasks. First, we use a Shifted Window U-Net Transformer diffusion-inspired architecture to reconstruct low-temperature conductance from thermally broadened high-temperature measurements, achieving high-fidelity recovery with $R^2 \approx {0.95}$ for local conductance and $R^2 \approx {0.91}$ for nonlocal conductance. Second, we train a Video Vision Transformer-based network to predict the low-temperature topological visibility directly from high-temperature conductance, obtaining $R^2 \approx {0.80}$. These results demonstrate that machine-learning models can recover and infer low-temperature Majorana features from experimentally easier high-temperature data, providing a practical route for rejecting poor devices early thus avoiding slow and resource-intensive dilution refrigeration for non-promising devices. This high-temperature screening approach could substantially accelerate the experimental feedback loop for Majorana nanowire device development.

cond-mat.mes-hall↗

arXiv2026

Representability-Aware Neural Networks for Reduced Density Matrices: Application to Fractional Chern Insulators

We develop a representability-aware and interpolable neural network (NN) framework for predicting two-particle reduced density matrices (2-RDMs). The NN incorporates a subset of representability conditions through its architecture and loss function, and can operate on different momentum meshes, enabling evaluating the representability conditions across multiple meshes, which we call interpolated representability condition. The framework can be used either to predict 2-RDMs on large momentum meshes by interpolating exact results from small meshes, or as a variational 2-RDM ansatz optimized by energy minimization on arbitrary meshes. We apply this approach to the fractional Chern insulator in the one-band projected model of twisted bilayer MoTe$_2$ at twist angle $3.89^\circ$ and hole filling $2/3$. Trained on exact-diagonalization (ED) 2-RDMs from meshes with $12$ or $18$ momentum points using six different NN architectures, the best NN is the residual multilayer perceptron, which predicts the $6\times6$ 2-RDM with $97.07\%-98.18\%$ accuracy relative to the ED 2-RDM but predicts an energy $77.353$ meV above ED ground-state energy. We then variationally optimize the NN on several meshes including $6\times6$, predicting a $6\times 6$ energy of just $0.104$ meV below ED while maintaining $98.94\%-98.96\%$ accuracy. Compared with the conventional boundary-point semidefinite programming, which gives an energy $5.560$ meV below ED with $96.40\%-98.94\%$ accuracy, the NN achieves a more accurate energy and similar accuracy while using only less than 1/20 as many parameters. Eventually, we add a symmetric mesh of $48$ momentum points to the variational optimization of the NN, and provide a prediction of the many-body ground-state energy and the many-body quantum metric on that mesh.

cond-mat.str-el↗

arXiv2026

Pruning-induced phases in fully-connected neural networks: the eumentia, the dementia, and the amentia

Modern neural networks are heavily overparameterized, and pruning, which removes redundant neurons or connections, has emerged as a key approach to compressing them without sacrificing performance. However, while practical pruning methods are well developed, whether pruning induces sharp phase transitions in the neural networks and, if so, to what universality class they belong, remain open questions. To address this, we study fully-connected neural networks trained on MNIST, independently varying the dropout (i.e., removing neurons) rate at both the training and evaluation stages to map the phase diagram. We identify three distinct phases: eumentia (the network learns), dementia (the network has forgotten), and amentia (the network cannot learn), sharply distinguished by the power-law scaling of the cross-entropy loss with the training dataset size. {In the eumentia phase, the algebraic decay of the loss, as documented in the machine learning literature as neural scaling laws, is from the perspective of statistical mechanics the hallmark of quasi-long-range order.} We demonstrate that the transition between the eumentia and dementia phases is accompanied by scale invariance, with a diverging length scale that exhibits hallmarks of a Berezinskii-Kosterlitz-Thouless-like transition; the phase structure is robust across different network widths and depths. Our results establish that dropout-induced pruning provides a concrete setting in which neural network behavior can be understood through the lens of statistical mechanics.

