arXiv subjects

Nicolas Dupuis

Publications and source records attributed to Nicolas Dupuis.

At least 19 recordsLinked to original sources

arXiv2026

Universal scaling of fluctuations and correlations across the superfluid transition

The critical behavior of a system near a continuous phase transition is commonly characterized by power laws and a set of universal critical exponents. Yet universality at phase transitions has even more fundamental manifestations. It dictates that all observables follow universal scaling functions, which may extend beyond simple power laws. Furthermore, microscopic details are captured entirely by only two system-specific scale factors, that rescale any measured quantity onto its universal form. In this work, we report the experimental validation of this prediction in ultracold lattice Bose gases undergoing the superfluid transition. We extract the scale factors by collapsing the order-parameter cumulants measured at varying entropies. We show that these factors specify scaling functions governing both the order-parameter distribution and two-point correlations. By measuring these scaling functions, we also determine three critical exponents $\beta$, $\gamma$ and $\nu$. Our results provide an experimental demonstration that universal scaling is simultaneously obeyed by multiple observables in a quantum many-body system.

cond-mat.quant-gas↗

arXiv2026

Efficient Classical Simulation of Heuristic Peaked Quantum Circuits

Peaked quantum circuits, whose output distribution is sharply concentrated on a single bitstring, have emerged as a promising candidate for verifiable quantum advantage, as the correctness of the quantum output can be checked by simply comparing against the known peak. Recent work by Gharibyan et al. arXiv:2510.25838 claimed heuristic quantum advantage using peaked circuits executed on Quantinuum's 56-qubit H2 processor. These peaked circuits concentrate their output on a single hidden bitstring by training a shallow simulable circuit variationally and inserting an obfuscated permutation to increase the depth to a level that makes classical simulation intractable, with estimated runtimes of years for the largest instances. We show that these circuits can be efficiently simulated classically. We describe a method that efficiently performs a full tensor network contraction, allowing near-exact sampling and extraction of the peaked bitstring. The method exploits the mirrored structure of the circuit and iteratively cancels both halves into a Matrix Product Operator (MPO), and avoids the obfuscated permutation by greedily reducing the MPO bond dimension through a process we call unswapping. The method can fully contract and extract the peak of the largest circuit in approximately one hour on a single GPU, around half the time it took to run on the quantum hardware.

quant-ph↗

arXiv2025

From Bose glass to many-body localization in a one-dimensional disordered Bose gas

We determine the finite-temperature phase diagram of a one-dimensional disordered Bose gas using bosonization and the nonperturbative functional renormalization group (RG). We discuss two different scenarios, based on distinct truncations of the effective action. In the first scenario, the Bose glass is destabilized at any finite temperature, giving rise to a normal fluid. Nevertheless, one can distinguish a low-temperature glassy regime, where disorder plays an important role on intermediate length and time scales, from a high-temperature regime, where disorder becomes irrelevant. In the second scenario, below a temperature $T_c$, the RG flow exhibits a singularity at a finite value of the RG momentum scale. We propose that this singularity signals a lack of thermalization and the existence of a localized phase for $T<T_c$. We provide a description of this low-temperature localized phase within a droplet picture and highlight a number of possible similarities with characteristics of many-body localized phases, including non-thermal behavior, avalanche instabilities and many-body resonances, the structure of the many-body spectrum, and slow dynamics in the ergodic phase. The normal fluid above $T_c$, and below a crossover temperature $T_g$, exhibits glassy properties on intermediate scales.

