arXiv subjects

Simone Montangero

Publications and source records attributed to Simone Montangero.

At least 37 records · Page 2Linked to original sources

arXiv2025

A new rung on the ladder: exploring topological frustration towards two dimensions

Topological frustration arises when boundary conditions impose geometric frustration in a quantum system, creating delocalized defects in the ground states and profoundly altering the low-energy properties. While previous studies have been concerned with one-dimensional systems, showing that the ground state structure can be described in terms of quasiparticle excitations, the two-dimensional setting remains unexplored. We address this gap by studying a three-legged antiferromagnetic quantum Ising ladder on a torus using tensor network methods, where topological frustration is induced by an odd number of spins along both spatial directions. Our results reveal the first instance in which topological frustration shifts the position of the quantum critical point. By studying the entanglement structure, we find that the ground state can be characterized as hosting three delocalized quasiparticles. This work builds the quasiparticle picture of topological frustration toward higher dimensions and more complex systems than those considered so far.

cond-mat.str-el↗

arXiv2025

The Augmented Tree Tensor Network Cookbook

An augmented tree tensor network (aTTN) is a tensor network ansatz constructed by applying a layer of unitary disentanglers to a tree tensor network. The disentanglers absorb a part of the system's entanglement. This makes aTTNs suitable for simulating higher-dimensional lattices, where the entanglement increases with the lattice size even for states that obey the area law. These lecture notes serve as a detailed guide for implementing the aTTN algorithms. We present a variational algorithm for ground state search and discuss the measurement of observables, and offer an open-source implementation within the Quantum TEA library. We benchmark the performance of the ground state search for different parameters and hyperparameters in the square lattice quantum Ising model and the triangular lattice Heisenberg model for up to $32 \times 32$ spins. The benchmarks identify the regimes where the aTTNs offer advantages in accuracy relative to computational cost compared to matrix product states and tree tensor networks.

quant-ph↗

arXiv2025

Many-body quantum dimerization in 2D atomic arrays

We consider a 2D atomic array coupled to different photonic environments, focusing on the half-filled excitation subspace, where strong photon interactions can give rise to complex many-body states. In particular, we demonstrate that the least radiant state in this sector is well described by a coherent superposition of all possible quantum dimer coverings: a resonating valence bond (RVB) liquid state. We discuss possible strategies to probe this exotic state, along with their limitations and challenges. Finally, we show that such a quantum dimer covering can also emerge as the ground state of the coherent Hamiltonian describing a 2D atomic array coupled to a photonic band-gap material.

quant-ph↗

arXiv2025

Constrained dynamics and confinement in the two-dimensional quantum Ising model

We investigate the dynamics of the quantum Ising model on two-dimensional square lattices up to $16 \times 16$ spins. In the ordered phase, the model is predicted to exhibit dynamically constrained dynamics, leading to confinement of elementary excitations and slow thermalization. After demonstrating the signatures of confinement, we probe the dynamics of interfaces in the constrained regime through sudden quenches of product states with domains of opposite magnetization. We find that the nature of excitations can be captured by perturbation theory throughout the confining regime, and identify the crossover to the deconfining regime. We systematically explore the effect of the transverse field on the modes propagating along flat interfaces and investigate the crossover from resonant to diffusive melting of a square of flipped spins embedded in a larger lattice.

quant-ph↗

arXiv2025

Quantum Many-Body Scarring in a Non-Abelian Lattice Gauge Theory

Quantum many-body scarring (QMBS) is an intriguing mechanism of weak ergodicity breaking that has recently spurred significant attention. Particularly prominent in Abelian lattice gauge theories (LGTs), an open question is whether QMBS nontrivially arises in non-Abelian LGTs. Here, we present evidence of robust QMBS in a non-Abelian SU(2) LGT with dynamical matter. Starting in product states that require little experimental overhead, we show that prominent QMBS arises for certain quenches, facilitated through meson and baryon-antibaryon excitations, highlighting its non-Abelian nature. The uncovered scarred dynamics manifests as long-lived coherent oscillations in experimentally accessible local observables as well as prominent revivals in the state fidelity. Our findings bring QMBS to the realm of non-Abelian LGTs, highlighting the intimate connection between scarring and gauge symmetry, and are amenable for observation in a recently proposed trapped-ion qudit quantum computer.

