arXiv subjects

Daniel Ranard

Publications and source records attributed to Daniel Ranard.

At least 19 recordsLinked to original sources

arXiv2026

Likelihood scoring for continuations of mathematical text: a self-supervised benchmark with tests for shortcut vulnerabilities

We introduce an automatically generated benchmark for predicting hidden text in technical papers. A paper supplies visible context $X$ and a hidden continuation $Y$; the evaluated model writes an auxiliary forecast string $Z$, and a separate scorer assigns next-token probability to $Y$ both with and without conditioning on $Z$. This gives a label-free test of whether $Z$ transmits information about the continuation, compared against controls where $Z$ is recent context rather than a forecast. Our main testbed is equation-suffix prediction: the predictor sees context and the first part of a displayed equation, then forecasts the rest. The task mixes surface-level arXiv/TeX text modeling with reasoning-sensitive inference; the suffix is one of many roughly equivalent continuations, so the benchmark is read statistically rather than item-by-item. On 1363 equation continuations from 138 recent physics and mathematics papers, forecasts from GPT-5.5, Opus 4.7, and GPT-5.4 nano all improve clipped likelihood over the context control under both Qwen3-8B and Kimi K2.6 scorers, distinguishing model families and reasoning-effort settings without human labels. To emulate shortcuts where $Z$ further primes the scorer rather than making a useful forecast, we also fine-tune the scorer on context-only prompts and apply it to held-out papers as a stronger control. GPT-5.5 forecasts still beat this fine-tuned control; GPT-5.4 nano forecasts do not. Longer prose/TeX continuations show positive but noisier lift over controls, concentrated near the beginning of the target. These results support cross-model likelihood scoring as a static benchmark and as a setup for probing shortcut vulnerabilities before reinforcement learning or model-selection optimization is applied.

cs.LG↗

arXiv2026

Approximate QCAs in one dimension using approximate algebras

Quantum cellular automata (QCAs) are automorphisms of tensor product algebras that preserve locality, with local quantum circuits as a simple example. We study approximate QCAs, where the locality condition is only satisfied up to a small error, as occurs for local quantum dynamics on the lattice. A priori, approximate QCAs could exhibit genuinely new behavior, failing to be well-approximated by any exact QCA. We show this does not occur in one dimension: every approximate QCA on a finite circle can be rounded to a strict QCA with approximately the same action on local operators, so these systems are classified by the same index as in the exact case. Previous work considered the case of the infinite line, by using global methods not amenable to finite systems. Our new approach proceeds locally and now applies to finite systems, including circles or homomorphisms from sub-intervals. We extract exact local boundary algebras from the approximate QCA restricted to local patches, then glue these to form a strict QCA. The key technical ingredient is a robust notion of the intersection of two subalgebras: when the projections onto two subalgebras approximately commute, we construct an exact subalgebra that serves as a stable proxy for their intersection. This construction uses a recent theorem of Kitaev on the rigidity of approximate $C^*$-algebras.

quant-ph↗

arXiv2025

The threshold for quantum-classical correspondence is $D \sim \hbar^{\frac43}$

In chaotic quantum systems, an initially localized quantum state can deviate strongly from the corresponding classical phase-space distribution after the Ehrenfest time $t_{\mathrm{E}} \sim \log(\hbar^{-1})$, even in the limit $\hbar \to 0$. Decoherence by the environment is often invoked to explain the persistence of the quantum-classical correspondence at longer timescales. Recent rigorous results for Lindblad dynamics with phase-space diffusion strength $D$ show that quantum and classical evolutions remain close for times that are exponentially longer than the Ehrenfest time whenever $D \gg \hbar^{\frac43}$, in units set by the classical Hamiltonian. At the same time, some heuristic arguments have suggested the weaker condition $D \gg \hbar^{2}$ always suffices. Here we construct an explicit Lindbladian that demonstrates that the scaling $D \sim \hbar^{\frac43}$ is indeed the threshold for quantum-classical correspondence beyond the Ehrenfest time. Our example uses a smooth time-dependent Hamiltonian and linear Lindblad operators generating homogeneous isotropic diffusion. It exhibits an $\hbar$-independent quantum-classical discrepancy at the Ehrenfest time whenever $D \ll \hbar^{\frac43}$, even for $\hbar$-independent "macroscopic" smooth observables.

quant-ph↗

arXiv2025

Lower bounding the MaxCut of high girth 3-regular graphs using the QAOA

We study MaxCut on 3-regular graphs of minimum girth $g$ for various $g$'s. We obtain new lower bounds on the maximum cut achievable in such graphs by analyzing the Quantum Approximate Optimization Algorithm (QAOA). For $g \geq 16$, at depth $p \geq 7$, the QAOA improves on previously known lower bounds. Our bounds are established through classical numerical analysis of the QAOA's expected performance. This analysis does not produce the actual cuts but establishes their existence. When implemented on a quantum computer, the QAOA provides an efficient algorithm for finding such cuts, using a constant-depth quantum circuit. To our knowledge, this gives an exponential speedup over the best known classical algorithm guaranteed to achieve cuts of this size on graphs of this girth. We also apply the QAOA to the Maximum Independent Set problem on the same class of graphs.

