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Maxime Dupont

Publications and source records attributed to Maxime Dupont.

At least 19 recordsLinked to original sources
arXiv2026

Quantum Preconditioning For Constrained Optimization Problems

We study the effect of quantum preconditioning on constrained combinatorial optimization problems, focusing on balanced graph bi-partitioning. The proposed approach uses two-point correlations between decision variables derived from the Quantum Approximate Optimization Algorithm (QAOA) to construct a modified objective function that is subsequently provided to mixed-integer programming (MIP) solvers. The preconditioned MIP formulation retains the original hard constraint, and all incumbent solutions are evaluated under the original objective. Computational experiments on dense, weighted complete-graph instances show that the preconditioned problem instances reach near-optimal solutions faster, with most of the benefit already realized at the shallowest QAOA depth tested. Solver callback trajectories show this arises from earlier discovery of high-quality incumbents during the solution search. These results support a hybrid optimization framework in which quantum algorithms provide problem-specific information to guide classical exact MIP solvers.

quant-ph↗
arXiv2026

Self-consistent mean-field quantum approximate optimization

We introduce a self-consistent mean-field quantum optimization algorithm that approximates the ground state of classical Ising Hamiltonians. The algorithm decomposes the problem into independent subproblems and treats the interactions between them in a mean-field manner. These interactions are captured by a common environment, constructed self-consistently through a variational quantum circuit, and which modifies the subproblems to account for mutual influence while maintaining computational independence. Consequently, subproblems can be solved individually, avoiding the computational cost of the full problem. We explore the properties of the generated environment and assess the algorithm's performance through extensive numerical simulations on Sherrington-Kirkpatrick spin glasses. Furthermore, we apply it experimentally to a weighted maximum clique problem applied to molecular docking. This framework enables the solution of problems that would otherwise exceed the qubit and gate counts of current quantum hardware.

quant-ph↗
arXiv2025

Critical Berezinskii-Kosterlitz-Thouless dynamics in the archetypal two-dimensional spin system Ba$_2$CuSi$_2$O$_6$Cl$_2$

We study the spin dynamics in the quasi-2D spin-$1/2$ dimer compound Ba$_2$CuSi$_2$O$_6$Cl$_2$, which exhibits a magnetic field-induced Bose-Einstein condensate (BEC) of triplons. Using nuclear magnetic resonance spin-lattice relaxation rate ($T_1^{-1}$) measurements combined with large-scale quantum Monte Carlo (QMC) simulations, we investigate critical fluctuations across the field-temperature phase diagram. Bridging the behavior observed in 1D and 3D systems, the $T_1^{-1}$ relaxation rate shows a pronounced peak extending well above the N\'eel temperature $T_N$, indicating strong two-dimensional Berezinskii-Kosterlitz-Thouless (BKT)-type fluctuations. A quantitative match between experimental and theoretical BEC phase boundaries validates an effective XXZ model. The study determines the intrinsic BKT transition temperature $T_{\mathrm{BKT}}$ from QMC, revealing a nearly field-independent $T_{\mathrm{BKT}}/T_N \approx 0.74$. Scaling analysis of the relaxation rate shows critical exponents consistent with 2D universality, and a narrow temperature window is identified where 2D physics dominates. These findings establish Ba$_2$CuSi$_2$O$_6$Cl$_2$ as a model system for exploring BKT dynamics in quantum magnets.

cond-mat.str-el↗
arXiv2025

Optimization via Quantum Preconditioning

State-of-the-art classical optimization solvers set a high bar for quantum computers to deliver utility in this domain. Here, we introduce a quantum preconditioning approach based on the quantum approximate optimization algorithm. It transforms the input problem into a more suitable form for a solver with the level of preconditioning determined by the depth of the quantum circuit. We demonstrate that best-in-class classical heuristics such as simulated annealing and the Burer-Monteiro algorithm can converge more rapidly when given quantum preconditioned input for various problems, including Sherrington-Kirkpatrick spin glasses, random 3-regular graph maximum-cut problems, and a real-world grid energy problem. Accounting for the additional time taken for preconditioning, the benefit offered by shallow circuits translates into a practical quantum-inspired advantage for random 3-regular graph maximum-cut problems through quantum circuit emulations. We investigate why quantum preconditioning makes the problem easier and test an experimental implementation on a superconducting device. We identify challenges and discuss the prospects for a hardware-based quantum advantage in optimization via quantum preconditioning.

