arXiv subjects

Cathy Li

Publications and source records attributed to Cathy Li.

11 recordsLinked to original sources

arXiv2026

Low Rank Structure of the Reduced Transition Matrix

The influence-matrix formalism provides an alternative route to the classical simulation of quantum dynamics. Because influence matrices retain information only about the effective bath seen by local observables, they are expected to be easier to simulate than the full wavefunction. Recent work, however, has shown that they carry strong temporal correlations even in maximally chaotic systems, making them difficult to represent efficiently. Here we show that the reduced transition matrix, a suitable combination of influence matrices that directly determines local expectation values, can nevertheless be efficiently approximated. We first show that the truncation error is controlled by its singular-value spectrum, which naturally motivates a low-rank approximation. We then prove that, for chaotic dual-unitary circuits, the associated entropy grows at most logarithmically in time. Our conclusions follow from exact results for random dual-unitary circuits and are further supported by numerical results for fixed instances of both dual-unitary and random circuits.

quant-ph↗

arXiv2026

State-dependent geometries from magic-enriched quantum codes

Quantum error-correcting codes provide a powerful framework for emergent spacetime, yet existing holographic code models describe only quantum fields on a fixed background: in subsystem erasure-correcting codes, the entropic area term is state independent and cannot capture gravitational backreaction. We argue that this limitation is intrinsic to exact subsystem complementary recovery and that incorporating backreaction instead requires approximate quantum error correction. We introduce a Ryu-Takayanagi-like entropy decomposition for approximate subsystem erasure-correcting codes, defining bulk matter entropy via optimal recovery and a complementary proto-area entropy as the difference between boundary entropy and recoverable bulk entropy. For a broad class of skewed quantum codes obtained by small nonlocal perturbations of exact codes, the proto-area increases monotonically with bulk entropy, closely aligning with the behavior of quantum extremal surfaces. We identify the origin of this response as a form of tripartite non-local magic in the Choi state of the encoding map, which vanishes in stabilizer codes and controls the leading matter-geometry coupling in approximate subsystem erasure-correcting codes.

hep-th↗

arXiv2025

Isaac Lab: A GPU-Accelerated Simulation Framework for Multi-Modal Robot Learning

We present Isaac Lab, the natural successor to Isaac Gym, which extends the paradigm of GPU-native robotics simulation into the era of large-scale multi-modal learning. Isaac Lab combines high-fidelity GPU parallel physics, photorealistic rendering, and a modular, composable architecture for designing environments and training robot policies. Beyond physics and rendering, the framework integrates actuator models, multi-frequency sensor simulation, data collection pipelines, and domain randomization tools, unifying best practices for reinforcement and imitation learning at scale within a single extensible platform. We highlight its application to a diverse set of challenges, including whole-body control, cross-embodiment mobility, contact-rich and dexterous manipulation, and the integration of human demonstrations for skill acquisition. Finally, we discuss upcoming integration with the differentiable, GPU-accelerated Newton physics engine, which promises new opportunities for scalable, data-efficient, and gradient-based approaches to robot learning. We believe Isaac Lab's combination of advanced simulation capabilities, rich sensing, and data-center scale execution will help unlock the next generation of breakthroughs in robotics research.

cs.RO↗

arXiv2024

Two-stage relaxation of operators through domain wall and magnon dynamics

The out-of-time ordered correlator (OTOC) has become a popular probe for quantum information spreading and thermalization. In systems with local interactions, the OTOC defines a characteristic butterfly lightcone that separates a regime not yet disturbed by chaos from one where time-evolved operators and the OTOC approach their equilibrium value. This relaxation has been shown to proceed in two stages, with the first stage exhibiting an extensive timescale and a decay rate slower than the gap of the transfer matrix -- known as the ``phantom eigenvalue". In this work, we investigate the two-stage relaxation of the OTOC towards its equilibrium value in various local quantum circuits. We apply a systematic framework based on an emergent statistical model, where the dynamics of two single-particle modes -- a domain wall and a magnon -- govern the decay rates. Specifically, a configuration with coexisting domain wall and magnon modes generates the phantom rate in the first stage, and competition between these modes determines the second stage. We also examine this relaxation within the operator cluster picture. The magnon modes translates into a bound state of clusters and domain wall into a random operator, giving consistent rates. Finally, we extend our findings from random in time circuits to a broad class of Floquet models.

