arXiv subjects

Qingyue Wu

Publications and source records attributed to Qingyue Wu.

6 recordsLinked to original sources

arXiv2026

Presynthesis: Towards Scaling Up Program Synthesis with Finer-Grained Abstract Semantics

Abstract semantics has proven to be instrumental for accelerating search-based program synthesis, by enabling the sound pruning of a set of incorrect programs (without enumerating them). One may expect faster synthesis with increasingly finer-grained abstract semantics. Unfortunately, to the best of our knowledge, this is not the case, yet. The reason is because, as abstraction granularity increases -- while fewer programs are enumerated -- pruning becomes more costly. This imposes a fundamental limit on the overall synthesis performance, which we aim to address in this work. Our key idea is to introduce an offline presynthesis phase, which consists of two steps. Given a DSL with abstract semantics, the first semantics modeling step constructs a tree automaton A for a space of inputs -- such that, for any program P and for any considered input I, A has a run that corresponds to P's execution on I under abstract semantics. Then, the second step builds an oracle O for A. This O enables fast pruning during synthesis, by allowing us to efficiently find exactly those DSL programs that satisfy a given input-output example under abstract semantics. We have implemented this presynthesis-based synthesis paradigm in a framework, Foresighter. On top of it, we have developed three instantiations for SQL, string transformation, and matrix manipulation. All of them significantly outperform prior work in the respective domains.

cs.PL↗

arXiv2024

Spread complexity and the saturation of wormhole size

Recent proposals equate the size of Einstein-Rosen bridges in JT gravity to spread complexity of a dual, double-scaled SYK theory (DSSYK). We show that the auxiliary ``chord basis'' of these proposals is an extrapolation from a sub-exponential part of the finite-dimensional physical Krylov basis of a spreading thermofield double state. The physical tridiagonal Hamiltonian coincides with the DSSYK approximation on the initial Krylov basis, but deviates markedly over an exponentially large part of the state space. We non-perturbatively extend the identification of ER bridge size and spread complexity to the complete Hilbert space, and show that it saturates at late times. We use methods for tridiagonalizing random Hamiltonians to study all universality classes to which large N SYK theories and JT gravities can belong. The saturation dynamics depends on the universality class, and displays ``white hole'' physics at late times where the ER bridge shrinks from maximum size to a plateau. We describe extensions of our results to higher dimensions.

hep-th↗

arXiv2024

Two types of quantum chaos: testing the limits of the Bohigas-Giannoni-Schmit conjecture

There are two types of quantum chaos: eigenbasis chaos and spectral chaos. The first type controls the early-time physics, e.g. the thermal relaxation and the sensitivity of the system to initial conditions. It can be traced back to the Eigenstate Thermalization Hypothesis (ETH), a statistical hypothesis about the eigenvectors of the Hamiltonian. The second type concerns very late-time physics, e.g. the ramp of the Spectral Form Factor. It can be traced back to Random Matrix Universality (RMU), a statistical hypothesis about the eigenvalues of the Hamiltonian. The Bohigas-Giannoni-Schmit (BGS) conjecture asserts a direct relationship between the two types of chaos for quantum systems with a chaotic semiclassical limit. The BGS conjecture is challenged by the Poissonian Hamiltonian ensembles, which can be used to model any quantum system displaying RMU. In this paper, we start by analyzing further aspects of such ensembles. On general and numerical grounds, we argue that these ensembles can have chaotic semiclassical limits. We then study the Poissonian ensemble associated with the Sachdev-Ye-Kitaev (SYK) model. While the distribution of couplings peaks around the original SYK model, the Poissonian ensemble is not $k$-local. This suggests that the link between ETH and RMU requires of physical $k$-locality as an assumption. We test this hypothesis by modifying the couplings of the SYK Hamiltonian via the Metropolis algorithm, rewarding directions in the space of couplings that do not display RMU. The numerics converge to a $k$-local Hamiltonian with eigenbasis chaos but without spectral chaos. We finally comment on ways out and corollaries of our results.

quant-ph↗

arXiv2023

Quantum chaos, integrability, and late times in the Krylov basis

Quantum chaotic systems are conjectured to display a spectrum whose fine-grained features (gaps and correlations) are well described by Random Matrix Theory (RMT). We propose and develop a complementary version of this conjecture: quantum chaotic systems display a Lanczos spectrum whose local means and covariances are well described by RMT. To support this proposal, we first demonstrate its validity in examples of chaotic and integrable systems. We then show that for Haar-random initial states in RMTs the mean and covariance of the Lanczos spectrum suffices to produce the full long time behavior of general survival probabilities including the spectral form factor, as well as the spread complexity. In addition, for initial states with continuous overlap with energy eigenstates, we analytically find the long time averages of the probabilities of Krylov basis elements in terms of the mean Lanczos spectrum. This analysis suggests a notion of eigenstate complexity, the statistics of which differentiate integrable systems and classes of quantum chaos. Finally, we clarify the relation between spread complexity and the universality classes of RMT by exploring various values of the Dyson index and Poisson distributed spectra.

hep-th↗

arXiv2022

A Tale of Two Hungarians: Tridiagonalizing Random Matrices

The Hungarian physicist Eugene Wigner introduced random matrix models in physics to describe the energy spectra of atomic nuclei. As such, the main goal of Random Matrix Theory (RMT) has been to derive the eigenvalue statistics of matrices drawn from a given distribution. The Wigner approach gives powerful insights into the properties of complex, chaotic systems in thermal equilibrium. Another Hungarian, Cornelius Lanczos, suggested a method of reducing the dynamics of any quantum system to a one-dimensional chain by tridiagonalizing the Hamiltonian relative to a given initial state. In the resulting matrix, the diagonal and off-diagonal Lanczos coefficients control transition amplitudes between elements of a distinguished basis of states. We connect these two approaches to the quantum mechanics of complex systems by deriving analytical formulae relating the potential defining a general RMT, or, equivalently, its density of states, to the Lanczos coefficients and their correlations. In particular, we derive an integral relation between the average Lanczos coefficients and the density of states, and, for polynomial potentials, algebraic equations that determine the Lanczos coefficients from the potential. We obtain these results for generic initial states in the thermodynamic limit. As an application, we compute the time-dependent ``spread complexity'' in Thermo-Field Double states and the spectral form factor for Gaussian and Non-Gaussian RMTs.

hep-th↗

arXiv2022

Quantum chaos and the complexity of spread of states

We propose a measure of quantum state complexity defined by minimizing the spread of the wave-function over all choices of basis. Our measure is controlled by the "survival amplitude" for a state to remain unchanged, and can be efficiently computed in theories with discrete spectra. For continuous Hamiltonian evolution, it generalizes Krylov operator complexity to quantum states. We apply our methods to the harmonic and inverted oscillators, particles on group manifolds, the Schwarzian theory, the SYK model, and random matrix models. For time-evolved thermofield double states in chaotic systems our measure shows four regimes: a linear "ramp" up to a "peak" that is exponential in the entropy, followed by a "slope" down to a "plateau". These regimes arise in the same physics producing the slope-dip-ramp-plateau structure of the Spectral Form Factor. Specifically, the complexity slope arises from spectral rigidity, distinguishing different random matrix ensembles.

hep-th↗