quant-ph↗

arXiv2024

Learning State Preparation Circuits for Quantum Phases of Matter

Many-body ground state preparation is an important subroutine used in the simulation of physical systems. In this paper, we introduce a flexible and efficient framework for obtaining a state preparation circuit for a large class of many-body ground states. We introduce polynomial-time classical algorithms that take reduced density matrices over $\mathcal{O}(1)$-sized balls as inputs, and output a circuit that prepares the global state. We introduce algorithms applicable to (i) short-range entangled states (e.g., states prepared by shallow quantum circuits in any number of dimensions, and more generally, invertible states) and (ii) long-range entangled ground states (e.g., the toric code on a disk). Both algorithms can provably find a circuit whose depth is asymptotically optimal. Our approach uses a variant of the quantum Markov chain condition that remains robust against constant-depth circuits. The robustness of this condition makes our method applicable to a large class of states, whilst ensuring a classically tractable optimization landscape.

quant-ph↗

arXiv2024

Strategies for running the QAOA at hundreds of qubits

We explore strategies aimed at reducing the amount of computation, both quantum and classical, required to run the Quantum Approximate Optimization Algorithm (QAOA). First, following Wurtz et al. [Phys.Rev A 104:052419], we consider the standard QAOA with instance-independent "tree" parameters chosen in advance. These tree parameters are chosen to optimize the MaxCut expectation for large girth graphs. We provide extensive numerical evidence supporting the performance guarantee for tree parameters conjectured in [Phys.Rev A 103:042612] and see that the approximation ratios obtained with tree parameters are typically well beyond the conjectured lower bounds, often comparable to performing a full optimization. This suggests that in practice, the QAOA can achieve near-optimal performance without the need for parameter optimization. Next, we modify the warm-start QAOA of Tate et al. [Quantum 7:1121]. The starting state for the QAOA is now an optimized product state associated with a solution of the Goemans-Williamson (GW) algorithm. Surprisingly, the tree parameters continue to perform well for the warm-start QAOA. We find that for random 3-regular graphs with hundreds of vertices, the expected cut obtained by the warm-start QAOA at depth $p \gtrsim 3$ is comparable to that of the standard GW algorithm. Our numerics on random instances do not provide general performance guarantees but do provide substantial evidence that there exists a regime of instance sizes in which the QAOA finds good solutions at low depth without the need for parameter optimization. For each instance studied, we classically compute the expected size of the QAOA distribution of cuts; producing the actual cuts requires running on a quantum computer.

quant-ph↗

arXiv2024

Classifying 2D topological phases: mapping ground states to string-nets

We prove the conjectured classification of topological phases in two spatial dimensions with gappable boundary, in a simplified setting. Two gapped ground states of lattice Hamiltonians are in the same quantum phase of matter, or topological phase, if they can be connected by a constant-depth quantum circuit. It is conjectured that the Levin-Wen string-net models exhaust all possible gapped phases with gappable boundary, and these phases are labeled by unitary modular tensor categories. We prove this under the assumption that every phase has a representative state with zero correlation length satisfying the entanglement bootstrap axioms, or a strict form of area law. Our main technical development is to transform these states into string-net states using constant-depth quantum circuits.

quant-ph↗

arXiv2024

Strict area law implies commuting parent Hamiltonian

We show that in two spatial dimensions, when a quantum state has entanglement entropy obeying a strict area law, meaning $S(A)=\alpha |\partial A| - \gamma$ for constants $\alpha, \gamma$ independent of lattice region $A$, then it admits a commuting parent Hamiltonian. More generally, we prove that the entanglement bootstrap axioms in 2D imply the existence of a commuting, local parent Hamiltonian with a stable spectral gap. We also extend our proof to states that describe gapped domain walls. Physically, these results imply that the states studied in the entanglement bootstrap program correspond to ground states of some local Hamiltonian, describing a stable phase of matter. Our result also suggests that systems with chiral gapless edge modes cannot obey a strict area law provided they have finite local Hilbert space.

