arXiv subjects

Karl Jansen

Publications and source records attributed to Karl Jansen.

At least 19 recordsLinked to original sources

arXiv2026

Data Free Training of Diffusion Models for Lattice Field Theories

Sampling equilibrium field configurations remains a major computational bottleneck in lattice field theory, motivating the development of generative samplers that can produce independent configurations. Diffusion models are promising for this purpose, but their standard denoising score matching objective requires samples from the target distribution, seemingly reintroducing the original sampling problem. Here, we show that diffusion models can instead be trained from their own generated samples using the target score identity, provided access to the unnormalized probability density. Importance-weighted formulations of this identity yield a consistent target throughout training, while unweighted variants define a self-consistent fixed-point training scheme. We benchmark the different approaches in two-dimensional $ϕ^4$ theory and identify effective choices that enable efficient training and sampling across the symmetric, critical, and broken phases. Ultimately, our data-free training approach achieves comparable performance to training on HMC reference data.

hep-lat↗

arXiv2026

Quantum convolutional neural networks for jet images classification

Recently, interest in quantum computing has significantly increased, driven by its potential advantages over classical techniques. Quantum machine learning (QML) exemplifies one of the important quantum computing applications that are expected to surpass classical machine learning in a wide range of instances. This paper addresses the performance of QML in the context of high-energy physics (HEP). As an example, we focus on the top-quark tagging, for which classical convolutional neural networks (CNNs) have been effective but fall short in accuracy when dealing with highly energetic jet images. In this paper, we use a quantum convolutional neural network (QCNN) for this task and compare its performance with CNN using a classical noiseless simulator. We compare various setups for the QCNN, varying the convolutional circuit, type of encoding, loss function, and batch sizes. For every quantum setup, we design a similar setup to the corresponding classical model for a fair comparison. Our results indicate that, using a classical simulator, QCNN with proper setups tend to perform better than their CNN counterparts, especially when the convolution block has a lower number of parameters. For the higher parameter regime, the QCNN circuit was adjusted according to the dimensional expressivity analysis (DEA) to lower the parameter count while preserving its optimal structure. The DEA circuit demonstrated improved results over the comparable classical CNN model.

quant-ph↗

arXiv2026

Multilevel Plaquette-Space Sampling for Lattice Gauge Theories with Local Constraint Solves

Lattice gauge theories are an important class of physical models with high-dimensional structured distributions that underpin first-principles calculations in particle, nuclear, and condensed-matter physics. Recent advances in generative modeling have opened new avenues for sampling Boltzmann distributions in lattice gauge theories, offering the potential to alleviate limitations of traditional Monte Carlo methods, including critical slowing down and topological freezing. However, generative samplers for lattice gauge theories are typically constructed in link space, where correlations become increasingly long-ranged toward weak coupling, posing a challenge for learning. Plaquettes provide a more natural representation, as the action is local in these variables. However, exact Bianchi constraints restrict them to a lower-dimensional manifold, complicating direct generative modeling. We introduce a multilevel normalizing-flow construction that samples directly in plaquette space while satisfying these constraints exactly. The key idea is a coarse-to fine factorization that transforms a globally coupled constraint problem into a sequence of local solves: at each refinement, every determined plaquette depends on at most four newly generated variables, while the size of the constraint problem remains independent of the lattice size. We validate the construction for $U(1)$ in two and four dimensions and for $SU(2)$ in two dimensions. Our multilevel Plaquette-Space Sampler (PSS) substantially outperforms link-space baselines, with the advantage increasing toward weak coupling, where the gauge coupling becomes small. This regime is particularly challenging for generative sampling and, in asymptotically free gauge theories, is relevant to continuum studies.