cond-mat.dis-nn↗

arXiv2025

Unreasonable effectiveness of unsupervised learning in identifying Majorana topology

In unsupervised learning, the training data for deep learning does not come with any labels, thus forcing the algorithm to discover hidden patterns in the data for discerning useful information. This, in principle, could be a powerful tool in identifying topological order since topology does not always manifest in obvious physical ways (e.g., topological superconductivity) for its decisive confirmation. The problem, however, is that unsupervised learning is a difficult challenge, necessitating huge computing resources, which may not always work. In the current work, we combine unsupervised and supervised learning using an autoencoder to establish that unlabeled data in the Majorana splitting in realistic short disordered nanowires may enable not only a distinction between `topological' and `trivial', but also where their crossover happens in the relevant parameter space. This may be a useful tool in identifying topology in Majorana nanowires.

cond-mat.dis-nn↗

arXiv2025

Ballistic transport in 1D Rashba systems in the context of Majorana nanowires

Recent work on Majorana-bound states in semiconductor-superconductor hybrid structures has elucidated the key role of unintentional (and unknown) disorder (producing low-energy Andreev-bound states) in the system, which is detrimental to the emergence of Majorana-carrying topological superconductivity artificially engineered through the combination of superconductivity, Zeeman spin splitting, and Rashba spin-orbit coupling. In particular, the disorder must be smaller than the superconducting gap for the appearance of Majorana modes, but the disorder-induced appearance of subgap Andreev-bound states suppresses the Majorana modes. We theoretically investigate, as a function of disorder, the normal state ballistic transport properties of nanowires with and without superconductors in order to provide guidance on how to experimentally estimate the level of disorder. Experimentally, the superconductivity is suppressed simply by rotating the magnetic field appropriately, so both physics can be studied in the same set-up. In particular, the presence of spin-orbit coupling and Zeeman splitting produces a helical gap in the 1D electronic band structure, which should have clear signatures in ballistic transport unless these signatures are suppressed by disorder and/or Fabry-P\'erot resonances associated with the finite wire sizes. Our work provides a benchmarking of when and what signatures of the putative helical gap (which is essential for the emergence of Majorana modes by leading to a single Fermi surface) could manifest in realistic nanowires.

cond-mat.mes-hall↗

arXiv2025

CMT-Benchmark: A Benchmark for Condensed Matter Theory Built by Expert Researchers

Large language models (LLMs) have shown remarkable progress in coding and math problem-solving, but evaluation on advanced research-level problems in hard sciences remains scarce. To fill this gap, we present CMT-Benchmark, a dataset of 50 problems covering condensed matter theory (CMT) at the level of an expert researcher. Topics span analytical and computational approaches in quantum many-body, and classical statistical mechanics. The dataset was designed and verified by a panel of expert researchers from around the world. We built the dataset through a collaborative environment that challenges the panel to write and refine problems they would want a research assistant to solve, including Hartree-Fock, exact diagonalization, quantum/variational Monte Carlo, density matrix renormalization group (DMRG), quantum/classical statistical mechanics, and model building. We evaluate LLMs by programmatically checking solutions against expert-supplied ground truth. We developed machine-grading, including symbolic handling of non-commuting operators via normal ordering. They generalize across tasks too. Our evaluations show that frontier models struggle with all of the problems in the dataset, highlighting a gap in the physical reasoning skills of current LLMs. Notably, experts identified strategies for creating increasingly difficult problems by interacting with the LLMs and exploiting common failure modes. The best model, GPT5, solves 30\% of the problems; average across 17 models (GPT, Gemini, Claude, DeepSeek, Llama) is 11.4\pm2.1\%. Moreover, 18 problems are solved by none of the 17 models, and 26 by at most one. These unsolved problems span Quantum Monte Carlo, Variational Monte Carlo, and DMRG. Answers sometimes violate fundamental symmetries or have unphysical scaling dimensions. We believe this benchmark will guide development toward capable AI research assistants and tutors.

