arXiv subjects

Enrico Rinaldi

Publications and source records attributed to Enrico Rinaldi.

At least 37 records · Page 2Linked to original sources

arXiv2026

Reinforcement Learning for Adaptive Composition of Quantum Circuit Optimisation Passes

Many quantum software development kits provide a suite of circuit optimisation passes. These passes have been highly optimised and tested in isolation. However, the order in which they are applied is left to the user, or else defined in general-purpose default pass sequences. While general-purpose sequences miss opportunities for optimisation which are particular to individual circuits, designing pass sequences bespoke to particular circuits requires exceptional knowledge about quantum circuit design and optimisation. Here we propose and demonstrate training a reinforcement learning agent to compose optimisation-pass sequences. In particular the agent's action space consists of passes for two-qubit gate count reduction used in default PyTKET pass sequences. For the circuits in our diverse test set, the (mean, median) fraction of two-qubit gates removed by the agent is $(57.7\%, \ 56.7 \%)$, compared to $(41.8 \%, \ 50.0 \%)$ for the next best default pass sequence.

quant-ph↗

arXiv2026

Deep Learning Approaches to Quantum Error Mitigation

We present a systematic investigation of deep learning methods applied to quantum error mitigation of noisy output probability distributions from measured quantum circuits. We compare different architectures, from fully connected neural networks to transformers, and we test different design/training modalities, identifying sequence-to-sequence, attention-based models as the most effective on our datasets. These models consistently produce mitigated distributions that are closer to the ideal outputs when tested on both simulated and real device data obtained from IBM superconducting quantum processing units (QPU) up to five qubits. Across several different circuit depths, our approach outperforms other baseline error mitigation techniques. We perform a series of ablation studies to examine: how different input features (circuit, device properties, noisy output statistics) affect performance; cross-dataset generalization across circuit families; and transfer learning to a different IBM QPU. We observe that generalization performance across similar devices with the same architecture works effectively, without needing to fully retrain models.

quant-ph↗

arXiv2025

A universal framework for the quantum simulation of Yang-Mills theory

We provide a universal framework for the quantum simulation of SU(N) Yang--Mills theories on fault-tolerant digital quantum computers adopting the orbifold lattice formulation. As warm-up examples, we also consider simple models, including scalar field theory and the Yang--Mills matrix model, to illustrate the universality of our formulation, which shows up in the fact that the truncated Hamiltonian can be expressed in the same simple form for any N, any dimension, and any lattice size, in stark contrast to the popular approach based on the Kogut--Susskind formulation. In all these cases, the truncated Hamiltonian can be programmed on a quantum computer using only standard tools well-established in the field of quantum computation. As a concrete application of this universal framework, we consider Hamiltonian time evolution by Suzuki--Trotter decomposition. This turns out to be a straightforward task due to the simplicity of the truncated Hamiltonian. We also provide a simple circuit structure that contains only CNOT and one-qubit gates, independent of the details of the theory investigated.

quant-ph↗

arXiv2025

Exponential improvement in quantum simulations of bosons

Hamiltonian quantum simulation of bosons on digital quantum computers requires truncating the Hilbert space to finite dimensions. The method of truncation and the choice of basis states can significantly impact the complexity of the quantum circuit required to simulate the system. For example, a truncation in the Fock basis where each boson is encoded with a register of $Q$ qubits, can result in an exponentially large number of Pauli strings required to decompose the truncated Hamiltonian. This, in turn, can lead to an exponential increase in $Q$ in the complexity of the quantum circuit. For lattice quantum field theories such as Yang-Mills theory and QCD, several Hamiltonian formulations and corresponding truncations have been put forward in recent years. There is no exponential increase in $Q$ when resorting to the orbifold lattice Hamiltonian, while we do not know how to remove the exponential complexity in $Q$ in the commonly used Kogut-Susskind Hamiltonian. Specifically, when using the orbifold lattice Hamiltonian, the continuum limit, or, in other words, the removal of the ultraviolet energy cutoff, is obtained with circuits whose resources scale like $Q$, while they scale like $\mathcal{O}(\exp(Q))$ for the Kogut-Susskind Hamiltonian: this can be seen as an exponential speed up in approaching the physical continuum limit for the orbifold lattice Hamiltonian formulation. We show that the universal framework, advocated by three of the authors (M.~H., S.~M., and E.~R.) and collaborators, provides a natural avenue to solve the exponential scaling of circuit complexity with $Q$, and it is the reason why using the orbifold lattice Hamiltonian is advantageous.