quant-ph↗
arXiv2024

A Multilevel Approach For Solving Large-Scale QUBO Problems With Noisy Hybrid Quantum Approximate Optimization

Quantum approximate optimization is one of the promising candidates for useful quantum computation, particularly in the context of finding approximate solutions to Quadratic Unconstrained Binary Optimization (QUBO) problems. However, the existing quantum processing units (QPUs) are relatively small, and canonical mappings of QUBO via the Ising model require one qubit per variable, rendering direct large-scale optimization infeasible. In classical optimization, a general strategy for addressing many large-scale problems is via multilevel/multigrid methods, where the large target problem is iteratively coarsened, and the global solution is constructed from multiple small-scale optimization runs. In this work, we experimentally test how existing QPUs perform as a sub-solver within such a multilevel strategy. We combine and extend (via additional classical processing) the recent Noise-Directed Adaptive Remapping (NDAR) and Quantum Relax $\&$ Round (QRR) algorithms. We first demonstrate the effectiveness of our heuristic extensions on Rigetti's transmon device Ankaa-2. We find approximate solutions to $10$ instances of fully connected $82$-qubit Sherrington-Kirkpatrick graphs with random integer-valued coefficients obtaining normalized approximation ratios (ARs) in the range $\sim 0.98-1.0$, and the same class with real-valued coefficients (ARs $\sim 0.94-1.0$). Then, we implement the extended NDAR and QRR algorithms as subsolvers in the multilevel algorithm for $6$ large-scale graphs with at most $\sim 27,000$ variables. The QPU (with classical post-processing steps) is used to find approximate solutions to dozens of problems, at most $82$-qubit, which are iteratively used to construct the global solution. We observe that quantum optimization results are competitive regarding the quality of solutions compared to classical heuristics used as subsolvers within the multilevel approach.

quant-ph↗
arXiv2024

Qubit-efficient quantum combinatorial optimization solver

Quantum optimization solvers typically rely on one-variable-to-one-qubit mapping. However, the low qubit count on current quantum computers is a major obstacle in competing against classical methods. Here, we develop a qubit-efficient algorithm that overcomes this limitation by mapping a candidate bit string solution to an entangled wave function of fewer qubits. We propose a variational quantum circuit generalizing the quantum approximate optimization ansatz (QAOA). Extremizing the ansatz for Sherrington-Kirkpatrick spin glass problems, we show valuable properties such as the concentration of ansatz parameters and derive performance guarantees. This approach could benefit near-term intermediate-scale and future fault-tolerant small-scale quantum devices.

quant-ph↗
arXiv2024

Benchmarking Quantum Optimization for the Maximum-Cut Problem on a Superconducting Quantum Computer

Achieving high-quality solutions faster than classical solvers on computationally hard problems is a challenge for quantum optimization to deliver utility. Using a superconducting quantum computer, we experimentally investigate the performance of a hybrid quantum-classical algorithm inspired by semidefinite programming approaches for solving the maximum-cut problem on 3-regular graphs up to several thousand variables. We leverage the structure of the input problems to address sizes beyond what current quantum machines can naively handle. We attain an average approximation ratio of 99% over a random ensemble of thousands of problem instances. We benchmark the quantum solver against similarly high-performing classical heuristics, including the Gurobi optimizer, simulated annealing, and the Burer-Monteiro algorithm. A run-time analysis shows that the quantum solver on large-scale problems is competitive against Gurobi but short of others on a projected 100-qubit quantum computer. We explore multiple leads to close the gap and discuss prospects for a practical quantum speedup.