cs.LG↗

arXiv2025

Order from chaos with adaptive circuits on quantum hardware

Programmable quantum devices provide a platform to control the coherent dynamics of quantum wavefunctions. Here we experimentally realize adaptive monitored quantum circuits, which incorporate conditional feedback into non-unitary evolution, to control quantum chaotic dynamics using a combination of local mid-circuit measurements and resets. The experiments are performed with an IBM superconducting quantum processor using up to 100 qubits that samples a quantum version of the classically chaotic Bernoulli map. This map scrambles quantum information, while local measurements and feedback attempt to steer the dynamics toward a state that is a fixed point of the map. This competition drives a dynamical phase transition between quantum and classical dynamics that we observe experimentally and describe theoretically using noisy simulations, matrix product states, and mappings to statistical mechanics models. Estimates of the universal critical properties are obtained to high accuracy on the quantum computer thanks to the large number of qubits utilized in the calculation. By successfully applying up to nearly 5000 entangling gates and 5000 non-unitary mid-circuit operations on systems up to 100 qubits, this experiment serves as a signpost on the route towards fault tolerance.

quant-ph↗

arXiv2025

Classical Simulations of Low Magic Quantum Dynamics

We develop classical simulation algorithms for adaptive quantum circuits that produce states with low levels of ``magic'' (i.e., non-stabilizerness). These algorithms are particularly well-suited to circuits with high rates of Pauli measurements, such as those encountered in quantum error correction and monitored quantum circuits. The measurements serve to limit the buildup of magic induced by non-Clifford operations arising from generic noise processes or unitary gates, respectively. Our algorithms also allow a systematic truncation procedure to achieve approximate simulation. To benchmark our approach, we study the dynamics of all-to-all monitored quantum circuits with a sub-extensive rate of T-gates per unit of circuit depth, where we can simulate previously inaccessible system sizes and depths. We characterize measurement-induced phase transitions in the output wavefunction, including in the entanglement, purification, and magic. We outline the utility of our algorithms to simulate dynamics with low magic and high entanglement, complementary to the leading matrix-product state approaches.

quant-ph↗

arXiv2025

Free-Fermion Dynamics with Measurements: Topological Classification and Adaptive Preparation of Topological States

We develop a general framework for classifying fermionic dynamical systems with measurements using symmetry and topology. We introduce two complementary classification schemes based on the Altland-Zirnbauer tenfold way: (1) the many-body evolution operator (mEO) symmetry class, which classifies fermionic dynamics at the many-body level and naturally extends to interacting dynamics, and (2) the single-particle transfer matrix (sTM) symmetry class, which classifies free-fermion dynamics at the single-particle level and connects to Anderson localization physics. In the free-fermion limit, we show that these two frameworks are equivalent via a novel dynamical bulk-boundary correspondence: the topology of the dynamical system's spacetime bulk determines the topology of the area-law entangled steady-state ensemble living on its temporal boundary. Next, we prove that symmetry-invariant, post-selection-free Gaussian measurements are realizable in only four of the ten mEO classes (A, AI, BDI, D); the remaining six require either post-selection or interacting (non-Gaussian) measurements. Building on these results, we construct general post-selection-free topological adaptive circuits that realize topological dynamical phases in any spatial dimension for the four admissible mEO classes. These circuits simultaneously provide a protocol for preparing and stabilizing free-fermion topological states in all ten symmetry classes. As a concrete demonstration, we construct and simulate 2+1d adaptive circuits that realize mEO-class-A topological dynamics, steering toward a steady-state ensemble of Chern insulators in ${\cal O}(1)$ circuit depth. Finally, we numerically characterize topological phase transitions, dynamical domain-wall modes, and robustness to coherent noise, identifying finite error thresholds at which trajectory-resolved and trajectory-averaged quantities undergo distinct phase transitions.