quant-ph↗

arXiv2025

Quantum Circuits for SU(3) Lattice Gauge Theory

Lattice gauge theories in varying dimensions, lattice volumes, and truncations offer a rich family of targets for Hamiltonian simulation on quantum devices. In return, formulating quantum simulations can provide new ways of thinking about the quantum structure of gauge theories. In this work, we consider pure $SU(3)$ gauge theory in two and three spatial dimensions in a streamlined version of the electric basis. We use a formulation of the theory that balances locality of the Hamiltonian and size of the gauge-invariant state space, and we classically pre-compute dictionaries of plaquette operator matrix elements for use in circuit construction. We build circuits for simulating time evolution on arbitrary lattice volumes, spanning circuits suitable for NISQ era hardware to future fault-tolerant devices. Relative to spin models, time evolution in lattice gauge theories involves more complex local unitaries, and the Hilbert space of all quantum registers may have large unphysical subspaces. Based on these features, we develop general, volume-scalable tools for optimizing circuit depth, including pruning and fusion algorithms for collections of large multi-controlled unitaries. We describe scalings of quantum resources needed to simulate larger circuits and some directions for future algorithmic development.

hep-lat↗

arXiv2025

Quantum Relational Knowledge Distillation

Knowledge distillation (KD) is a widely adopted technique for compressing large models into smaller, more efficient student models that can be deployed on devices with limited computational resources. Among various KD methods, Relational Knowledge Distillation (RKD) improves student performance by aligning relational structures in the feature space, such as pairwise distances and angles. In this work, we propose Quantum Relational Knowledge Distillation (QRKD), which extends RKD by incorporating quantum relational information. Specifically, we map classical features into a Hilbert space, interpret them as quantum states, and compute quantum kernel values to capture richer inter-sample relationships. These quantum-informed relations are then used to guide the distillation process. We evaluate QRKD on both vision and language tasks, including CNNs on MNIST and CIFAR-10, and GPT-2 on WikiText-2, Penn Treebank, and IMDB. Across all benchmarks, QRKD consistently improves student model performance compared to classical RKD. Importantly, both teacher and student models remain classical and deployable on standard hardware, with quantum computation required only during training. This work presents the first demonstration of quantum-enhanced knowledge distillation in a fully classical deployment setting.

quant-ph↗

arXiv2025

Variational Monte Carlo with Neural Network Quantum States for Yang-Mills Matrix Model

We apply the variational Monte Carlo method based on neural network quantum states, using a neural autoregressive flow architecture as our ansatz, to determine the ground state wave function of the bosonic SU($N$) Yang-Mills-type two-matrix model at strong coupling. Previous literature hinted at the inaccuracy of such an approach at strong coupling. In this work, the accuracy of the results is tested using lattice Monte Carlo simulations: we benchmark the expectation value of the energy of the ground state for system sizes $N$ that are beyond brute-force exact diagonalization methods. We observe that the variational method with neural network states reproduces the right ground state energy when the width of the network employed in this work is sufficiently large. We confirm that the correct result is obtained for $N=2$ and $3$, while obtaining a precise value for $N=4$ requires more resources than the amount available for this work.

hep-th↗

arXiv2025

Simulating sparse SYK model with a randomized algorithm on a trapped-ion quantum computer