quant-ph↗

arXiv2023

Universal lower bound on topological entanglement entropy

Entanglement entropies of two-dimensional gapped ground states are expected to satisfy an area law, with a constant correction term known as the topological entanglement entropy (TEE). In many models, the TEE takes a universal value that characterizes the underlying topological phase. However, the TEE is not truly universal: it can differ even for two states related by constant-depth circuits, which are necessarily in the same phase. The difference between the TEE and the value predicted by the anyon theory is often called the spurious topological entanglement entropy. We show that this spurious contribution is always nonnegative, thus the value predicted by the anyon theory provides a universal lower bound. This observation also leads to a definition of TEE that is invariant under constant-depth quantum circuits.

quant-ph↗

arXiv2023

The QAOA gets stuck starting from a good classical string

The Quantum Approximate Optimization Algorithm (QAOA) is designed to maximize a cost function over bit strings. While the initial state is traditionally a uniform superposition over all strings, it is natural to try expediting the QAOA: first use a classical algorithm to produce some good string, and then run the standard QAOA starting in the computational basis state associated with that string. Here we report numerical experiments that show this method of initializing the QAOA fails dramatically, exhibiting little to no improvement of the cost function. We provide multiple analytical arguments for this lack of improvement, each of which can be made rigorous under different regimes or assumptions, including at nearly linear depths. We emphasize that our negative results only apply to our simple incarnation of the warm-start QAOA and may not apply to other approaches in the literature. We hope that our theoretical analysis will inform future algorithm design.

quant-ph↗

arXiv2023

Classical correspondence beyond the Ehrenfest time for open quantum systems with general Lindbladians

Quantum and classical systems evolving under the same formal Hamiltonian $H$ may dramatically differ after the Ehrenfest timescale $t_E \sim \log(\hbar^{-1})$, even as $\hbar \to 0$. Coupling the system to a Markovian environment results in a Lindblad equation for the quantum evolution. Its classical counterpart is given by the Fokker-Planck equation on phase space, which describes Hamiltonian flow with friction and diffusive noise. The quantum and classical evolutions may be compared via the Wigner-Weyl representation. Due to decoherence, they are conjectured to match closely for times far beyond the Ehrenfest timescale as $\hbar \to 0$. We prove a version of this correspondence, bounding the error between the quantum and classical evolutions for any sufficiently regular Hamiltonian $H(x,p)$ and Lindblad functions $L_k(x,p)$. The error is small when the strength of the diffusion $D$ associated to the Lindblad functions satisfies $D \gg \hbar^{4/3}$, which allows vanishing noise in the classical limit. Our method uses a time-dependent semiclassical mixture of variably squeezed Gaussian states. The states evolve according to a local harmonic approximation to the Lindblad dynamics. Both the exact quantum trajectory and its classical counterpart can be expressed as perturbations of this semiclassical mixture, with the errors bounded using Duhamel's principle. We present heuristic arguments suggesting the $4/3$ exponent is optimal and defines a boundary in the sense that asymptotically weaker diffusion permits a breakdown of quantum-classical correspondence at the Ehrenfest timescale. In a shorter companion paper, we treat the special case of Hamiltonians that decompose into kinetic and potential energy with linear Lindblad operators, with explicit bounds that can be applied directly to physical systems.

math-ph↗

arXiv2023

Ehrenfest's theorem beyond the Ehrenfest time

In closed quantum systems, wavepackets can spread exponentially in time due to chaos, forming long-range superpositions in just seconds for ordinary macroscopic systems. A weakly coupled environment is conjectured to decohere the system and restore the quantum-classical correspondence while necessarily introducing diffusive noise -- but at what coupling strength, and under which conditions? For Markovian open systems with Hamiltonians of the form $H = p^2/2m+V(x)$ and Hermitian linear Lindblad operators, we prove the quantum and classical evolutions are close whenever the strength of the environment-induced diffusion satisfies $D \gg (\hbar/s_H)^{4/3} D_H$, where $s_H$ and $D_H$ are characteristic action and diffusion scales that we define precisely using the classical Hamiltonian $H$. The bound applies for all observables and for times exponentially longer than the Ehrenfest timescale, which is when the correspondence can break down in closed systems. The strength of the diffusive noise can vanish in the classical limit to give the appearance of reversible dynamics. The $4/3$ exponent may be optimal, suggested by heuristic arguments and prior numerical evidence. Based on our bound, we give an efficient classical algorithm for simulating quantum Lindblad dynamics, which becomes provably accurate when the strength of environmental coupling exceeds the above threshold.

quant-ph↗

arXiv2023

A spin-energy operator inequality for Heisenberg-coupled qubits

We slightly strengthen an operator inequality identified by Correggi et al. that lower bounds the energy of a Heisenberg-coupled graph of $s=1/2$ spins using the total spin. In particular, $ΔH \ge C Δ\vec{S}^2$ for a graph-dependent constant $C$, where $ΔH$ is the energy above the ground state and $Δ\vec{S}^2$ is the amount by which the square of the total spin $\vec{S} = \sum_i \vecσ_i/2$ falls below its maximum possible value. We obtain explicit constants in the special case of a cubic lattice. We briefly discuss the interpretation of this bound in terms of low-energy, approximately non-interacting magnons in spin wave theory and contrast it with another inequality found by Bärwinkel et al.