hep-lat↗

arXiv2026

Sector-Resolved Flow Sampling for Topologically Frozen Lattice Gauge Theories

Topological fluctuations are essential to nonperturbative gauge theories but become increasingly difficult to sample toward the continuum limit, where Markov chains can freeze in sectors of fixed topological charge. We introduce a generative sampler, a mixture of sector-resolved samplers (MSRS) that explicitly resolves these sectors and exploits a key advantage of generative models, the ability to directly evaluate the domain-restricted partition function and thereby determine the relative weights of disconnected sectors. We train a generative model in a reference topological sector combined with a bijective topological shift that deterministically maps its samples to other sectors. We demonstrate the method in two-dimensional compact U (1) lattice gauge theory, where it reproduces the topological-charge distribution and yields an unbiased susceptibility in a regime where hybrid Monte Carlo is frozen and overrelaxation gives inaccurate estimates. Our approach also outperforms existing flow-based samplers by orders of magnitude. These results demonstrate that explicit sector resolution provides a promising route to overcoming topological barriers in lattice gauge theory.

hep-lat↗

arXiv2026

Real-time measurement error mitigation for one-way quantum computation

We propose a quantum error mitigation scheme for single-qubit measurement errors, particularly suited for one-way quantum computation. Contrary to well established error mitigation methods for circuit-based quantum computation that require the circuits to be run several times, our method is capable of mitigating measurement errors in real-time, during the processing measurements of the one-way computation. For that, an ancillary qubit register is entangled with the to-be-measured qubit and additionally measured afterwards. By using a voting protocol on all measurement outcomes, occurring measurement errors can be mitigated in real-time while the one-way computation continues. We provide an analytical expression for the probability to detect a measurement error depending on the error rate and the number of ancilla qubits. From this, we derive an estimate of the ancilla register size for a given measurement error rate and a required success probability to detect a measurement error. Additionally, we also consider the CNOT gate error in our mitigation method and investigate how this influences the probability to detect a measurement error. Finally, we show in proof-of-principle simulations and in experiments executed on IBM quantum hardware that our method is capable of reducing the measurement errors significantly in a one-way quantum computation with only a small number of ancilla qubits.

quant-ph↗

arXiv2026

Convergence and efficiency proof of quantum imaginary time evolution for bounded order systems

Many current and near-future applications of quantum computing utilise parametric families of quantum circuits and variational methods that can suffer from obstacles including non-convergence to the global minimum due to local minima, critical slowing down, or exponential resource scaling. Here we show that quantum imaginary time evolution can overcome these obstacles if the underlying physical system satisfies a set of conditions. This includes many relevant applications such as ground state preparation for local theories in physics or chemistry, combinatorial optimisation problems, or quantum machine learning. In particular, we analyse the quantum imaginary time evolution showing convergence guarantees to the global minimum without critical slowing down and providing a priori estimates on the required evolution time which scale linearly in system size and inverse energy gap. Furthermore, a provided complexity analysis shows that quantum imaginary time evolution can be efficiently compiled into a parametric quantum circuit, finding the optimal parameters included, for a large class of physically relevant problems.

quant-ph↗

arXiv2026

Prior-Informed Adaptive Shifts for Sequential Minimal Optimization in Variational Quantum Eigensolvers

Sequential minimal optimization methods, such as the Rotosolve and the Nakanishi-Fujii-Todo algorithm (NFT), are widely used for Variational Quantum Eigensolvers (VQEs). These methods optimize one parameter direction at a time, requiring measurements at only a few locations along that direction. In the presence of measurement shot noise, however, their performance depends critically on the choice of measurement locations, and recent studies suggest that equidistant measurements are optimal. However, we often observe that equidistant measurements are not always optimal in practice. We argue that this discrepancy between theory and practice arises from the fact that two assumptions underlying previous analyses do not generally hold: (1) the absence of prior knowledge about the energy minimizer, and (2) the use of the uncertainty of the estimated energy as a proxy for optimization performance. In this paper, we develop a new theory for determining optimal measurement locations. First, we show that incorporating prior information about the minimizer is beneficial. Early in optimization, when little is known about the pivot, i.e., the current minimizer, equidistant measurements are indeed near-optimal, but as the prior belief sharpens the optimal locations move away from equidistant. Second, rather than analyzing the uncertainty of the estimated minimum energy, we study the uncertainty of the estimator of the minimizer itself, which leads to substantially different strategies. Based on this analysis, we propose Prior-informed Adaptive Shifts (PAS), a method that automatically adjusts measurement locations during optimization. Numerical experiments across different shot counts and problems validate our theoretical findings and demonstrate that PAS adaptively recovers whichever fixed shift is best in each regime without it being specified in advance.