cond-mat.quant-gas↗

arXiv2025

Two-body contact of a Bose gas near the superfluid--Mott-insulator transition

The two-body contact is a fundamental quantity of a dilute Bose gas that relates the thermodynamics to the short-distance two-body correlations. For a Bose gas in an optical lattice, near the superfluid--Mott-insulator transition, we show that a ``universal'' contact $C_{\rm univ}$ can be defined from the singular part $P-P_{\rm MI}$ of the pressure ($P_{\rm MI}$ is the pressure of the Mott insulator). Its expression $C_{\rm univ}=C_{\rm DBG}(|n-n^{\rm MI}|,a^*)$ coincides with that of a dilute Bose gas provided we consider the effective ``scattering length'' $a^*$ of the quasi-particles at the quantum critical point (QCP) rather than the scattering length in vacuum, and the excess density $|n-n^{\rm MI}|$ of particles (or holes) with respect to the Mott insulator. Close to the transition, we find that the singular part $n^{\rm sing}_{\bf k} = n_{\bf k} - n^{\rm MI}_{\bf k}$ of the momentum distribution exhibits a high-momentum tail of the form $Z_{\rm QP} C_{\rm univ}/|{\bf k}|^4$ over a broad region of the Brillouin zone, where $Z_{\rm QP}$ is the quasi-particle weight of the elementary excitations at the QCP. Our results demonstrate that the notion of contact extends to strongly correlated lattice bosons, and we argue that the contact $C_{\rm univ}$ can be measured in state-of-the-art experiments on Bose gases in optical lattices and magnetic insulators.

cond-mat.quant-gas↗

arXiv2025

Strong-coupling RPA theory of a Bose gas near the superfluid--Mott-insulator transition: universal thermodynamics and two-body contact

We present a strong-coupling expansion of the Bose-Hubbard model based on a mean-field treatment of the hopping term, while onsite fluctuations are taken into account exactly. This random phase approximation (RPA) describes the universal features of the generic Mott-insulator--superfluid transition (induced by a density change) and the superfluid state near the phase transition. The critical quasi-particles at the quantum critical point have a quadratic dispersion with an effective mass $m^*$ and their mutual interaction is described by an effective $s$-wave scattering length $a^*$. The singular part of the pressure takes the same form as in a dilute Bose gas, provided we replace the boson mass $m$ and the scattering length in vacuum $a$ by $m^*$ and $a^*$, and the density $n$ by the excess density $|n-n_{\rm MI}|$ of particles (or holes) with respect to the Mott insulator. We define a ``universal'' two-body contact $C_{\rm univ}$ that controls the high-momentum tail $\sim 1/|{\bf k}|^4$ of the singular part $n^{\rm sing}_{\bf k}$ of the momentum distribution. We also apply the strong-coupling RPA to a lattice model of hard-core bosons and find that the high-momentum distribution is controlled by a universal contact, in complete agreement with the Bose-Hubbard model. Finally, we discuss a continuum model of bosons in an optical lattice and define two additional two-body contacts: a short-distance ``universal'' contact $C_{\rm univ}^{\rm sd}$ which controls the high-momentum tail of $n^{\rm sing}_{\bf k}$ at scales larger than the inverse lattice spacing, and a ``full'' contact $C$ which controls the high-momentum tail of the full momentum distribution $n_{\bf k}$.

cond-mat.quant-gas↗

arXiv2025

Universal Crossover in the Three-Channel Charge Kondo Model at High Transparency

Quantum impurity models provide a central framework for correlated electron physics, with quantum dots enabling controlled experimental realizations. While their weak-coupling behavior is well understood through mappings to Kondo Hamiltonians, the opposite regime of highly transparent contacts has lacked a controlled theoretical description. Using the functional renormalization group (FRG), we resolve this regime for the three-channel charge Kondo device of Ref.~\cite{iftikhar2018}, benchmarking against conformal field theory by reproducing the universal zero-frequency conductance and, crucially, going beyond it to obtain the full frequency crossover of the conductance and the full temperature crossover of the impurity entropy, together with a continuous line of fixed points for interacting leads. These results establish FRG as a powerful nonperturbative tool for quantum impurity problems in regimes inaccessible to conventional approaches, with direct implications for mesoscopic experiments.

cond-mat.mes-hall↗

arXiv2025

Observation of universal non-Gaussian statistics of the order parameter across a continuous phase transition

