arXiv subjects

Dries Sels

Publications and source records attributed to Dries Sels.

At least 37 records · Page 2Linked to original sources

arXiv2025

Quantum many-body simulations with PauliStrings.jl

We present the Julia package PauliStrings ( https://github.com/nicolasloizeau/PauliStrings.jl ) for quantum many-body simulations, which performs fast operations on the Pauli group by encoding Pauli strings in binary. All of the Pauli string algebra is encoded into low-level logic operations on integers, and is made efficient by various truncation methods which allow for systematic extrapolation of the results. We illustrate the effectiveness of our package by (i) performing Heisenberg time evolution through direct numerical integration and (ii) by constructing a Liouvillian Krylov space. We benchmark the results against tensor network methods, and we find our package performs favorably. In addition, we show that this representation allows for easy encoding of any geometry. We present results for chaotic and integrable spin systems in 1D as well as some examples in 2D. Currently, the main limitations are the inefficiency of representing non-trivial pure states (or other low-rank operators), as well as the need to introduce dissipation to probe long-time dynamics.

quant-ph↗

arXiv2025

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

Many-body delocalization from embedded thermal inclusion

We numerically study quantum avalanches in one-dimensional disordered spin systems by attaching two XXZ spin chains. One chain has low disorder representing a rare Griffith's region, or thermal inclusion, and the second has larger disorder, i.e., disorder larger than the observed finite-size crossover. Comparing dynamics of this system to identical systems with uniformly large disorder, we find evidence for exponentially slow thermalization (in disorder) within the many-body localized regime when the rare region is present. We observe a decay of the spin imbalance in the bulk of the large disorder region that persists to long times ($\sim10^{4}$) and find a universal behavior of the spectral function.

cond-mat.dis-nn↗

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↗

arXiv2024

Universal semiclassical dynamics in disordered two-dimensional systems

The dynamics of disordered two-dimensional systems is much less understood than the dynamics of disordered chains, mainly due to the lack of appropriate numerical methods. We demonstrate that a single-trajectory version of the fermionic truncated Wigner approximation (fTWA) gives unexpectedly accurate results for the dynamics of one-dimensional (1D) systems with moderate or strong disorder. Additionally, the computational complexity of calculations carried out within this approximation is small enough to enable studies of two-dimensional (2D) systems larger than standard fTWA. Using this method, we analyze the dynamics of interacting spinless fermions propagating on disordered 1D and 2D lattices. We find for both spatial dimensions that the imbalance exhibits a universal dependence on the rescaled time $t/ξ_W$, where in 2D the time-scale $ξ_W$ follows a stretched-exponential dependence on disorder strength.

cond-mat.stat-mech↗

arXiv2024

Platform tailored co-design of gate-based quantum simulation

The utility of near-term quantum computers and simulators is likely to rely upon software-hardware co-design, with error-aware algorithms and protocols optimized for the platforms they are run on. Here, we show how knowledge of noise in a system can be exploited to improve the design of gate-based quantum simulation algorithms. We concretely demonstrate this co-design in the context of a trapped ion quantum simulation of the dynamics of a Heisenberg spin model. Specifically, we derive a theoretical noise model describing unitary gate errors due to heating of the ions' collective motion, finding that the temporal correlations in the noise induce an optimal gate depth. We then illustrate how tailored feedforward control can be used to mitigate unitary gate errors and improve the simulation outcome. Our results provide a practical guide to the co-design of gate-based quantum simulation algorithms.

quant-ph↗

arXiv2024

Quantum enhanced Markov chains require fine-tuned quenches

Quantum-enhanced Markov chain Monte Carlo, an algorithm in which configurations are proposed through a measured quantum quench and accepted or rejected by a classical algorithm, has been proposed as a possible method for robust quantum speedup on imperfect quantum devices. While this procedure is resilient to noise and control imperfections, the potential for quantum advantage is unclear. By upper-bounding the gap of the Markov chain, we identify competing factors that limit the algorithm's performance. One needs the quantum dynamics to efficiently delocalize the system over a range of classical states, however, it is also detrimental to introduce too much entropy through the quench. Specifically, we show that in the long-time limit, the gap of the Markov chain is bounded by the inverse participation ratio of the classical states in the eigenstate basis, showing there is no advantage when quenching to an ergodic system. For the paradigmatic Sherrington-Kirkpatrick and 3-spin model, we identify the regime of optimal spectral gap scaling and link it to the system's eigenstate properties.

