arXiv subjects

Dries Sels

Publications and source records attributed to Dries Sels.

At least 19 recordsLinked to original sources

arXiv2026

Absence of quantum advantage for approximate spin glass optimization

We perform a semiclassical, large-spin S, analysis of the quantum approximate optimization algorithm (QAOA) on the Sherrington-Kirkpatrick (SK) model, using the truncated Wigner approximation. Fixing the QAOA angles to their previously determined optimal S=1/2 values, we observe a non-monotonic dependence of the final energy on the spin. At small S the semiclassics is dominated by noise, while the large-S limit is constrained by the exponential growth of the initial fluctuations. For a depth-p QAOA one achieves the optimal balance at S of order p, resulting in a convergence of the final energy to the Parisi value like log(p)/p. We find that the semiclassics slightly outperforms the true spin-1/2 QAOA, and thus suggest they both converge to the Parisi value in the same way. Finally, removing all the initial noise, and re-optimizing the parameters to account for that change, results in superior performance with 1/p convergence.

quant-ph↗

arXiv2026

Truncated Wigner dynamics of biclique quantum spin glasses

Quantum spin glasses are often considered testbeds for studying quantum optimization algorithms and as such have been the subject of various quantum advantage claims. Here we investigate the near adiabatic dynamics of biclique quantum spin glasses within the (discrete) truncated Wigner approximation (TWA). Benchmarks on small systems show that TWA recovers sample-to-sample fluctuations of the Edwards-Anderson order parameter, over a wide range of annealing times, with increasing fidelity when the system size increases. We extract critical exponents from the Binder cumulant in line with theoretical expectations, reproducing recent quantum experiments. The computational cost of the method is minimal and it can easily be applied to tens of thousands of qubits.

cond-mat.dis-nn↗

arXiv2026

Tensor network surrogate models for variational quantum computation

We adopt a two-dimensional tensor-network (TN) ansatz to simulate variational quantum algorithms on two-dimensional qubit architectures, demonstrating its capability to accurately simulate deep circuits through the Quantum Approximate Optimization Algorithm (QAOA) applied to Ising spin-glass problems on heavy-hexagonal and square lattices. For heavy-hexagonal problems with up to three-body interactions, parameters trained on small instances and transferred to systems an order of magnitude larger improve the sampled energy distribution only up to intermediate depths, indicating a fundamental limit of parameter concentration as a transfer strategy. By extending the training itself with TN simulations on larger system sizes, we avoid local minima and obtain lower-energy samples. Analyses of entanglement growth and importance sampling show that the simulation remains classically feasible with moderate bond dimension. We find that parameter concentration also persists on square lattices, albeit at substantially higher computational cost to perform reliable sampling. Overall, our TN framework not only provides an efficient and controlled framework for benchmarking variational quantum algorithms on two-dimensional lattices, but also serves as an effective surrogate model for training variational algorithms.

quant-ph↗

arXiv2026

Variational Iterative Rotation Algorithm: Combinatorial Optimization with Classical Kicked Tops

We investigate a classical formulation of the Quantum Approximate Optimization Algorithm (QAOA), realized as a Hamiltonian dynamical system of classical kicked tops, which we call the Variational Iterative Rotation Algorithm (VIRAL). The variational parameters are the transverse and longitudinal rotation angles at each of the p layers of the circuit. We find that VIRAL outperforms QAOA on the canonical Sherrington-Kirkpatrick spin-glass benchmark at all circuit depths, with the energy density converging to the ground state value linearly in 1/p. For large circuit depths, the optimized dynamics follows a Floquet protocol in which a pitchfork bifurcation destabilizes the equatorial fixed point and drives the spins toward polar Ising configurations. Our results demonstrate that the effectiveness of QAOA-like protocols derives primarily from their underlying iterative rotation structure, and that a classical implementation of it outperforms its quantum counterpart. We further elucidate its efficiency by reducing the many-body classical evolution to an effective Landau-Lifshitz dynamics for a single spin in a stochastic magnetic field. In this picture, the covariance matrix of the effective field reveals a nearly rank-one structure in which a single mode dominates the stochastic dynamics. In contrast, quantum fluctuations make the noise covariance of the effective quantum model of higher rank, hampering the control of the system. We propose nanometer-scale magnetic tunnel junctions as a natural physical platform for implementing VIRAL, where spin rotations can be realized using magnetic fields and spin torques.