quant-ph↗

arXiv2022

A converse to Lieb-Robinson bounds in one dimension using index theory

Unitary dynamics with a strict causal cone (or "light cone") have been studied extensively, under the name of quantum cellular automata (QCAs). In particular, QCAs in one dimension have been completely classified by an index theory. Physical systems often exhibit only approximate causal cones; Hamiltonian evolutions on the lattice satisfy Lieb-Robinson bounds rather than strict locality. This motivates us to study approximately locality preserving unitaries (ALPUs). We show that the index theory is robust and completely extends to one-dimensional ALPUs. As a consequence, we achieve a converse to the Lieb-Robinson bounds: any ALPU of index zero can be exactly generated by some time-dependent, quasi-local Hamiltonian in constant time. For the special case of finite chains with open boundaries, any unitary satisfying the Lieb-Robinson bound may be generated by such a Hamiltonian. We also discuss some results on the stability of operator algebras which may be of independent interest.

quant-ph↗

arXiv2021

Emergent classicality in general multipartite states and channels

In a quantum measurement process, classical information about the measured system spreads throughout the environment. Meanwhile, quantum information about the system becomes inaccessible to local observers. Here we prove a result about quantum channels indicating that an aspect of this phenomenon is completely general. We show that for any evolution of the system and environment, for everywhere in the environment excluding an $O(1)$-sized region we call the "quantum Markov blanket," any locally accessible information about the system must be approximately classical, i.e. obtainable from some fixed measurement. The result strengthens the earlier result of arXiv:1310.8640 in which the excluded region was allowed to grow with total environment size. It may also be seen as a new consequence of the principles of no-cloning or monogamy of entanglement. Our proof offers a constructive optimization procedure for determining the "quantum Markov blanket" region, as well as the effective measurement induced by the evolution. Alternatively, under channel-state duality, our result characterizes the marginals of multipartite states.

quant-ph↗

arXiv2020

Fluctuations of subsystem entropies at late times

We study the fluctuations of subsystem entropies in closed quantum many-body systems after thermalization. Using a combination of analytics and numerics for both random quantum circuits and Hamiltonian dynamics, we find that the statistics of such entropy fluctuations is drastically different than in the classical setting. For instance, shortly after a system thermalizes, the probability of entropy fluctuations for a subregion is suppressed in the dimension of the Hilbert space of the complementary subregion. This suppression becomes increasingly stringent as a function of time, ultimately depending on the exponential of the Hilbert space dimension, until extremely late times when the amount of suppression saturates. We also use our results to estimate the total number of rare fluctuations at large timescales. We find that the "Boltzmann brain" paradox is largely ameliorated in quantum many-body systems, in contrast with the classical setting.

quant-ph↗

arXiv2020

Kitaev's quantum double model as an error correcting code

Kitaev's quantum double models in 2D provide some of the most commonly studied examples of topological quantum order. In particular, the ground space is thought to yield a quantum error-correcting code. We offer an explicit proof that this is the case for arbitrary finite groups. Actually a stronger claim is shown: any two states with zero energy density in some contractible region must have the same reduced state in that region. Alternatively, the local properties of a gauge-invariant state are fully determined by specifying that its holonomies in the region are trivial. We contrast this result with the fact that local properties of gauge-invariant states are not generally determined by specifying all of their non-Abelian fluxes -- that is, the Wilson loops of lattice gauge theory do not form a complete commuting set of observables. We also note that the methods developed by P. Naaijkens (PhD thesis, 2012) under a different context can be adapted to provide another proof of the error correcting property of Kitaev's model. Finally, we compute the topological entanglement entropy in Kitaev's model, and show, contrary to previous claims in the literature, that it does not depend on whether the "log dim R" term is included in the definition of entanglement entropy.

quant-ph↗

arXiv2019

Target Space Entanglement Entropy

We define a notion of target space entanglement entropy. Rather than partitioning the base space on which the theory is defined, we consider partitions of the target space. This is the physical case of interest for first-quantized theories, such as worldsheet string theory. We associate to each subregion of the target space a suitably chosen sub-algebra of observables $\mathcal{A}$. The entanglement entropy is calculated as the entropy of the density matrix restricted to $\mathcal{A}$. As an example, we illustrate our framework by computing spatial entanglement in first-quantized many-body quantum mechanics. The algebra $\mathcal{A}$ is chosen to reproduce the entanglement entropy obtained by embedding the state in the fixed particle sub-sector of the second-quantized Hilbert space. We then generalize our construction to the quantum field-theoretical setting.

hep-th↗