quant-ph↗

arXiv2025

Quantum criticality and tunable Griffiths phase in superconducting twisted trilayer graphene

When dimensionality is reduced, enhanced quantum fluctuations can destroy long-range phase coherence, driving a superconductor insulator transition, SIT, where disorder and electronic correlations give rise to novel many-body states. Here, we report the first observation of a magnetic field tuned SIT in mirrorsymmetric twisted trilayer graphene, TTG. Remarkably, signatures of quantum criticality persist over an exceptionally broad range of magnetic fields and are well described by the formation of a quantum Griffiths phase, a regime in which rare spatially extended regions develop local order within a globally disordered phase. This leads to a quantum phase transition governed by an infinite-randomness fixed point and characterized by ultraslow relaxation dynamics. Near the quantum critical region, transport measurements reveal strongly nonlinear electrical behavior, including a current-driven reentrant transition from insulating to superconducting transport, providing direct evidence of local superconducting order. By tilting the magnetic field, we are able to collapse the broad Griffiths regime into a single quantum critical point, QCP, demonstrating a striking level of control over disorder induced quantum dynamics. Our results further show that TTG strongly violates the Pauli limit and establishes twisted trilayer graphene as a tunable platform for exploring quantum phase fluctuations, Cooper pair localization, and unconventional superconductivity.

cond-mat.mes-hall↗

arXiv2025

Majorana zero modes in semiconductor-superconductor hybrid structures: Defining topology in short and disordered nanowires through Majorana splitting

Majorana zero modes (MZMs) are bound midgap topological excitations at the ends of a 1D topological superconductor, which must come in pairs. If the two MZMs in the pair are sufficiently well-separated by a distance much larger than their individual localization lengths, then the MZMs behave as non-Abelian anyons which can be braided to carry out fault-tolerant topological quantum computation. In this `topological' regime of well-separated MZMs, their overlap is exponentially small, leading to exponentially small Majorana splitting, thus enabling the MZMs to be topologically protected by the superconducting gap. In real experimental samples, however, the existence of disorder and the finite length of the 1D wire considerably complicate the situation, leading to ambiguities in defining `topology' since the Majorana splitting between the two end modes may not necessarily be small in disordered wires of short length. We theoretically study this situation by calculating the splitting in experimentally relevant short disordered wires, and explicitly investigating the applicability of the `exponential protection' constraint as a function of disorder, wire length, and other system parameters in realistic models of nanowires currently being used experimentally. We find that the exponential regime is highly constrained, and is suppressed for disorder somewhat less than the topological superconducting gap. We provide detailed results and discuss the implications of our theory for the currently active experimental search for MZMs in superconductor-semiconductor hybrid platforms. A general consequence of our work is that `topology' in finite disordered wires may not be uniquely defined, necessitating a careful analysis which depends on the context.

cond-mat.mes-hall↗

arXiv2025

Rashba spin-orbit coupling and artificially engineered topological superconductors

One of the most important physical effects in condensed matter physics is the Rashba spin-orbit coupling (RSOC), introduced in seminal works by Emmanuel Rashba. In this article, we discuss, describe, and review (providing critical perspectives on) the crucial role of RSOC in the currently active research area of topological quantum computation. Most, if not all, of the current experimental topological quantum computing platforms use the idea of Majorana zero modes as the qubit ingredient because of their non-Abelian anyonic property of having an intrinsic quantum degeneracy, which enables nonlocal encoding protected by a topological energy gap. It turns out that RSOC is a crucial ingredient in producing a low-dimensional topological superconductor in the laboratory, and such topological superconductors naturally have isolated localized midgap Majorana zero modes. In addition, increasing the RSOC strength enhances the topological gap, thus enhancing the topological immunity of the qubits to decoherence. Thus, Rashba's classic work on SOC may lead not only to the realization of localized non-Abelian anyons, but also fault tolerant quantum computation.