quant-ph↗
arXiv2023

Quantum-Enhanced Greedy Combinatorial Optimization Solver

Combinatorial optimization is a broadly attractive area for potential quantum advantage, but no quantum algorithm has yet made the leap. Noise in quantum hardware remains a challenge, and more sophisticated quantum-classical algorithms are required to bolster their performance. Here, we introduce an iterative quantum heuristic optimization algorithm to solve combinatorial optimization problems. The quantum algorithm reduces to a classical greedy algorithm in the presence of strong noise. We implement the quantum algorithm on a programmable superconducting quantum system using up to 72 qubits for solving paradigmatic Sherrington-Kirkpatrick Ising spin glass problems. We find the quantum algorithm systematically outperforms its classical greedy counterpart, signaling a quantum enhancement. Moreover, we observe an absolute performance comparable with a state-of-the-art semidefinite programming method. Classical simulations of the algorithm illustrate that a key challenge to reaching quantum advantage remains improving the quantum device characteristics.

quant-ph↗
arXiv2023

Quantum many-body Jarzynski equality and dissipative noise on a digital quantum computer

The quantum Jarzynski equality and the Crooks relation are fundamental laws connecting equilibrium processes with nonequilibrium fluctuations. They are promising tools to benchmark quantum devices and measure free energy differences. While they are well established theoretically and also experimental realizations for few-body systems already exist, their experimental validity in the quantum many-body regime has not been observed so far. Here, we present results for nonequilibrium protocols in systems with up to sixteen interacting degrees of freedom obtained on trapped ion and superconducting qubit quantum computers, which test the quantum Jarzynski equality and the Crooks relation in the many-body regime. To achieve this, we overcome present-day limitations in the preparation of thermal ensembles and in the measurement of work distributions on noisy intermediate-scale quantum devices. We discuss the accuracy to which the Jarzynski equality holds on different quantum computing platforms subject to platform-specific errors. The analysis reveals the validity of Jarzynski's equality in a regime with energy dissipation, compensated for by a fast unitary drive. This provides new insights for analyzing errors in many-body quantum simulators.

cond-mat.stat-mech↗
arXiv2023

Design and execution of quantum circuits using tens of superconducting qubits and thousands of gates for dense Ising optimization problems

We develop a hardware-efficient ansatz for variational optimization, derived from existing ansatze in the literature, that parametrizes subsets of all interactions in the Cost Hamiltonian in each layer. We treat gate orderings as a variational parameter and observe that doing so can provide significant performance boosts in experiments. We carried out experimental runs of a compilation-optimized implementation of fully-connected Sherrington-Kirkpatrick Hamiltonians on a 50-qubit linear-chain subsystem of Rigetti Aspen-M-3 transmon processor. Our results indicate that, for the best circuit designs tested, the average performance at optimized angles and gate orderings increases with circuit depth (using more parameters), despite the presence of a high level of noise. We report performance significantly better than using a random guess oracle for circuits involving up to approx 5000 two-qubit and approx 5000 one-qubit native gates. We additionally discuss various takeaways of our results toward more effective utilization of current and future quantum processors for optimization.

quant-ph↗
arXiv2023

Extending relax-and-round combinatorial optimization solvers with quantum correlations

We introduce a relax-and-round approach embedding the quantum approximate optimization algorithm (QAOA) with $p\geq 1$ layers. We show for many problems, including Sherrington-Kirkpatrick spin glasses, that at $p=1$, it is as accurate as its classical counterpart, and maintains the infinite-depth optimal performance guarantee of the QAOA. Employing a different rounding scheme, we prove the method shares the performance of the Goemans-Williamson algorithm for the maximum cut problem on certain graphs. We pave the way for an overarching quantum relax-and-round framework with performance on par with some of the best classical algorithms.

quant-ph↗
arXiv2023

Evidence for deconfined $U(1)$ gauge theory at the transition between toric code and double semion

Building on quantum Monte Carlo simulations, we study the phase diagram of a one-parameter Hamiltonian interpolating between trivial and topological Ising paramagnets in two dimensions, which are dual to the toric code and the double semion. We discover an intermediate phase with stripe order which spontaneously breaks the protecting Ising symmetry. Remarkably, we find evidence that this intervening phase is gapless due to the incommensurability of the stripe pattern and that it is dual to a $U(1)$ gauge theory exhibiting Cantor deconfinement.