quant-ph↗

arXiv2024

Re-entrant phase transitions induced by localization of zero-modes

Common wisdom dictates that physical systems become less ordered when heated to higher temperature. However, several systems display the opposite phenomenon and move to a more ordered state upon heating, e.g. at low temperature piezoelectric quartz is paraelectric and it only becomes piezoelectric when heated to sufficiently high temperature. The presence, or better, the re-entrance of unordered phases at low temperature is more prevalent than one might think. Although specific models have been developed to understand the phenomenon in specific systems, a universal explanation is lacking. Here we propose a universal simple microscopic theory which predicts the existence of two critical temperatures in inhomogeneous systems, where the lower one marks the re-entrance into the less ordered phase. We show that the re-entrant phase transition is caused by disorder-induced spatial localization of the zero-mode on a finite, i.e. sub-extensive, region of the system. Specifically, this trapping of the zero-mode disconnects the fluctuations of the order parameter in distant regions of the system, thus triggering the loss of long-range order and the re-entrance into the disordered phase. This makes the phenomenon quite universal and robust to the underlying details of the model, and explains its ubiquitous observation.

cond-mat.dis-nn↗

arXiv2024

Extracting Off-Diagonal Order from Diagonal Basis Measurements

Quantum gas microscopy has developed into a powerful tool to explore strongly correlated quantum systems. However, discerning phases with topological or off-diagonal long range order requires the ability to extract these correlations from site-resolved measurements. Here, we show that a multi-scale complexity measure can pinpoint the transition to and from the bond ordered wave phase of the one-dimensional extended Hubbard model with an off-diagonal order parameter, sandwiched between diagonal charge and spin density wave phases, using only diagonal descriptors. We study the model directly in the thermodynamic limit using the recently developed variational uniform matrix product states algorithm, and draw our samples from degenerate ground states related by global spin rotations, emulating the projective measurements that are accessible in experiments. Our results will have important implications for the study of exotic phases using optical lattice experiments.

cond-mat.str-el↗

arXiv2024

Solving combinatorial optimization problems through stochastic Landau-Lifshitz-Gilbert dynamical systems

We present a method to approximately solve general instances of combinatorial optimization problems using the physical dynamics of 3d rotors obeying Landau-Lifshitz-Gilbert dynamics. Conventional techniques to solve discrete optimization problems that use simple continuous relaxation of the objective function followed by gradient descent minimization are inherently unable to avoid local optima, thus producing poor-quality solutions. Our method considers the physical dynamics of macrospins capable of escaping from local minima, thus facilitating the discovery of high-quality, nearly optimal solutions, as supported by extensive numerical simulations on a prototypical quadratic unconstrained binary optimization (QUBO) problem. Our method produces solutions that compare favorably with those obtained using state-of-the-art minimization algorithms (such as simulated annealing) while offering the advantage of being physically realizable by means of arrays of stochastic magnetic tunnel junction devices.

cond-mat.dis-nn↗

arXiv2024

Confinement in the Transverse Field Ising model on the Heavy Hex lattice

We study the emergence of confinement in the transverse field Ising model on a decorated hexagonal lattice. Using an infinite tensor network state optimised with belief propagation we show how a quench from a broken symmetry state leads to striking nonthermal behaviour underpinned by persistent oscillations and saturation of the entanglement entropy. We explain this phenomenon by constructing a minimal model based on the confinement of elementary excitations, which take the form of various flavors of hadronic quasiparticles due to the unique structure of the lattice. Our model is in excellent agreement with our numerical results. For quenches to larger values of the transverse field and/or from non-symmetry broken states, our numerical results displays the expected signatures of thermalisation: a linear growth of entanglement entropy in time, propagation of correlations and the saturation of observables to their thermal averages. These results provide a physical explanation for the unexpected simulability of a recent large scale quantum computation.

quant-ph↗

arXiv2024

Bounding speedup of quantum-enhanced Markov chain Monte Carlo

Sampling tasks are a natural class of problems for quantum computers due to the probabilistic nature of the Born rule. Sampling from useful distributions on noisy quantum hardware remains a challenging problem. A recent paper [Layden, D. et al. Nature 619, 282-287 (2023)] proposed a quantum-enhanced Markov chain Monte Carlo algorithm where moves are generated by a quantum device and accepted or rejected by a classical algorithm. While this procedure is robust to noise and control imperfections, its potential for quantum advantage is unclear. Here we show that there is no speedup over classical sampling on a worst-case unstructured sampling problem. We present an upper bound to the Markov gap that rules out a speedup for any unital quantum proposal.

quant-ph↗

arXiv2024

Efficient tensor network simulation of IBM's Eagle kicked Ising experiment

We report an accurate and efficient classical simulation of a kicked Ising quantum system on the heavy-hexagon lattice. A simulation of this system was recently performed on a 127 qubit quantum processor using noise mitigation techniques to enhance accuracy (Nature volume 618, p.~500-505 (2023)). Here we show that, by adopting a tensor network approach that reflects the geometry of the lattice and is approximately contracted using belief propagation, we can perform a classical simulation that is significantly more accurate and precise than the results obtained from the quantum processor and many other classical methods. We quantify the tree-like correlations of the wavefunction in order to explain the accuracy of our belief propagation-based approach. We also show how our method allows us to perform simulations of the system to long times in the thermodynamic limit, corresponding to a quantum computer with an infinite number of qubits. Our tensor network approach has broader applications for simulating the dynamics of quantum systems with tree-like correlations.