quant-ph↗

arXiv2026

Imaginarity as a necessary resource for trainability in QAOA

The quantum approximate optimization algorithm (QAOA) tackles combinatorial problems by tuning a quantum circuit in a classical loop, often guided by gradients. We show that the gradient used to tune the circuit's final parameter is bounded by imaginarity, which weights phase relationships between candidate solutions by how strongly the circuit connects them and how differently the problem scores them. Imaginarity is necessary but not sufficient for a nonzero gradient. We extend the bound to three common noise models and compare it numerically with the gradient in Max-Cut simulations.

quant-ph↗

arXiv2026

(2+1)D quantum electrodynamics at finite density on a quantum computer

In this paper, we explore (2+1)D quantum electrodynamics (QED) at finite density on a quantum computer, including two fermion flavors. Our method employs an efficient gauge-invariant ansatz together with a quantum circuit structure that enforces Gauss's law. As a proof of principle, we benchmark our simulation protocol on a small lattice system, demonstrating the identification of phase transitions in terms of the particle number of the fermion flavors. Classical simulations are used to obtain optimized variational parameters, which are then deployed in inference runs on IBM quantum hardware. We conclude by discussing hardware limitations and prospects for scaling this method to larger systems.

hep-lat↗

arXiv2026

Toward Hamiltonian simulations of Maxwell-Chern-Simons theory: constant modes and gauge field truncation

Maxwell-Chern-Simons (MCS) theory in $2+1$ dimensions provides a paradigmatic example of a topological gauge theory with both dynamical and topological degrees of freedom. Its Euclidean formulation suffers from a sign problem, making Hamiltonian numerical approaches particularly attractive. As a first step toward the non-perturbative Hamiltonian study of MCS theory, we investigate the constant mode sector on a spatial torus. Being analytically solvable in the continuum, it provides an ideal benchmark for understanding how the topological properties of the theory are encoded in a finite-dimensional lattice Hilbert space. We construct a finite-dimensional discretization of the torus of flat connections and show that the resulting lattice problem maps onto a generalized Harper-Hofstadter model with twisted boundary conditions. We identify the commensurability conditions under which the finite lattice exactly reproduces the magnetic translation algebra and the topological degeneracy of the continuum theory. A systematic analysis of gauge field truncation and its convergence toward the continuum limit is then presented.

hep-th↗

arXiv2026

A Finite-Volume Scheme for the Continuum Extrapolation of Lattice Step-Scaling in (2+1)D Hamiltonian U(1) Gauge Theory

We propose a finite-volume scheme to perform controlled continuum extrapolations of the lattice step-scaling function, a key ingredient for determining the running coupling in a Hamiltonian lattice gauge theory in small volumes. As a testbed, we employ a dual Hamiltonian formulation of pure U(1) gauge theory in (2+1) dimensions and an operator basis that remains efficient toward weak coupling. We describe the implementation of static external charges on the spatial lattice and study, using matrix product states, the resulting confining string, from which we extract the static potential and a force-based renormalized coupling. Using the proposed finite-volume scheme, we demonstrate a stable continuum limit of the step-scaling function on the lattice sizes accessible to present Hamiltonian simulations. The method is readily extendable to other gauge groups and dimensions, providing a pathway toward Hamiltonian step-scaling studies in other theories.