quant-ph↗

arXiv2024

The cool and the cruel: separating hard parts of LWE secrets

Sparse binary LWE secrets are under consideration for standardization for Homomorphic Encryption and its applications to private computation. Known attacks on sparse binary LWE secrets include the sparse dual attack and the hybrid sparse dual-meet in the middle attack which requires significant memory. In this paper, we provide a new statistical attack with low memory requirement. The attack relies on some initial lattice reduction. The key observation is that, after lattice reduction is applied to the rows of a q-ary-like embedded random matrix $\mathbf A$, the entries with high variance are concentrated in the early columns of the extracted matrix. This allows us to separate out the "hard part" of the LWE secret. We can first solve the sub-problem of finding the "cruel" bits of the secret in the early columns, and then find the remaining "cool" bits in linear time. We use statistical techniques to distinguish distributions to identify both the cruel and the cool bits of the secret. We provide concrete attack timings for recovering secrets in dimensions $n=256$, $512$, and $768$. For the lattice reduction stage, we leverage recent improvements in lattice reduction (e.g. flatter) applied in parallel. We also apply our new attack in the RLWE setting for $2$-power cyclotomic rings, showing that these RLWE instances are much more vulnerable to this attack than LWE.

cs.CR↗

arXiv2024

Salsa Fresca: Angular Embeddings and Pre-Training for ML Attacks on Learning With Errors

Learning with Errors (LWE) is a hard math problem underlying recently standardized post-quantum cryptography (PQC) systems for key exchange and digital signatures. Prior work proposed new machine learning (ML)-based attacks on LWE problems with small, sparse secrets, but these attacks require millions of LWE samples to train on and take days to recover secrets. We propose three key methods -- better preprocessing, angular embeddings and model pre-training -- to improve these attacks, speeding up preprocessing by $25\times$ and improving model sample efficiency by $10\times$. We demonstrate for the first time that pre-training improves and reduces the cost of ML attacks on LWE. Our architecture improvements enable scaling to larger-dimension LWE problems: this work is the first instance of ML attacks recovering sparse binary secrets in dimension $n=1024$, the smallest dimension used in practice for homomorphic encryption applications of LWE where sparse binary secrets are proposed.

cs.CR↗

arXiv2023

SALSA PICANTE: a machine learning attack on LWE with binary secrets

Learning with Errors (LWE) is a hard math problem underpinning many proposed post-quantum cryptographic (PQC) systems. The only PQC Key Exchange Mechanism (KEM) standardized by NIST is based on module~LWE, and current publicly available PQ Homomorphic Encryption (HE) libraries are based on ring LWE. The security of LWE-based PQ cryptosystems is critical, but certain implementation choices could weaken them. One such choice is sparse binary secrets, desirable for PQ HE schemes for efficiency reasons. Prior work, SALSA, demonstrated a machine learning-based attack on LWE with sparse binary secrets in small dimensions ($n \le 128$) and low Hamming weights ($h \le 4$). However, this attack assumes access to millions of eavesdropped LWE samples and fails at higher Hamming weights or dimensions. We present PICANTE, an enhanced machine learning attack on LWE with sparse binary secrets, which recovers secrets in much larger dimensions (up to $n=350$) and with larger Hamming weights (roughly $n/10$, and up to $h=60$ for $n=350$). We achieve this dramatic improvement via a novel preprocessing step, which allows us to generate training data from a linear number of eavesdropped LWE samples ($4n$) and changes the distribution of the data to improve transformer training. We also improve the secret recovery methods of SALSA and introduce a novel cross-attention recovery mechanism allowing us to read off the secret directly from the trained models. While PICANTE does not threaten NIST's proposed LWE standards, it demonstrates significant improvement over SALSA and could scale further, highlighting the need for future investigation into machine learning attacks on LWE with sparse binary secrets.