cond-mat.quant-gas↗

arXiv2025

Optimal sampling of tensor networks targeting wave function's fast decaying tails

We introduce an optimal strategy to sample quantum outcomes of local measurement strings for isometric tensor network states. Our method generates samples based on an exact cumulative bounding function, without prior knowledge, in the minimal amount of tensor network contractions. The algorithm avoids sample repetition and, thus, is efficient at sampling distribution with exponentially decaying tails. We illustrate the computational advantage provided by our optimal sampling method through various numerical examples, involving condensed matter, optimization problems, and quantum circuit scenarios. Theory predicts up to an exponential speedup reducing the scaling for sampling the space up to an accumulated unknown probability $ε$ from $\mathcal{O}(ε^{-1})$ to $\mathcal{O}(\log(ε^{-1}))$ for a decaying probability distribution. We confirm this in practice with over one order of magnitude speedup or multiple orders improvement in the error depending on the application. Our sampling strategy extends beyond local observables, e.g., to quantum magic.

quant-ph↗

arXiv2025

Benchmarking Quantum Red TEA on CPUs, GPUs, and TPUs

We benchmark simulations of many-body quantum systems on heterogeneous hardware platforms using CPUs, GPUs, and TPUs. We compare different linear algebra backends, e.g., NumPy versus the PyTorch, JAX, or TensorFlow libraries, as well as a mixed-precision-inspired approach and optimizations for the target hardware. Quantum Red TEA out of the Quantum TEA library specifically addresses handling tensors with different libraries or hardware, where the tensors are the building blocks of tensor network algorithms. The benchmark problem is a variational search of a ground state in an interacting model. This is a ubiquitous problem in quantum many-body physics, which we solve using tensor network methods. This approximate state-of-the-art method compresses quantum correlations which is key to overcoming the exponential growth of the Hilbert space as a function of the number of particles. We present a way to obtain speedups of a factor of 34 when tuning parameters on the CPU, and an additional factor of 2.76 on top of the best CPU setup when migrating to GPUs.

quant-ph↗

arXiv2025

Hybrid Tree Tensor Networks for quantum simulation

Hybrid Tensor Networks (hTN) offer a promising solution for encoding variational quantum states beyond the capabilities of efficient classical methods or noisy quantum computers alone. However, their practical usefulness and many operational aspects of hTN-based algorithms, like the optimization of hTNs, the generalization of standard contraction rules to an hybrid setting, and the design of application-oriented architectures have not been thoroughly investigated yet. In this work, we introduce a novel algorithm to perform ground state optimizations with hybrid Tree Tensor Networks (hTTNs), discussing its advantages and roadblocks, and identifying a set of promising applications. We benchmark our approach on two paradigmatic models, namely the Ising model at the critical point and the Toric code Hamiltonian. In both cases, we successfully demonstrate that hTTNs can improve upon classical equivalents with equal bond dimension in the classical part.

quant-ph↗

arXiv2024

Optimisation of ultrafast singlet fission in 1D rings towards unit efficiency

Singlet fission (SF) is an electronic transition that in the last decade has been under the spotlight for its applications in optoelectronics, from photovoltaics to spintronics. Despite considerable experimental and theoretical advancements, optimising SF in materials like multichromophoric systems and molecular crystals remains a challenge, due to the complexity of its analysis beyond perturbative methods. Here, we tackle the case of 1D rings, aiming to promote singlet fission and prevent its back-reaction. We study ultrafast SF non-perturbatively, by numerically solving a spin-boson model, via exact propagation and tensor network methods. By optimising over a parameter space relevant to organic molecular materials, we identify two classes of solutions that can take SF efficiency beyond 85% in the non-dissipative (coherent) regime, and to 99% when exciton-phonon interactions can be tuned. After discussing the experimental feasibility of the optimised solutions, we conclude by proposing that this approach can be extended to a wider class of optoelectronic optimisation problems.