cond-mat.str-el↗
arXiv2023

Navigating the noise-depth tradeoff in adiabatic quantum circuits

Adiabatic quantum algorithms solve computational problems by slowly evolving a trivial state to the desired solution. On an ideal quantum computer, the solution quality improves monotonically with increasing circuit depth. By contrast, increasing the depth in current noisy computers introduces more noise and eventually deteriorates any computational advantage. What is the optimal circuit depth that provides the best solution? Here, we address this question by investigating an adiabatic circuit that interpolates between the paramagnetic and ferromagnetic ground states of the one-dimensional quantum Ising model. We characterize the quality of the final output by the density of defects $d$, as a function of the circuit depth $N$ and noise strength $σ$. We find that $d$ is well-described by the simple form $d_\mathrm{ideal}+d_\mathrm{noise}$, where the ideal case $d_\mathrm{ideal}\sim N^{-1/2}$ is controlled by the Kibble-Zurek mechanism, and the noise contribution scales as $d_\mathrm{noise}\sim Nσ^2$. It follows that the optimal number of steps minimizing the number of defects goes as $\simσ^{-4/3}$. We implement this algorithm on a noisy superconducting quantum processor and find that the dependence of the density of defects on the circuit depth follows the predicted non-monotonous behavior and agrees well with noisy simulations. Our work allows one to efficiently benchmark quantum devices and extract their effective noise strength $σ$.

quant-ph↗
arXiv2023

Calibrating the Classical Hardness of the Quantum Approximate Optimization Algorithm

Trading fidelity for scale enables approximate classical simulators such as matrix product states (MPS) to run quantum circuits beyond exact methods. A control parameter, the so-called bond dimension $χ$ for MPS, governs the allocated computational resources and the output fidelity. Here, we characterize the fidelity for the quantum approximate optimization algorithm by the expectation value of the cost function it seeks to minimize and find that it follows a scaling law $F\bigl(\lnχ\bigr/N\bigr)$ with $N$ the number of qubits. With $\lnχ$ amounting to the entanglement that an MPS can encode, we show that the relevant variable for investigating the fidelity is the entanglement per qubit. Importantly, our results calibrate the classical computational power required to achieve the desired fidelity and benchmark the performance of quantum hardware in a realistic setup. For instance, we quantify the hardness of performing better classically than a noisy superconducting quantum processor by readily matching its output to the scaling function. Moreover, we relate the global fidelity to that of individual operations and establish its relationship with $χ$ and $N$. We sharpen the requirements for noisy quantum computers to outperform classical techniques at running a quantum optimization algorithm in speed, size, and fidelity.

quant-ph↗
arXiv2022

Multipartite entanglement in the 1-D spin-$\frac{1}{2}$ Heisenberg Antiferromagnet

Multipartite entanglement refers to the simultaneous entanglement between multiple subsystems of a many-body quantum system. While multipartite entanglement can be difficult to quantify analytically, it is known that it can be witnessed through the Quantum Fisher information (QFI), a quantity that can also be related to dynamical Kubo response functions. In this work, we first show that the finite temperature QFI can generally be expressed in terms of a static structure factor of the system, plus a correction that vanishes as $T\rightarrow 0$. We argue that this implies that the static structure factor witnesses multipartite entanglement near quantum critical points at temperatures below a characteristic energy scale that is determined by universal properties, up to a non-universal amplitude. Therefore, in systems with a known static structure factor, we can deduce finite temperature scaling of multipartite entanglement and low temperature entanglement depth without knowledge of the full dynamical response function of the system. This is particularly useful to study 1D quantum critical systems in which sub-power-law divergences can dominate entanglement growth, where the conventional scaling theory of the QFI breaks down. The 1D spin-$\frac{1}{2}$ antiferromagnetic Heisenberg model is an important example of such a system, and we show that multipartite entanglement in the Heisenberg chain diverges non-trivially as $\sim \log(1/T)^{3/2}$. We verify these predictions with calculations of the QFI using conformal field theory and matrix product state simulations. Finally we discuss the implications of our results for experiments to probe entanglement in quantum materials, comparing to neutron scattering data in KCuF$_3$, a material well-described by the Heisenberg chain.