The Sachdev-Ye-Kitaev (SYK) model describes a strongly correlated quantum system that shows a strong signature of quantum chaos. Due to its chaotic nature, the simulation of real-time dynamics becomes quickly intractable by means of classical numerics, and thus, quantum simulation is deemed to be an attractive alternative. Nevertheless, quantum simulations of the SYK model on noisy quantum processors are severely limited by the complexity of its Hamiltonian. In this work, we simulate the real-time dynamics of a sparsified version of the SYK model with 24 Majorana fermions on a trapped-ion quantum processor. We adopt a randomized quantum algorithm, TETRIS, and develop an error mitigation technique tailored to the algorithm. Leveraging the hardware's high-fidelity quantum operations and all-to-all connectivity of the qubits, we successfully calculate the Loschmidt amplitude for sufficiently long times so that its decay is observed. Based on the experimental and further numerical results, we assess the future possibility of larger-scale simulations of the SYK model by estimating the required quantum resources. Moreover, we present a scalable mirror-circuit benchmark based on the randomized SYK Hamiltonian and the TETRIS algorithm, which we argue provides a better estimate of the decay of fidelity for local observables than standard mirror-circuits.

quant-ph↗

arXiv2025

Noise resilience of deterministic analog combinatorial optimization solvers

Several continuous dynamical systems have recently been proposed as special-purpose analog computers designed to solve combinatorial optimization problems such as $k$-SAT or the Ising problem. While combinatorial optimization problems are known to be NP-hard, and thus scale, in the worst case, exponentially with the problem size, these analog solvers promise substantial speed-up and scaling advantages in finding the solution. The underlying algorithms, which can be cast in the form of differential equations, generically involve highly chaotic dynamics and thus assume that the system variables can be processed with, in principle, arbitrary precision. However, both actual physical systems as well as finite digital machines, which are used to virtually emulate the dynamics, can process the evolution only with finite precision, be it because of intrinsic noise or because of limited precision in number representation. We investigate the impact of such noise on the solution-finding capability. To this end, we focus on two representative analog solvers, designed to address the Ising problem and the $k$-SAT problem, respectively. Our numerical analysis reveals that the ability of these algorithms to find solutions exhibits a threshold behavior under the addition of noise, where the solution-finding capability remains mostly uncompromised below a noise threshold, while it rapidly deteriorates above the threshold. As we show, these noise tolerance thresholds decrease with the problem size, following an approximate algebraic scaling. This allows us to infer principal limits on the problem sizes that can be efficiently tackled with these solvers under given noise levels.

nlin.CD↗

arXiv2025

The density of states method for symplectic gauge theories at finite temperature

We study the finite-temperature behaviour of the $Sp(4)$ Yang-Mills lattice theory in four dimensions, by applying the Logarithmic Linear Relaxation (LLR) algorithm. We demonstrate the presence of coexisting (metastable) phases, when the system is in the proximity of the transition. We measure observables such as the free energy, the expectation value of the plaquette operator and of the Polyakov loop, as well as the specific heat, and the Binder cumulant. We use these results to obtain a high-precision measurement of the critical coupling at the confinement-deconfinement transition, and assess its systematic uncertainty, for one value of the lattice extent in the time direction. Furthermore, we perform an extensive study of the finite-volume behaviour of the lattice system, by repeating the measurements for fixed lattice time extent, while increasing the spatial size of the lattice. We hence characterise the first-order transition on the lattice, and present the first results in the literature on this theory for the infinite volume extrapolation of lattice quantities related to latent heat and interface tension. Gauge theories with $Sp(4)$ group have been proposed as new dark sectors to provide a fundamental origin for the current phenomenological evidence of dark matter. A phase transition at high temperature, in such a new dark sector, occurring in the early universe, might have left a relic stochastic background of gravitational waves. Our results represent a milestone toward establishing whether such a new physics signal is detectable in future experiments, as they enter the calculation of the parameters, $α$ and $β$, controlling the power spectrum of gravitational waves. We also outline the process needed in the continuum extrapolation of our measurements, and test its feasibility on one additional choice of temporal extent of the lattice.