Second-order phase transitions are characterised by critical scaling and universality. The singular behaviour of thermodynamic quantities at the transition, in particular, is determined by critical exponents of the universality class of the transition. However, critical properties are also characterised by the probability distribution of the order parameter across the transition, where non-Gaussian statistics are expected, but remain largely unexplored. Here, making use of single-atom-resolved detection in momentum space, we measure the full probability distribution of the order-parameter amplitude across a continuous phase transition in an interacting lattice Bose gas. We find that fluctuations are captured by an effective potential -- reconstructed from the measured probability distribution by analogy with Landau theory -- displaying a non-trivial minimum in the superfluid (ordered) phase, which vanishes at the transition point. Additionally, we observe non-Gaussian statistics of the order parameter near the transition, distinguished by non-zero high-order cumulants undergoing abrupt sign changes. We show numerically that these sign changes of the cumulants obey critical scaling in homogeneous systems, and that their experimental behaviour is not reproduced by classical models, whereas it is captured by a low-temperature quantum model. Our results underscore the crucial role of order parameter statistics in probing critical phenomena and universality.

cond-mat.quant-gas↗

arXiv2025

Quantum Verifiable Rewards for Post-Training Qiskit Code Assistant

Qiskit is an open-source quantum computing framework that allows users to design, simulate, and run quantum circuits on real quantum hardware. We explore post-training techniques for LLMs to assist in writing Qiskit code. We introduce quantum verification as an effective method for ensuring code quality and executability on quantum hardware. To support this, we developed a synthetic data pipeline that generates quantum problem-unit test pairs and used it to create preference data for aligning LLMs with DPO. Additionally, we trained models using GRPO, leveraging quantum-verifiable rewards provided by the quantum hardware. Our best-performing model, combining DPO and GRPO, surpasses the strongest open-source baselines on the challenging Qiskit-HumanEval-hard benchmark.

quant-ph↗

arXiv2025

Revisiting Group Relative Policy Optimization: Insights into On-Policy and Off-Policy Training

We revisit Group Relative Policy Optimization (GRPO) in both on-policy and off-policy optimization regimes. Our motivation comes from recent work on off-policy Proximal Policy Optimization (PPO), which improves training stability, sampling efficiency, and memory usage. In addition, a recent analysis of GRPO suggests that estimating the advantage function with off-policy samples could be beneficial. Building on these observations, we adapt GRPO to the off-policy setting. We show that both on-policy and off-policy GRPO objectives yield an improvement in the reward. This result motivates the use of clipped surrogate objectives in the off-policy version of GRPO. We then compare the empirical performance of reinforcement learning with verifiable rewards in post-training using both GRPO variants. Our results show that off-policy GRPO either significantly outperforms or performs on par with its on-policy counterpart.

cs.LG↗

arXiv2025

Customizing a Large Language Model for VHDL Design of High-Performance Microprocessors

The use of Large Language Models (LLMs) in hardware design has taken off in recent years, principally through its incorporation in tools that increase chip designer productivity. There has been considerable discussion about the use of LLMs in RTL specifications of chip designs, for which the two most popular languages are Verilog and VHDL. LLMs and their use in Verilog design has received significant attention due to the higher popularity of the language, but little attention so far has been given to VHDL despite its continued popularity in the industry. There has also been little discussion about the unique needs of organizations that engage in high-performance processor design, and techniques to deploy AI solutions in these settings. In this paper, we describe our journey in developing a Large Language Model (LLM) specifically for the purpose of explaining VHDL code, a task that has particular importance in an organization with decades of experience and assets in high-performance processor design. We show how we developed test sets specific to our needs and used them for evaluating models as we performed extended pretraining (EPT) of a base LLM. Expert evaluation of the code explanations produced by the EPT model increased to 69% compared to a base model rating of 43%. We further show how we developed an LLM-as-a-judge to gauge models similar to expert evaluators. This led us to deriving and evaluating a host of new models, including an instruction-tuned version of the EPT model with an expected expert evaluator rating of 71%. Our experiments also indicate that with the potential use of newer base models, this rating can be pushed to 85% and beyond. We conclude with a discussion on further improving the quality of hardware design LLMs using exciting new developments in the Generative AI world.