hep-lat↗

arXiv2026

Bias Analysis and Regularization of Sequential Minimal Optimization in Variational Quantum Eigensolvers

The Nakanishi Fujii Todo (NFT) algorithm, also known as Rotosolve, implements Sequential Minimal Optimization for Variational Quantum Eigensolvers (SMO-VQE) by exploiting the trigonometric dependence of the energy on individual circuit parameters. This enables analytical one-dimensional minimization using only a few , typically two, energy evaluations, but introduces bias in the estimated energy. Although performing additional measurements every few tens of iterations can mitigate bias accumulation, we find that such corrections often degrade optimization performance. In this paper, we analyze the origin and accumulation of bias during the SMO-VQE process. Specifically, we show that the bias can be accurately estimated without additional measurements. Furthermore, we find that bias correction destabilizes optimization along directions with small curvature, whereas the original biased estimator implicitly acts as a regularizer. Based on these insights, we propose a simple regularization method that implements error accumulation while maintaining unbiased energy estimation. The resulting algorithm consistently improves performance across different system sizes, circuit depths, target Hamiltonians, and measurement shots, with minimal hyperparameter tuning.

quant-ph↗

arXiv2026

Bayesian Parameter Shift Rule in Variational Quantum Eigensolvers

Parameter shift rules (PSRs) are key techniques for efficient gradient estimation in variational quantum eigensolvers (VQEs). In this paper, we propose its Bayesian variant, where Gaussian processes with appropriate kernels are used to estimate the gradient of the VQE objective. Our Bayesian PSR offers flexible gradient estimation from observations at arbitrary locations with uncertainty information and reduces to the generalized PSR in special cases. In stochastic gradient descent (SGD), the flexibility of Bayesian PSR allows the reuse of observations in previous steps, which accelerates the optimization process. Furthermore, the accessibility to the posterior uncertainty, along with our proposed notion of gradient confident region (GradCoRe), enables us to minimize the observation costs in each SGD step. Our numerical experiments show that the VQE optimization with Bayesian PSR and GradCoRe significantly accelerates SGD and outperforms the state-of-the-art methods, including sequential minimal optimization.

cs.LG↗

arXiv2026

A Path to Quantum Simulations of Topological Phases: (2+1)D Quantum Electrodynamics with Wilson Fermions

Quantum simulation offers a powerful approach to studying quantum field theories, particularly (2+1)D quantum electrodynamics (QED$_3$) with Wilson fermions, which hosts a rich landscape of physical phenomena. A key challenge in lattice formulations is the proper realization of topological phases and the Chern-Simons terms, where fermion discretization plays a crucial role. In this work, we highlight the differences between staggered and Wilson fermions coupled to $\text{U}(1)$ gauge fields in the Hamiltonian formulation. We analyze why staggered fermions fail to induce (2+1)D topological phases, while Wilson fermions admit a variety of topological phases including Chern insulator and quantum spin Hall phases. Additionally, we uncover a rich phase diagram for the two-flavor Wilson fermion model in the presence of a chemical potential. Our findings resolve existing ambiguities in Hamiltonian formulations and provide a theoretical foundation for future quantum simulations of lattice field theories with topological phases. We further outline connections to experimental platforms, offering guidance for implementations on near-term quantum computing architectures. A complementary presentation of the analytical calculations, the identification of robust topological structure and response, and extensive numerical results is contained in a joint submission [1].

hep-lat↗

arXiv2026

Hamiltonian Lattice QED$_3$ with One and Two Flavors of Wilson Fermions: Topological Structure and Response