cond-mat.mes-hall↗

arXiv2025

Control-driven critical fluctuations across quantum trajectories

Monitored quantum circuits in which entangling unitary dynamics compete with projective local measurements can host measurement-induced phase transitions witnessed by entanglement measures at late times. Adding feedback conditioned on the measurement outcomes gives rise to another type of phase transition witnessed by local order parameters and correlation functions. These transitions, known as control or absorbing-state transitions, generically occur within the area-law entanglement phase and are thought to be governed by classical physics in that their critical exponents match those of the classical limit of the model. In this work, we examine quantum features of these transitions, focusing on a Bernoulli circuit model with a well-defined classical limit, in the presence of unitary dynamics, measurements, and feedback. First we demonstrate that, in the local basis defined by the absorbing state, the steady-state quantum coherence undergoes a phase transition at the control transition, where its logarithm changes discontinuously from volume- to area-law scaling. Second, we analyze the control transition from the perspective of fluctuations in observables, which carry two contributions: classical fluctuations over circuit realizations (present in the classical limit), and quantum fluctuations over trajectories and states (both absent in the classical limit). Both contributions can be estimated in experiments without post-selection. The circuit-to-circuit fluctuations, the dominant contribution, carry the critical behavior of the classical limit. However, the subleading quantum fluctuations that represent fluctuations between different quantum ``worlds'' also go critical at the control transition. These critical quantum fluctuations at the control transition also occur in other models, and we discuss how they can be measured experimentally without post-selection.

quant-ph↗

arXiv2025

CURIE: Evaluating LLMs On Multitask Scientific Long Context Understanding and Reasoning

Scientific problem-solving involves synthesizing information while applying expert knowledge. We introduce CURIE, a scientific long-Context Understanding,Reasoning and Information Extraction benchmark to measure the potential of Large Language Models (LLMs) in scientific problem-solving and assisting scientists in realistic workflows. This benchmark introduces ten challenging tasks with a total of 580 problems and solution pairs curated by experts in six disciplines - materials science, condensed matter physics, quantum computing, geospatial analysis, biodiversity, and proteins - covering both experimental and theoretical work-flows in science. We evaluate a range of closed and open LLMs on tasks in CURIE which requires domain expertise, comprehension of long in-context information,and multi-step reasoning. While Gemini Flash 2.0 and Claude-3 show consistent high comprehension across domains, the popular GPT-4o and command-R+ fail dramatically on protein sequencing tasks. With the best performance at 32% there is much room for improvement for all models. We hope that insights gained from CURIE can guide the future development of LLMs in sciences. Evaluation code and data are in https://github.com/google/curie

cs.CL↗

arXiv2024

Topological Modes in Monitored Quantum Dynamics

Dynamical quantum systems both driven by unitary evolutions and monitored through measurements have proved to be fertile ground for exploring new dynamical quantum matters. While the entanglement structure and symmetry properties of monitored systems have been intensively studied, the role of topology in monitored dynamics is much less explored. In this work, we investigate novel topological phenomena in the monitored dynamics through the lens of free-fermion systems. Free-fermion monitored dynamics were previously shown to be unified with the Anderson localization problem under the Altland-Zirnbauer symmetry classification. Guided by this unification, we identify the topological area-law-entangled phases in the former setting through the topological classification of disordered insulators and superconductors in the latter. As examples, we focus on 1+1D free-fermion monitored dynamics in two symmetry classes, DIII and A. We construct quantum circuit models to study different topological area-law phases and their domain walls in the respective symmetry classes. We find that the domain wall between topologically distinct area-law phases hosts dynamical topological modes whose entanglement is protected from being quenched by the measurements in the monitored dynamics. We demonstrate how to manipulate these topological modes by programming the domain-wall dynamics. In particular, for topological modes in class DIII, which behave as unmeasured Majorana modes, we devise a protocol to braid them and study the entanglement generated in the braiding process.