quant-ph↗

arXiv2023

Digital quantum simulation of NMR experiments

Simulations of nuclear magnetic resonance (NMR) experiments can be an important tool for extracting information about molecular structure and optimizing experimental protocols but are often intractable on classical computers for large molecules such as proteins and for protocols such as zero-field NMR. We demonstrate the first quantum simulation of an NMR spectrum, computing the zero-field spectrum of the methyl group of acetonitrile using four qubits of a trapped-ion quantum computer. We reduce the sampling cost of the quantum simulation by an order of magnitude using compressed sensing techniques. We show how the intrinsic decoherence of NMR systems may enable the zero-field simulation of classically hard molecules on relatively near-term quantum hardware and discuss how the experimentally demonstrated quantum algorithm can be used to efficiently simulate scientifically and technologically relevant solid-state NMR experiments on more mature devices. Our work opens a practical application for quantum computation.

quant-ph↗

arXiv2023

Variational adiabatic transport of tensor networks

We discuss a tensor network method for constructing the adiabatic gauge potential -- the generator of adiabatic transformations -- as a matrix product operator, which allows us to adiabatically transport matrix product states. Adiabatic evolution of tensor networks offers a wide range of applications, of which two are explored in this paper: improving tensor network optimization and scanning phase diagrams. By efficiently transporting eigenstates to quantum criticality and performing intermediary density matrix renormalization group (DMRG) optimizations along the way, we demonstrate that we can compute ground and low-lying excited states faster and more reliably than a standard DMRG method at or near quantum criticality. We demonstrate a simple automated step size adjustment and detection of the critical point based on the norm of the adiabatic gauge potential. Remarkably, we are able to reliably transport states through the critical point of the models we study.

quant-ph↗

arXiv2023

Asymptotic behavior of continuous weak measurement and its application to real-time parameter estimation

The asymptotic quantum trajectory of weak continuous measurement for the magnetometer is investigated. The magnetometer refers to a setup where the field-to-estimate and the measured moment are orthogonal, and the quantum state is governed by the stochastic master equation which, in addition to a deterministic part, depends on the measurement outcomes. We find that the asymptotic behavior is insensitive to the initial state in the following sense: given one realization, the quantum trajectories starting from arbitrary initial states asymptotically converge to the {\em same} realization-specific {\em pure} state. For single-qubit systems, we are able to prove this statement within the framework of Probability Theory by deriving and analyzing an effective one-dimensional stochastic equation. Numerical simulations strongly indicate that the same statement holds for multi-qubit systems. Built upon this conclusion, we consider the problem of real-time parameter estimation whose feasibility hinges on the insensitivity to the initial state, and explicitly propose and test a scheme where the quantum state and the field-to-estimate are updated simultaneously.

quant-ph↗

arXiv2023

Slowly decaying zero mode in a weakly non-integrable boundary impurity model

The transverse field Ising model (TFIM) on the half-infinite chain possesses an edge zero mode. This work considers an impurity model -- TFIM perturbed by a boundary integrability breaking interaction. For sufficiently large transverse field, but in the ordered phase of the TFIM, the zero mode is observed to decay. The decay is qualitatively different from zero modes where the integrability breaking interactions are non-zero all along the chain. It is shown that for the impurity model, the zero mode decays by relaxing to a non-local quasi-conserved operator, the latter being exactly conserved when the opposite edge of the chain has no non-commuting perturbations so as to ensure perfect degeneracy of the spectrum. In the thermodynamic limit, the quasi-conserved operator vanishes, and a regime is identified where the decay of the zero mode obeys Fermi's Golden Rule. A toy model for the decay is constructed in Krylov space and it is highlighted how Fermi's Golden Rule may be recovered from this toy model.

cond-mat.str-el↗

arXiv2023

Variational quantum dynamics of two-dimensional rotor models

We present a numerical method to simulate the dynamics of continuous-variable quantum many-body systems. Our approach is based on custom neural-network many-body quantum states. We focus on dynamics of two-dimensional quantum rotors and simulate large experimentally relevant system sizes by representing a trial state in a continuous basis and using state-of-the-art sampling approaches based on Hamiltonian Monte Carlo. We demonstrate the method can access quantities like the return probability and vorticity oscillations after a quantum quench in two-dimensional systems of up to 64 (8 $\times$ 8) coupled rotors. Our approach can be used for accurate nonequilibrium simulations of continuous systems at previously unexplored system sizes and evolution times, bridging the gap between simulation and experiment.

quant-ph↗