cond-mat.dis-nn↗

arXiv2026

Adiabatic dressing of quantum enhanced Markov chains

Quantum-enhanced Markov chain Monte Carlo, a hybrid quantum-classical algorithm in which configurations are proposed by a quantum proposer and accepted or rejected by a classical algorithm, has been introduced as a possible method for robust quantum speedup. Previous work has identified competing factors that limit the algorithm's performance: the quantum dynamics should delocalize the system across a range of classical states to propose configurations beyond the reach of simple classical updates, whereas excessive delocalization produces configurations unlikely to be accepted, slowing the chain's convergence. Here, we show that controlling the degree of delocalization by adiabatically dressing the quench protocol can significantly enhance the Markov gap in paradigmatic spin-glass models.

quant-ph↗

arXiv2026

Counterdiabatic Hamiltonian Monte Carlo

Hamiltonian Monte Carlo (HMC) is a state of the art method for sampling from distributions with differentiable densities, but can converge slowly when applied to challenging multimodal problems. Running HMC with a time varying Hamiltonian, in order to interpolate from an initial tractable distribution to the target of interest, can address this problem. In conjunction with a weighting scheme to eliminate bias, this can be viewed as a special case of Sequential Monte Carlo (SMC) sampling \cite{doucet2001introduction}. However, this approach can be inefficient, since it requires slow change between the initial and final distribution. Inspired by \cite{sels2017minimizing}, where a learned \emph{counterdiabatic} term added to the Hamiltonian allows for efficient quantum state preparation, we propose \emph{Counterdiabatic Hamiltonian Monte Carlo} (CHMC), which can be viewed as an SMC sampler with a more efficient kernel. We establish its relationship to recent proposals for accelerating gradient-based sampling with learned drift terms, and demonstrate on simple benchmark problems.

stat.ML↗

arXiv2026

Reinforcement learning for path integrals in quantum statistical physics

Machine learning is rapidly finding its way into the field of computational quantum physics. One of the most popular and widely studied approaches in this direction is to use neural networks to model quantum states (NQS) in the Hamiltonian formulation of quantum mechanics. However, an alternative angle of attack to leverage machine learning in physics is through the path integral formulation, which has so far received far more limited attention. In this paper, we explore how reinforcement learning can be used to compute a class of Euclidean path integrals that yield the thermal density matrix of a quantum system, thereby enabling the computation of the free energy or other thermal expectation values. In particular, we propose a two-step approach with the unique feature that after a variational approximation for a quantity is obtained in a first step, it can then be used to efficiently compute the exact result in a second step. We benchmark this method on several simple systems and then apply it to the quantum rotor chain.

quant-ph↗

arXiv2026

Switching Characteristics of Electrically Connected Stochastically Actuated Magnetic Tunnel Junction Nanopillars

We investigate the stochastic dynamics of nanoscale perpendicular magnetic tunnel junctions (pMTJs) and the correlations that arise when they are electrically coupled. Individual junctions exhibit thermally activated spin-transfer torque switching with transition probabilities that are well described by a Poisson process. When two junctions are connected in parallel, circuit-mediated redistribution of voltages that occurs in real time as the junction resistances change leads to correlated switching behavior. A minimal stochastic model based on single-junction statistical switching properties and Kirchhoff's laws captures the coupled switching probabilities, while a Markov-chain formalism describes nonequilibrium steady states under multi-pulse driving. Further, these circuit-mediated interactions can be mapped onto the parameters of an Ising Hamiltonian, providing an interpretation in terms of effective spin-spin interactions. Our results demonstrate how simple electrical connections can generate Ising-like couplings and tunable stochastic dynamics in nanoscale magnets.

cond-mat.mes-hall↗

arXiv2025

Less is more: subspace reduction for counterdiabatic driving of Rydberg atom arrays

This study explores the use of subspace methods in combination with counterdiabatic driving in a Rydberg atom system to solve the Maximum Independent Set (MIS) problem. Although exact counterdiabatic driving offers excellent performance, it comes at an unscalable computational cost. In this work, we demonstrate that counterdiabatic driving can be significantly improved by restricting the analysis to a relevant subspace of the system. We first show that both direct diagonalization and the Krylov method for obtaining the counterdiabatic matrix can be accelerated through the use of subspace techniques, while still maintaining strong performance. We then demonstrate that the cost function used in the standard Krylov method can be further optimized by employing a subspace-based cost function. These findings open up new possibilities for applying counterdiabatic driving in a practical and efficient manner to a variety of quantum systems.