hep-lat↗

arXiv2025

Gamma-ray Bursts as Distance Indicators by a Statistical Learning Approach

Gamma-ray bursts (GRBs) can be probes of the early universe, but currently, only 26% of GRBs observed by the Neil Gehrels Swift Observatory GRBs have known redshifts ($z$) due to observational limitations. To address this, we estimated the GRB redshift (distance) via a supervised statistical learning model that uses optical afterglow observed by Swift and ground-based telescopes. The inferred redshifts are strongly correlated (a Pearson coefficient of 0.93) with the observed redshifts, thus proving the reliability of this method. The inferred and observed redshifts allow us to estimate the number of GRBs occurring at a given redshift (GRB rate) to be 8.47-9 $yr^{-1} Gpc^{-1}$ for $1.9<z<2.3$. Since GRBs come from the collapse of massive stars, we compared this rate with the star formation rate highlighting a discrepancy of a factor of 3 at $z<1$.

astro-ph.HE↗

arXiv2025

Toward QCD on Quantum Computer: Orbifold Lattice Approach

We propose an orbifold lattice formulation of QCD suitable for quantum simulations. We show explicitly how to encode gauge degrees of freedom into qubits using noncompact variables, and how to write down a simple truncated Hamiltonian in the coordinate basis. We show that SU(3) gauge group variables and quarks in the fundamental representation can be implemented straightforwardly on qubits, for arbitrary truncation of the gauge manifold.

hep-th↗

arXiv2024

Analysis of the confinement string in (2 + 1)-dimensional Quantum Electrodynamics with a trapped-ion quantum computer

Compact lattice Quantum Electrodynamics is a complex quantum field theory with dynamical gauge and matter fields and it has similarities with Quantum Chromodynamics, in particular asymptotic freedom and confinement. We consider a (2+1)-dimensional lattice discretization of Quantum Electrodynamics with the inclusion of dynamical fermionic matter. We define a suitable quantum algorithm to measure the static potential as a function of the distance between two charges on the lattice and we use a variational quantum calculation to explore the Coulomb, confinement and string breaking regimes. A symmetry-preserving and resource-efficient variational quantum circuit is employed to prepare the ground state of the theory at various values of the coupling constant, corresponding to different physical distances, allowing the accurate extraction of the static potential from a quantum computer. We demonstrate that results from quantum experiments on the Quantinuum H1-1 trapped-ion device and emulator, with full connectivity between qubits, agree with classical noiseless simulations using circuits with 10 and 24 qubits. Moreover, we visualize the electric field flux configurations that mostly contribute in the wave-function of the quantum ground state in the different regimes of the potential, thus giving insights into the mechanisms of confinement and string breaking. These results are a promising step forward in the grand challenge of solving higher dimensional lattice gauge theory problems with quantum computing algorithms.

hep-lat↗

arXiv2024

Simulating matrix models with tensor networks

Matrix models, as quantum mechanical systems without explicit spatial dependence, provide valuable insights into higher-dimensional gauge and gravitational theories, especially within the framework of string theory, where they can describe quantum black holes via the holographic principle. Simulating these models allows for exploration of their kinematic and dynamic properties, particularly in parameter regimes that are analytically intractable. In this study, we examine the potential of tensor network techniques for such simulations. Specifically, we construct ground states as matrix product states and analyse features such as their entanglement structure.

hep-th↗

arXiv2024

Updates on the density of states method in finite temperature symplectic gauge theories