quant-ph↗

arXiv2024

Digital quantum simulation of a (1+1)D SU(2) lattice gauge theory with ion qudits

We present a quantum simulation strategy for a (1+1)D SU(2) non-abelian lattice gauge theory with dynamical matter, a hardcore-gluon Hamiltonian Yang-Mills, tailored to a six-level trapped-ion qudit quantum processor, as recently experimentally realized. We employ a qudit encoding fulfilling gauge invariance, an SU(2) Gauss law. We discuss the experimental feasibility of generalized Mölmer-Sörensen gates used to efficiently simulate the dynamics. We illustrate how a shallow circuit with these resources is sufficient to implement scalable digital quantum simulation of the model. We also numerically show that this model, albeit simple, can dynamically manifest physically-relevant properties specific to non-abelian field theories, such as baryon excitations.

quant-ph↗

arXiv2024

Finite-temperature Rydberg arrays: quantum phases and entanglement characterization

As one of the most prominent platforms for analog quantum simulators, Rydberg atom arrays are a promising tool for exploring quantum phases and transitions. While the ground state properties of one-dimensional Rydberg systems are already thoroughly examined, we extend the analysis towards the finite-temperature scenario. For this purpose, we develop a tensor network-based numerical toolbox for constructing the quantum many-body states at thermal equilibrium, which we exploit to probe classical correlations as well as entanglement monotones. We clearly observe ordered phases continuously shrinking due to thermal fluctuations at finite system sizes. Moreover, by examining the entanglement of formation and entanglement negativity of a half-system bipartition, we numerically confirm that a conformal scaling law of entanglement extends from the zero-temperature critical points into the low-temperature regime.

quant-ph↗

arXiv2024

Optimal control transport of neutral atoms in optical tweezers at finite temperature

The transport of neutral atoms in Rydberg quantum computers is a crucial step of the initial arrangement of the grid as well as to the dynamic connectivity, recently successfully demonstrated. We study the application of optimal control and the quantum speed limit for the transport of neutral atoms in optical tweezers at finite temperatures and analyze how laser noise affects transport fidelity. Open-loop optimal control significantly enhances transport fidelity, achieving an improvement up to $89\%$ for the lowest analyzed temperature of $1\,μ$K for a distance of three micrometers. Furthermore, we simulate how the transport fidelity behaves in release-and-capture measurements, which are realizable in the experiment to estimate transport efficiency and implement closed-loop optimal control.

quant-ph↗

arXiv2024

Digital quantum simulation of lattice fermion theories with local encoding

We numerically analyze the feasibility of a platform-neutral, general strategy to perform quantum simulations of fermionic lattice field theories under open boundary conditions. The digital quantum simulator requires solely one- and two-qubit gates and is scalable since integrating each Hamiltonian term requires a finite (non-scaling) cost. The exact local fermion encoding we adopt relies on auxiliary $\mathbb{Z}_2$ lattice gauge fields by adding a pure gauge Hamiltonian term akin to the Toric Code. By numerically emulating the quantum simulator real-time dynamics, we observe a timescale separation for spin- and charge-excitations in a spin-$\frac{1}{2}$ Hubbard ladder in the $t-J$ model limit.

quant-ph↗

arXiv2024

The Role of Bases in Quantum Optimal Control

Quantum Optimal Control (QOC) supports the advance of quantum technologies by tackling its problems at the pulse level: Numerical approaches iteratively work towards a given target by parametrising the applied time-dependent fields with a finite set of variables. The effectiveness of the resulting optimisation depends on the complexity of the problem and the number of variables. We consider different parametrisations in terms of basis functions, asking whether the choice of the applied basis affects the quality of the optimisation. Furthermore, we consider strategies to choose the most suitable basis. For the comparison, we test three different randomisable bases - introducing the sinc and sigmoid bases as alternatives to the Fourier basis - on QOC problems of varying complexity. For each problem, the basis-specific convergence rates result in a unique ranking. Especially for expensive evaluations, e.g., in closed-loop, a potential speed-up by a factor of up to 10 may be crucial for the optimisation's feasibility. We conclude that a problem-dependent basis choice is an influential factor for QOC efficiency and provide advice for its approach.