quant-ph↗

arXiv2025

Anderson localization: A view from Krylov space

The Krylov subspace expansion is a workhorse method for sparse numerics that has been increasingly explored as source of physical insight into many-body dynamics in recent years. In this work we revisit the venerable Anderson model of localization in dimensions $d=1, 2, 3, 4$ to construct local integrals of motion (LIOM) in Krylov space. These appear as zero eigenvalue edge states of an effective hopping problem in the Krylov superoperator subspace and can be analytically constructed given the Lanczos coefficients. We exploit this idea, focusing on $d=3$, to study the manifestation of the disorder driven Anderson transition in the anatomy of LIOMs. We find that the increasing complexity of the Krylov operators results in a suppression of the fluctuations of the Lanczos coefficients. As such, one can study the phenomenology of the integrals of motion in the disorder averaged Krylov chain. We find edge states localized on vanishing fraction of Krylov space (of dimension $D_K=V^2$ for cubes of volume $V$), both in localized and extended phases. Importantly, in the localized phase, disorder induces powerlaw decaying dimerization in the (Krylov) hopping problem, producing stretched exponential decay of the LIOMs in Krylov space with a stretching exponent $1/2d$. Metallic LIOMs are completely delocalized albeit across only $\propto \sqrt{D_K}$ states. Critical LIOMs exhibit powerlaw decay with an exponent matching the expected value of $0.29$.

cond-mat.dis-nn↗

arXiv2025

Adiabatic transport of neural network quantum states

Variational methods have offered controllable and powerful tools for capturing many-body quantum physics for decades. The recent introduction of expressive neural network quantum states has enabled the accurate representation of a broad class of complex wavefunctions for many Hamiltonians of interest. We introduce a first-principles method for building neural network representations of many-body excited states by adiabatically continuing eigenstates of simple Hamiltonians into the strongly correlated regime. With controlled access to the full many-body gap, we obtain accurate estimates of critical exponents. Successive eigenstate estimates can be run entirely in parallel, enabling precise targeting of excited-state properties without reference to the rest of the spectrum, opening the door to large-scale numerical investigations of universal properties of entire phases of matter.

quant-ph↗

arXiv2025

Double descent: When do neural quantum states generalize?

Neural quantum states (NQS) provide flexible and compact wavefunction parameterizations for numerical studies of quantum many-body physics. In particular, NQS aim to circumvent the exponential scaling of the Hilbert space by compressing quantum many-body wavefunctions with a tractable amount of parameters. While inspired by deep learning, it remains unclear to what extent NQS share characteristics with neural networks used for standard machine learning tasks. We demonstrate that, in a simplified supervised setting, NQS exhibit the double descent phenomenon, a key feature of modern deep learning, where generalization worsens as network size increases before improving again in an overparameterized regime. Notably, we find the second descent to occur only for network sizes much larger than the Hilbert space dimension, i.e. network sizes that are out of reach for problems of practical interest. Within our setting, this observation places typical NQS in the underparameterized regime. We also observe that the optimal network size in the underparameterized regime depends on the number of unique training samples. While the double descent phenomenon does indeed translate to the NQS setting, potential practical consequences of our findings point more towards the need for symmetry-aware, physics-informed architecture design, rather than directly adopting machine learning heuristics.

cond-mat.dis-nn↗

arXiv2025

Time-optimal single-scalar control on a qubit of unitary dynamics

Optimal control theory is applied to analyze the time-optimal solution with a single scalar control knob in a two-level quantum system without quantum decoherence. Emphasis is \change{placed} on the dependence on the maximum control strength $u_\text{max}$. General constraints on the optimal protocol are derived and used to rigorously parameterize the time-optimal solution. Two concrete problems are investigated. For generic state preparation problems, both multiple bang-bang and bang-singular-bang are legitimate and should be considered. Generally, the optimal is bang-bang for small $u_\text{max}$, and there exists a state-dependent critical amplitude above which singular control emerges. For the X-gate operation of a qubit, the optimal protocol \change{is exclusively} multiple bang-bang. The minimum gate time is about 80\% of that based on the resonant Rabi $\pi$-pulse over a wide range of control strength; in the $u_\text{max} \rightarrow 0$ limit this ratio is derived to be $\pi/4$. To develop practically feasible protocols, we present methods to smooth the abrupt changes in the bang-bang control while preserving perfect gate fidelity. \change{The presence of bang-bang segments in the time-optimal protocol} indicates that the high-frequency components and a full calculation (instead of the commonly adopted Rotating Wave Approximation) are essential for the ultimate quantum speed limit.