First-order phase transitions in the early universe have rich phenomenological implications, such as the production of a potentially detectable signal of stochastic relic background gravitational waves. The hypothesis that new, strongly coupled dynamics, hiding in a new dark sector, could be detected in this way, via the telltale signs of its confinement/deconfinement phase transition, provides a fascinating opportunity for interdisciplinary synergy between lattice field theory and astro-particle physics. But its viability relies on completing the challenging task of providing accurate theoretical predictions for the parameters characterising the strongly coupled theory. Density of states methods, and in particular the linear logarithmic relaxation (LLR) method, can be used to address the intrinsic numerical difficulties that arise due the meta-stable dynamics in the vicinity of the critical point. For example, it allows one to obtain accurate determinations of thermodynamic observables that are otherwise inaccessible, such as the free energy. In this contribution, we present an update on results of the analysis of the finite temperature deconfinement phase transition in a pure gauge theory with a symplectic gauge group, $Sp(4)$, by using the LLR method. We present a first analysis of the properties of the transition in the thermodynamic limit, and provide a road map for future work, including a brief preliminary discussion that will inform future publications.

hep-lat↗

arXiv2024

Learning to generate high-dimensional distributions with low-dimensional quantum Boltzmann machines

In recent years, researchers have been exploring ways to generalize Boltzmann machines (BMs) to quantum systems, leading to the development of variations such as fully-visible and restricted quantum Boltzmann machines (QBMs). Due to the non-commuting nature of their Hamiltonians, restricted QBMs face trainability issues, whereas fully-visible QBMs have emerged as a more tractable option, as recent results demonstrate their sample-efficient trainability. These results position fully-visible QBMs as a favorable choice, offering potential improvements over fully-visible BMs without suffering from the trainability issues associated with restricted QBMs. In this work, we show that low-dimensional, fully-visible QBMs can learn to generate distributions typically associated with higher-dimensional systems. We validate our findings through numerical experiments on both artificial datasets and real-world examples from the high energy physics problem of jet event generation. We find that non-commuting terms and Hamiltonian connectivity improve the learning capabilities of QBMs, providing flexible resources suitable for various hardware architectures. Furthermore, we provide strategies and future directions to maximize the learning capacity of fully-visible QBMs.

quant-ph↗

arXiv2024

The computational power of random quantum circuits in arbitrary geometries

Empirical evidence for a gap between the computational powers of classical and quantum computers has been provided by experiments that sample the output distributions of two-dimensional quantum circuits. Many attempts to close this gap have utilized classical simulations based on tensor network techniques, and their limitations shed light on the improvements to quantum hardware required to frustrate classical simulability. In particular, quantum computers having in excess of $\sim 50$ qubits are primarily vulnerable to classical simulation due to restrictions on their gate fidelity and their connectivity, the latter determining how many gates are required (and therefore how much infidelity is suffered) in generating highly-entangled states. Here, we describe recent hardware upgrades to Quantinuum's H2 quantum computer enabling it to operate on up to $56$ qubits with arbitrary connectivity and $99.843(5)\%$ two-qubit gate fidelity. Utilizing the flexible connectivity of H2, we present data from random circuit sampling in highly connected geometries, doing so at unprecedented fidelities and a scale that appears to be beyond the capabilities of state-of-the-art classical algorithms. The considerable difficulty of classically simulating H2 is likely limited only by qubit number, demonstrating the promise and scalability of the QCCD architecture as continued progress is made towards building larger machines.

quant-ph↗

arXiv2024

A model of randomly-coupled Pauli spins

We construct a model of Pauli spin operators with all-to-all 4-local interactions by replacing Majorana fermions in the SYK model with spin operators. Equivalently, we replace fermions with hard-core bosons. We study this model numerically and compare the properties with those of the SYK model. We observe a striking quantitative coincidence between the spin model and the SYK model, which suggests that this spin model is strongly chaotic and, perhaps, can play some role in holography. We also discuss the path-integral approach with multi-local fields and the possibility of quantum simulations. This model may be an interesting target for quantum simulations because Pauli spins are easier to implement than fermions on qubit-based quantum devices.

hep-th↗