quant-ph↗

arXiv2024

Simulating (2+1)D SU(2) Yang-Mills Lattice Gauge Theory at finite density with tensor networks

We numerically simulate a non-Abelian lattice gauge theory in two spatial dimensions, with tensor networks (TN), up to intermediate sizes (>30 matter sites) well beyond exact diagonalization. We focus on the SU(2) Yang-Mills model in Hamiltonian formulation, with dynamical matter and minimally truncated gauge field (hardcore gluon). Thanks to the TN sign-problem-free approach, we characterize the phase diagram of the model at zero and finite baryon number as a function of the quark bare mass and color charge. At intermediate system sizes, we detect a liquid phase of quark-pair bound-state quasiparticles (baryons), whose mass is finite towards the continuum limit. Interesting phenomena arise at the transition boundary where color-electric and color-magnetic terms are maximally frustrated: For low quark masses, we see traces of potential deconfinement, while for high masses, signatures of a possible topological order.

hep-lat↗

arXiv2024

Tensor Networks for Lattice Gauge Theories beyond one dimension: a Roadmap

Tensor network methods are a class of numerical tools and algorithms to study many-body quantum systems in and out of equilibrium, based on tailored variational wave functions. They have found significant applications in simulating lattice gauge theories approaching relevant problems in high-energy physics. Compared to Monte Carlo methods, they do not suffer from the sign problem, allowing them to explore challenging regimes such as finite chemical potentials and real-time dynamics. Further development is required to tackle fundamental challenges, such as accessing continuum limits or computations of large-scale quantum chromodynamics. In this work, we review the state-of-the-art of Tensor Network methods and discuss a possible roadmap for algorithmic development and strategies to enhance their capabilities and extend their applicability to open high-energy problems. We provide tailored estimates of the theoretical and computational resource scaling for attacking large-scale lattice gauge theories.

hep-lat↗

arXiv2024

Ab-initio tree-tensor-network digital twin for quantum computer benchmarking in 2D

Large-scale numerical simulations of the Hamiltonian dynamics of a Noisy Intermediate Scale Quantum (NISQ) computer - a digital twin - could play a major role in developing efficient and scalable strategies for tuning quantum algorithms for specific hardware. Via a two-dimensional tensor network digital twin of a Rydberg atom quantum computer, we demonstrate the feasibility of such a program. In particular, we quantify the effects of gate crosstalks induced by the van der Waals interaction between Rydberg atoms: according to an 8$\times$8 digital twin simulation based on the current state-of-the-art experimental setups, the initial state of a five-qubit repetition code can be prepared with a high fidelity, a first indicator for a compatibility with fault-tolerant quantum computing. The preparation of a 64-qubit Greenberger-Horne-Zeilinger (GHZ) state with about 700 gates yields a $99.9\%$ fidelity in a closed system while achieving a speedup of $35\%$ via parallelization.

quant-ph↗

arXiv2024

Strongly interacting photons in 2D waveguide QED

One dimensional confinement in waveguide Quantum Electrodynamics (QED) plays a crucial role to enhance light-matter interactions and to induce a strong quantum nonlinear optical response. In two or higher dimensional settings, this response is reduced since photons can be emitted within a larger phase space, opening the question whether strong photon-photon interaction can be still achieved. In this study, we positively answer this question for the case of a 2D square array of atoms coupled to the light confined into a two-dimensional waveguide. More specifically, we demonstrate the occurrence of long-lived two-photon repulsive and bound states with genuine 2D features. Furthermore, we observe signatures of these effects also in free-space atomic arrays in the form of weakly-subradiant in-band scattering resonances. Our findings provide a paradigmatic signature of the presence of strong photon-photon interactions in 2D waveguide QED.

quant-ph↗