quant-ph↗
arXiv2022

Simulating dirty bosons on a quantum computer

The physics of dirty bosons highlights the intriguing interplay of disorder and interactions in quantum systems, playing a central role in describing, for instance, ultracold gases in a random potential, doped quantum magnets, and amorphous superconductors. Here, we demonstrate how quantum computers can be used to elucidate the physics of dirty bosons in one and two dimensions. Specifically, we explore the disorder-induced delocalized-to-localized transition using adiabatic state preparation. In one dimension, the quantum circuits can be compressed to small enough depths for execution on currently available quantum computers. In two dimensions, the compression scheme is no longer applicable, thereby requiring the use of large-scale classical state vector simulations to emulate quantum computer performance. In addition, simulating interacting bosons via emulation of a noisy quantum computer allowed us to study the effect of quantum hardware noise on the physical properties of the simulated system. Our results suggest that scaling laws control how noise modifies observables versus its strength, the circuit depth, and the number of qubits. Moreover, we observe that noise impacts the delocalized and localized phases differently. A better understanding of how noise alters the genuine properties of the simulated system is essential for leveraging noisy intermediate-scale quantum devices for simulation of dirty bosons, and indeed for condensed matter systems in general.

cond-mat.dis-nn↗
arXiv2022

Spectral function of the $J_1-J_2$ Heisenberg model on the triangular lattice

Spectral probes, such as neutron scattering, are crucial for characterizing excitations in quantum many-body systems and the properties of quantum materials. Among the most elusive phases of matter are quantum spin liquids, which have no long-range order even at zero temperature and host exotic fractionalized excitations with non-trivial statistics. These phases can occur in frustrated quantum magnets, such as the paradigmatic Heisenberg model with nearest and next-nearest neighbor exchange interactions on the triangular lattice, the so-called $J_1-J_2$ model. In this work, we compute the spectral function using large scale matrix product state simulations across the three different phases of this model's phase diagram, including a quantum spin liquid phase at intermediate $J_2/J_1$. Despite a plethora of theoretical and experimental studies, the exact nature of this phase is still contested, with the dominant candidates being a gapped $\mathbb{Z}_2$, a gapless $U(1)$ Dirac, and a spinon Fermi surface quantum spin liquid state. We find a V-shaped spectrum near the center of the Brillouin zone ($Γ$ point), a key signature of a spinon Fermi surface, observed in prior neutron scattering experiments. However, we find a small gap near the $Γ$ point, ruling out such a phase. Furthermore, we find localized gapless excitations at the corner of the Brillouin zone boundary (K point) and the middle of the edge of the Brillouin zone boundary (M point), ruling out the gapped $\mathbb{Z}_2$ spin liquid phase. Our results imply that the intermediate spin liquid phase is a gapless $U(1)$ Dirac spin liquid, and provide clear signatures to detect this phase in future neutron scattering experiments.

cond-mat.str-el↗
arXiv2022

An entanglement perspective on the quantum approximate optimization algorithm

Many quantum algorithms seek to output a specific bitstring solving the problem of interest--or a few if the solution is degenerate. It is the case for the quantum approximate optimization algorithm (QAOA) in the limit of large circuit depth, which aims to solve quadratic unconstrained binary optimization problems. Hence, the expected final state for these algorithms is either a product state or a low-entangled superposition involving a few bitstrings. What happens in between the initial $N$-qubit product state $\vert 0\rangle^{\otimes N}$ and the final one regarding entanglement? Here, we consider the QAOA algorithm for solving the paradigmatic Max-Cut problem on different types of graphs. We study the entanglement growth and spread resulting from randomized and optimized QAOA circuits and find that there is a volume-law entanglement barrier between the initial and final states. We also investigate the entanglement spectrum in connection with random matrix theory. In addition, we compare the entanglement production with a quantum annealing protocol aiming to solve the same Max-Cut problems. Finally, we discuss the implications of our results for the simulation of QAOA circuits with tensor network-based methods relying on low-entanglement for efficiency, such as matrix product states.

quant-ph↗