cs.AR↗

arXiv2025

Resilience of the quantum critical line in the Schmid transition

Schmid predicted that a single Josephson junction coupled to a resistive environment undergoes a quantum phase transition to an insulating phase when the shunt resistance $R$ exceeds the resistance quantum $h/(4 e^ 2)$. Recent measurements and theoretical studies have sparked a debate on whether the location of this transition depends on the ratio between the Josephson and the charging energies. We employ a combination of multiple innovative analytical and numerical techniques, never before explicitly applied to this problem, to decisively demonstrate that the transition line between superconducting and insulating behavior is indeed independent of this energy ratio. First, we apply field-theory renormalization group methods and find that the $β$ function vanishes along the critical line up to the third order in the Josephson energy. We then identify a simple fermionic model that precisely captures the low-energy physics on the critical line, regardless of the energy ratio. This conformally invariant fermionic model is verified by comparing the expected spectrum with exact diagonalization calculations of the resistively shunted Josephson junction, showing excellent agreement even for moderate system sizes. Importantly, this identification provides a rigorous non-perturbative proof that the transition line is maintained at $R=h/(4 e^ 2)$ for all ratios of Josephson to charging energies. The line is further resilient to other ultraviolet cutoffs such as the plasma frequency of the resistive environment. Finally, we implement an adiabatic approach to validate the duality at large Josephson energy.

cond-mat.str-el↗

arXiv2024

Mott-glass phase induced by long-range correlated disorder in a one-dimensional Bose gas

We determine the phase diagram of a one-dimensional Bose gas in the presence of disorder with short- and long-range correlations, the latter decaying with distance as $1/|x|^{1+σ}$. When $σ<0$, the Berezinskii-Kosterlitz-Thouless transition between the superfluid and the localized phase is driven by the long-range correlations and the Luttinger parameter $K$ takes the critical value $K_c(σ)=3/2-σ/2$. The localized phase is a Bose glass for $σ>σ_c=3-π^2/3\simeq -0.289868$, and a Mott glass -- characterized by a vanishing compressibility and a gapless conductivity -- when $σ<σ_c$. Our conclusions, based on the nonperturbative functional renormalization group and perturbative renormalization group, are confirmed by the study of the case $σ=-1$, corresponding to a perfectly correlated disorder in space, where the model is exactly solvable in the semiclassical limit $K\to 0^+$.

cond-mat.quant-gas↗

arXiv2024

Superfluid--Bose-glass transition in a system of disordered bosons with long-range hopping in one dimension

We study the superfluid--Bose-glass transition in a one-dimensional lattice boson model with power-law decaying hopping amplitude $t_{i-j}\sim 1/|i-j|^α$, using bosonization and the nonperturbative functional renormalization group (FRG). When $α$ is smaller than a critical value $α_c<3$, the U(1) symmetry is spontaneously broken, which leads to a density mode with nonlinear dispersion and dynamical exponent $z=(α-1)/2$; the superfluid phase is then stable for sufficiently weak disorder, contrary to the case of short-range hopping where the superfluid phase is destabilized by an infinitesimal disorder when the Luttinger parameter is smaller than $3/2$. In the presence of disorder, long-range hopping has however no effect in the infrared limit and the FRG flow eventually becomes similar to that of a boson system with short-range hopping. This implies that the superfluid phase, when stable, exhibits a density mode with linear dispersion ($z=1$) and the superfluid--Bose-glass transition remains in the Berezinskii-Kosterlitz-Thouless universality class, while the Bose-glass fixed point is insensitive to long-range hopping. We compare our findings with a recent numerical study.

cond-mat.quant-gas↗

arXiv2024

Qiskit HumanEval: An Evaluation Benchmark For Quantum Code Generative Models

Quantum programs are typically developed using quantum Software Development Kits (SDKs). The rapid advancement of quantum computing necessitates new tools to streamline this development process, and one such tool could be Generative Artificial intelligence (GenAI). In this study, we introduce and use the Qiskit HumanEval dataset, a hand-curated collection of tasks designed to benchmark the ability of Large Language Models (LLMs) to produce quantum code using Qiskit - a quantum SDK. This dataset consists of more than 100 quantum computing tasks, each accompanied by a prompt, a canonical solution, a comprehensive test case, and a difficulty scale to evaluate the correctness of the generated solutions. We systematically assess the performance of a set of LLMs against the Qiskit HumanEval dataset's tasks and focus on the models ability in producing executable quantum code. Our findings not only demonstrate the feasibility of using LLMs for generating quantum code but also establish a new benchmark for ongoing advancements in the field and encourage further exploration and development of GenAI-driven tools for quantum code generation.