cs.CR↗

arXiv2023

An efficient algorithm for integer lattice reduction

A lattice of integers is the collection of all linear combinations of a set of vectors for which all entries of the vectors are integers and all coefficients in the linear combinations are also integers. Lattice reduction refers to the problem of finding a set of vectors in a given lattice such that the collection of all integer linear combinations of this subset is still the entire original lattice and so that the Euclidean norms of the subset are reduced. The present paper proposes simple, efficient iterations for lattice reduction which are guaranteed to reduce the Euclidean norms of the basis vectors (the vectors in the subset) monotonically during every iteration. Each iteration selects the basis vector for which projecting off (with integer coefficients) the components of the other basis vectors along the selected vector minimizes the Euclidean norms of the reduced basis vectors. Each iteration projects off the components along the selected basis vector and efficiently updates all information required for the next iteration to select its best basis vector and perform the associated projections.

cs.CR↗

arXiv2023

Quantum Error Correction from Complexity in Brownian SYK

We study the robustness of quantum error correction in a one-parameter ensemble of codes generated by the Brownian SYK model, where the parameter quantifies the encoding complexity. The robustness of error correction by a quantum code is upper bounded by the "mutual purity" of a certain entangled state between the code subspace and environment in the isometric extension of the error channel, where the mutual purity of a density matrix $\rho_{AB}$ is the difference $\mathcal{F}_\rho (A:B) \equiv \mathrm{Tr}\;\rho_{AB}^2 - \mathrm{Tr}\;\rho_A^2\;\mathrm{Tr}\;\rho_B^2$. We show that when the encoding complexity is small, the mutual purity is $O(1)$ for the erasure of a small number of qubits (i.e., the encoding is fragile). However, this quantity decays exponentially, becoming $O(1/N)$ for $O(\log N)$ encoding complexity. Further, at polynomial encoding complexity, the mutual purity saturates to a plateau of $O(e^{-N})$. We also find a hierarchy of complexity scales associated to a tower of subleading contributions to the mutual purity that quantitatively, but not qualitatively, adjust our error correction bound as encoding complexity increases. In the AdS/CFT context, our results suggest that any portion of the entanglement wedge of a general boundary subregion $A$ with sufficiently high encoding complexity is robustly protected against low-rank errors acting on $A$ with no prior access to the encoding map. From the bulk point of view, we expect such bulk degrees of freedom to be causally inaccessible from the region $A$ despite being encoded in it.

hep-th↗

arXiv2022

Quantum Error Correction in the Black Hole Interior

We study the quantum error correction properties of the black hole interior in a toy model for an evaporating black hole: Jackiw-Teitelboim gravity entangled with a non-gravitational bath. After the Page time, the black hole interior degrees of freedom in this system are encoded in the bath Hilbert space. We use the gravitational path integral to show that the interior density matrix is correctable against the action of quantum operations on the bath which (i) do not have prior access to details of the black hole microstates, and (ii) do not have a large, negative coherent information with respect to the maximally mixed state on the bath, with the lower bound controlled by the black hole entropy and code subspace dimension. Thus, the encoding of the black hole interior in the radiation is robust against generic, low-rank quantum operations. For erasure errors, gravity comes within an $O(1)$ distance of saturating the Singleton bound on the tolerance of error correcting codes. For typical errors in the bath to corrupt the interior, they must have a rank that is a large multiple of the bath Hilbert space dimension, with the precise coefficient set by the black hole entropy and code subspace dimension.

hep-th↗

arXiv2021

Complexity Growth in Integrable and Chaotic Models

We use the SYK family of models with $N$ Majorana fermions to study the complexity of time evolution, formulated as the shortest geodesic length on the unitary group manifold between the identity and the time evolution operator, in free, integrable, and chaotic systems. Initially, the shortest geodesic follows the time evolution trajectory, and hence complexity grows linearly in time. We study how this linear growth is eventually truncated by the appearance and accumulation of conjugate points, which signal the presence of shorter geodesics intersecting the time evolution trajectory. By explicitly locating such "shortcuts" through analytical and numerical methods, we demonstrate that: (a) in the free theory, time evolution encounters conjugate points at a polynomial time; consequently complexity growth truncates at $O(\sqrt{N})$, and we find an explicit operator which "fast-forwards" the free $N$-fermion time evolution with this complexity, (b) in a class of interacting integrable theories, the complexity is upper bounded by $O({\rm poly}(N))$, and (c) in chaotic theories, we argue that conjugate points do not occur until exponential times $O(e^N)$, after which it becomes possible to find infinitesimally nearby geodesics which approximate the time evolution operator. Finally, we explore the notion of eigenstate complexity in free, integrable, and chaotic models.

hep-th↗