quant-ph↗

arXiv2024

Rabi and Ramsey oscillations of a Majorana qubit in a quantum dot-superconductor array

The Kitaev chain can be engineered within a quantum dot-superconductor array, hosting Majorana zero modes at fine-tuned sweet spots. In this work, we propose and simulate the occurrence of Rabi and Ramsey oscillations to feasibly construct a minimal Majorana qubit in the quantum dot setup. Our real-time results incorporate realistic effects, e.g., charge noise and leakage, reflecting the latest experimental progress. We demonstrate that Majorana qubits with larger energy gaps exhibit significantly enhanced performance -- longer dephasing times, higher quality factors, reduced leakage probabilities, and improved visibilities -- compared to those with smaller gaps and with conventional quantum dot-based charge qubits. We introduce a method for reading out Majorana qubits via quantum capacitance measurements. Our work paves the way for future experiments on realizing Majorana qubits in quantum dot-superconductor arrays.

cond-mat.mes-hall↗

arXiv2024

Local and nonlocal stochastic control of quantum chaos: Measurement- and control-induced criticality

We theoretically study the topology of the phase diagram of a family of quantum models inspired by the classical Bernoulli map under stochastic control. The quantum models inherit a control-induced phase transition from the classical model and also manifest an entanglement phase transition intrinsic to the quantum setting. This measurement-induced phase transition has been shown in various settings to either coincide or split off from the control transition, but a systematic understanding of the necessary and sufficient conditions for the two transitions to coincide in this case has so far been lacking. In this work, we generalize the control map to allow for either local or global control action. While this does not affect the classical aspects of the control transition that is described by a random walk, it significantly influences the quantum dynamics, leading to the universality class of the measurement-induced transition being dependent on the locality of the control operation. In the presence of a global control map, the two transitions coincide and the control-induced phase transition dominates the measurement-induced phase transition. Contrarily, the two transitions split in the presence of the local control map or additional projective measurements and generically take on distinct universality classes. For local control, the measurement-induced phase transition recovers the Haar logarithmic conformal field theory universality class found in feedback-free models. However, for global control, a novel universality class with correlation length exponent $\nu \approx 0.7$ emerges from the interplay of control and projective measurements. This work provides a more refined understanding of the relationship between the control- and measurement-induced phase transitions.

quant-ph↗

arXiv2024

Disordered Majorana nanowires: Studying disorder without any disorder

The interplay of disorder and short finite wire length is the crucial physics hindering progress in the semiconductor-superconductor nanowire platform for realizing non-Abelian Majorana zero modes (MZM). Disorder effectively segments the nanowire into isolated patches of quantum dots (QD) which act as subgap Andreev bound states often mimicking MZMs. In this work, we propose and develop a new theoretical approach to model disorder, effectively a spatially varying effective mass model, which does not rely on incorporating unknown microscopic details of disorder into the Hamiltonian. This model effectively segments the wire into multiple QDs, characterized by highly enhanced effective mass at impurity sites leading to the segmentation of the wire into effective random QDs. We find that this model can reproduce disorder physics, providing a crystal clear way to understand the effects of disorder by comparing the mean free path to the superconducting coherence length. In addition, this model allows precise control over the disorder regime, enabling us to evaluate the reliability of topological invariants (TI) in predicting MZMs. We find that TIs alone may yield a significant false positive rate as indicators for topology in the actual wire with increasing disorder strength. Therefore, we propose new indicators to characterize the spatial distribution of the zero-energy state, emphasizing the key necessity for isolated MZMs localized at wire ends. Employing this set of new indicators for stringent characterizations, we explore their experimental relevance to the measured differential conductance spectra. Our findings highlight the critical role of isolated localized states, beyond the TI, in identifying topological MZMs. We believe that this approach is a powerful tool for studying realistic Majorana nanowires where disorder and short wire length obfuscate the underlying topological physics.

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