quant-ph↗

arXiv2024

Functional Renormalization Group for fermions on a one dimensional lattice at arbitrary filling

A formalism based on the fermionic functional-renormalization-group approach to interacting electron models defined on a lattice is presented. One-loop flow equations for the coupling constants and susceptibilities in the particle-particle and particle-hole channels are derived in weak-coupling conditions. It is shown that lattice effects manifest themselves through the curvature of the spectrum and the dependence of the coupling constants on momenta. This method is then applied to the one-dimensional extended Hubbard model; we thoroughly discuss the evolution of the phase diagram, and in particular the fate of the bond-centered charge-density-wave phase, as the system is doped away from half-filling. Our findings are compared to the predictions of the field-theory continuum limit and available numerical results.

cond-mat.str-el↗

arXiv2024

Qiskit Code Assistant: Training LLMs for generating Quantum Computing Code

Code Large Language Models (Code LLMs) have emerged as powerful tools, revolutionizing the software development landscape by automating the coding process and reducing time and effort required to build applications. This paper focuses on training Code LLMs to specialize in the field of quantum computing. We begin by discussing the unique needs of quantum computing programming, which differ significantly from classical programming approaches or languages. A Code LLM specializing in quantum computing requires a foundational understanding of quantum computing and quantum information theory. However, the scarcity of available quantum code examples and the rapidly evolving field, which necessitates continuous dataset updates, present significant challenges. Moreover, we discuss our work on training Code LLMs to produce high-quality quantum code using the Qiskit library. This work includes an examination of the various aspects of the LLMs used for training and the specific training conditions, as well as the results obtained with our current models. To evaluate our models, we have developed a custom benchmark, similar to HumanEval, which includes a set of tests specifically designed for the field of quantum computing programming using Qiskit. Our findings indicate that our model outperforms existing state-of-the-art models in quantum computing tasks. We also provide examples of code suggestions, comparing our model to other relevant code LLMs. Finally, we introduce a discussion on the potential benefits of Code LLMs for quantum computing computational scientists, researchers, and practitioners. We also explore various features and future work that could be relevant in this context.

quant-ph↗

arXiv2023

On the nature of the Schmid transition in a resistively shunted Josephson junction

We study the phase diagram of a resistively shunted Josephson junction (RSJJ) in the framework of the boundary sine-Gordon model. Using the non-perturbative functional renormalization group (FRG) we find that the transition is not controlled by a single fixed point but by a line of fixed points, and compute the continuously varying critical exponent $ν$. We argue that the conductance also varies continuously along the transition line. In contrast to the traditional phase diagram of the RSJJ -- an insulating ground state when the shunt resistance $R$ is larger than $R_q=h/(2e)^2$ and a superconducting one when $R<R_q$ -- the FRG predicts the transition line in the plane $(α,E_J/E_C)$ to bend in the region $α=R_q/R<1$ but we cannot discard the possibility of a vertical line at $α=1$ ($E_J$ and $E_C$ denote the Josephson and charging energies of the junction, respectively). Our results regarding the phase diagram and the nature of the transition are compared with Monte Carlo simulations and numerical renormalization group results.

cond-mat.supr-con↗

arXiv2023

Mott-glass phase of a one-dimensional quantum fluid with long-range interactions

We investigate the ground-state properties of quantum particles interacting via a long-range repulsive potential ${\cal V}_σ(x)\sim 1/|x|^{1+σ}$ ($-1<σ$) or ${\cal V}_σ(x)\sim -|x|^{-1-σ}$ ($-2\leq σ<-1$) that interpolates between the Coulomb potential ${\cal V}_0(x)$ and the linearly confining potential ${\cal V}_{-2}(x)$ of the Schwinger model. In the absence of disorder the ground state is a Wigner crystal when $σ\leq 0$. Using bosonization and the nonperturbative functional renormalization group we show that any amount of disorder suppresses the Wigner crystallization when $-3/2<σ\leq 0$; the ground state is then a Mott glass, i.e., a state that has a vanishing compressibility and a gapless optical conductivity. For $σ<-3/2$ the ground state remains a Wigner crystal.

cond-mat.quant-gas↗