quant-ph↗

arXiv2025

Opening Krylov space to access all-time dynamics via dynamical symmetries

Solving short and long time dynamics of closed quantum many-body systems is one of the main challenges of both atomic and condensed matter physics. For locally interacting closed systems, the dynamics of local observables can always be expanded into (pseudolocal) eigenmodes of the Liouvillian, so called dynamical symmetries. They come in two classes - transient operators, which decay in time and perpetual operators, which either oscillate forever or stay the same (conservation laws). These operators provide a full characterization of the dynamics of the system. Deriving these operators, apart from a very limited class of models, has not been possible. Here, we present a method to numerically and analytically derive some of these dynamical symmetries in infinite closed systems by introducing a naturally emergent open boundary condition on the Krylov chain. This boundary condition defines a partitioning of the Krylov space into system and environment degrees of freedom, where non-local operators make up an effective bath for the local operators. We demonstrate the practicality of the method on some numerical examples and derive analytical results in two idealized cases. Our approach lets us directly relate the operator growth hypothesis to thermalization and exponential decay of observables in chaotic systems.

quant-ph↗

arXiv2025

Dynamics of disordered quantum systems with two- and three-dimensional tensor networks

Large scale quantum annealing dynamics of Ising spin glasses were recently implemented on D-Wave's Advantage$2$ system on a range of lattices. Following extensive comparison to existing numerical methods, these experiments were claimed to be beyond the reach of classical computation. Here, we simulate these spin glass models with lattice-specific tensor networks, using belief propagation (BP) to keep up with the entanglement generated during the time evolution and then extracting expectation values with more sophisticated variants of BP. We find that state-of-the-art accuracies can be achieved with modest computational resources. Moreover, our results are scalable in both two and three dimensions, which we leverage to verify universal Kibble-Zurek physics on systems involving hundreds of qubits.

quant-ph↗

arXiv2025

Counterdiabatic Driving with Performance Guarantees

Counterdiabatic (CD) driving has the potential to speed up adiabatic quantum state preparation by suppressing unwanted excitations. However, existing approaches either require intractable classical computations or are based on approximations which do not have performance guarantees. We propose and analyze a non-variational, system-agnostic CD expansion method and analytically show that it converges exponentially quickly in the expansion order. In finite systems, the required resources scale inversely with the spectral gap, which we argue is asymptotically optimal. To extend our method to the thermodynamic limit and suppress errors stemming from high-frequency transitions, we leverage finite-time adiabatic protocols. In particular, we show that a time determined by the quantum speed limit is sufficient to prepare the desired ground state, without the need to optimize the adiabatic trajectory. Numerical tests of our method on the quantum Ising chain show that our method can outperform state-of-the-art variational CD approaches.

quant-ph↗

arXiv2024

Nonperturbative decay of bipartite discrete time crystals

We study prethermal time-crystalline order in periodically driven quantum Ising models on disorder-free decorated lattices. Using a tensor network ansatz for the state which reflects the geometry of a unit cell of the lattice, we show through finite entanglement scaling that the system has an exponentially long-lived subharmonic response in the thermodynamic limit, which decays nonperturbatively in deviations from a perfect periodic drive. The resulting prethermal discrete time crystal is not only stable to imperfections in the transverse field, but also exhibits a bipartite rigidity to generic perturbations in the longitudinal field. We call this state a bipartite discrete time crystal and reveal a rich prethermal phase diagram, including multiple regions of bipartite time-crystalline order, uniform time-crystalline order and thermalization, with boundaries depending delicately on the topology of the decorated lattice. Our results thus uncover a variety of time crystals which may be realized on current digital quantum processors and analog quantum simulators.

quant-ph↗

arXiv2024

A Toffoli Gadget for Magnetic Tunnel Junctions Boltzmann Machines

Magnetic Tunnel Junctions (MTJs) are of great interest for non-conventional computing applications. The Toffoli gate is a universal reversible logic gate, enabling the construction of arbitrary boolean circuits. Here, we present a proof-of-concept construction of a gadget which encodes the Toffoli gate's truth table into the ground state of coupled uniaxial nanomagnets that could form the free layers of perpendicularly magnetized MTJs. This construction has three input bits, three output bits, and one ancilla bit. We numerically simulate the seven macrospins evolving under the stochastic Landau-Lifshitz-Gilbert (s-LLG) equation. We investigate the effect of the anisotropy-to-exchange-coupling strength ratio $H_A/H_\text{ex}$ on the working of the gadget. We find that for $H_A/H_\text{ex} \lesssim 0.93$, the spins evolve to the Toffoli gate truth table configurations under LLG dynamics alone, while higher $H_A/H_\text{ex}$ ratios require thermal annealing due to suboptimal metastable states. Under our chosen annealing procedure, the s-LLG simulation with thermal annealing achieves a 100% success rate up to $H_A/H_\text{ex}\simeq3.0$. The feasibility of constructing MTJ-free-layer-based Toffoli gates highlights their potential in designing new types of MTJ-based circuits.

cond-mat.mes-hall↗