The quantum simulation of topological phases in (2+1)D quantum electrodynamics with Wilson fermions provides a promising route toward realizing topological phenomena in near-term lattice experiments. We show that the commonly used staggered-fermion discretizations in Hamiltonian gauge theories possesses an exact time-reversal symmetry, which forbids the emergence of nontrivial topological phases and has led to confusion in the existing literature. In this work, we resolve this obstacle by systematically analyzing fermion discretization effects in (2+1)D lattice Hamiltonians of fermions coupled to U(1) gauge fields that satisfy Gauss' law. We show that Wilson fermions, already in the minimal one-flavor theory, naturally enable topological regimes with nonzero Chern numbers, and that the two-flavor extension at finite chemical potential further enriches the accessible topological structure. We develop gauge-invariant diagnostics of topological response, including many-body Chern numbers and current correlators that remain robust probes at weak coupling. Finally, through extensive exact diagonalization calculations across both flavor settings, we characterize the spectrum, correlators, and topological invariants, providing a concrete foundation for near-term quantum simulations of topological phases in lattice field theories. The implications of this work for quantum simulations of lattice field theory are analyzed in a joint submission [1].

hep-lat↗

arXiv2026

Isogeny Graphs in Superposition and Quantum Onion Routing

Onion routing provides anonymity by layering encryption so that no relay can link sender to destination. A quantum analogue faces a core obstacle: layered quantum encryption generally requires symmetric encryption schemes, whereas classically one would rely on public-key encryption. We propose a symmetric-encryption-based quantum onion routing (QOR) scheme by instantiating each layer with the abelian ideal class group action from the Theory of Complex Multiplication. Session keys are established locally via a Diffie-Hellman key exchange between neighbors in the chain of communication. Furthermore, we propose a novel ''non-local'' key exchange between the sender and receiver. The underlying problem remains hard even for quantum adversaries and underpins the security of current post-quantum schemes. We connect our construction to isogeny graphs and their association schemes, using the Bose-Mesner algebra to formalize commutativity and guide implementation. We give two implementation paths: (i) a universal quantum oracle evaluating the class group action with polynomially many quantum resources, and (ii) an intrinsically quantum approach via continuous-time quantum walks (CTQWs), outlined here and developed in a companion paper. A small Qiskit example illustrates the mechanics (by design, not the efficiency) of the QOR.

quant-ph↗

arXiv2026

Computing Statistical Properties of Velocity Fields on Current Quantum Hardware

Quantum algorithms are gaining attention in Computational Fluid Dynamics (CFD) for their favorable scaling, as encoding physical fields into quantum probability amplitudes enables representation of two to the power of n spatial points with only n qubits. A key challenge in Quantum CFD is the efficient readout of simulation results, a topic that has received limited attention in literature. This work presents methods to extract statistical properties of spatial velocity fields, such as central moments and structure functions, directly from parameterized ansatz circuits, avoiding full quantum state tomography. As a proof of concept, we implement our approach for 1D velocity fields, encoding 16 spatial points with 4 qubits, and analyze both a sine wave signal and four snapshots from Burgers' equation evolution. Using Qedma's error mitigation software QESEM, we demonstrate that such computations achieve high accuracy on current quantum devices, specifically IBMQ's Heron2 system ibm_fez.

quant-ph↗

arXiv2025

A Comprehensive Stress Test of Truncated Hilbert Space Bases against Green's function Monte Carlo in U(1) Lattice Gauge Theory

A representation of Lattice Gauge Theories (LGT) suitable for simulations with tensor network state methods or with quantum computers requires a truncation of the Hilbert space to a finite dimensional approximation. In particular for U(1) LGTs, several such truncation schemes are known, which we compare with each other using tensor network states. We show that a functional basis obtained from single plaquette Hamiltonians -- which we call plaquette state basis -- outperforms the other schemes in two spatial dimensions for plaquette, ground state energy and mass gap, as it is delivering accurate results for a wide range of coupling strengths with a minimal number of basis states. We also show that this functional basis can be efficiently used in three spatial dimensions. Green's function Monte Carlo appears to be a highly useful tool to verify tensor network states results, which deserves further investigation in the future.

hep-lat↗