arXiv subjects

Matthias Heller

Publications and source records attributed to Matthias Heller.

At least 19 recordsLinked to original sources

arXiv2026

Factorizing binary tensors into quantics tensor trains

The conversion of functions to quantics tensor trains is a well-established procedure and can either be done analytically or numerically. Numerical conversion schemes are based on singular value decompositions, where access to the full tensor is necessary, or on cross interpolations, which only depend on sampling a function. When dealing with large binary tensors, the first approach becomes prohibitively expensive while the second approach might fail to converge due to the non-smoothness of the data. In this work, we provide insight into how binary tensors, where the positions of the non-zero entries are defined by some Boolean function, can be converted into quantics tensor trains with a hybrid analytical-numerical approach utilizing the rank product. The proposed construction scheme nicely reproduces results from the literature and can be used for discrete convolutions, the construction of discrete wavelet transforms or slicing and assignment operations of multi-dimensional quantics tensor trains.

physics.comp-ph↗

arXiv2026

trainsum -- A Python package for quantics tensor trains

We present trainsum, a versatile Python package for doing computations with multidimensional quantics tensor trains: https://github.com/fh-igd-iet/trainsum. Using the Array API standard together with opt_einsum, trainsum allows the effortless approximation of tensors or functions by tensor trains independent of their shape or dimensionality. Once approximated, our package can perform normal arithmetic operations with quantics tensor trains, including addition, Einstein summations and element-wise transformations. It can be therefore used for generic computations with applications in simulation, data compression, machine learning and data analysis.

cs.MS↗

arXiv2026

Bipartitioning of Graph States for Distributed Measurement-Based Quantum Computing

Measurement-Based Quantum Computing (MBQC) is inherently well-suited for Distributed Quantum Computing (DQC): once a resource state is prepared and distributed across a network of quantum nodes, computation proceeds through local measurements coordinated by classical communication. However, since non-local gates acting on different Quantum Processing Units (QPUs) are a bottleneck, it is crucial to optimize the qubit assignment to minimize inter-node entanglement of the shared resource. For graph state resources shared across two QPUs, this task reduces to finding bipartitions with minimal cut rank. We introduce a simulated annealing-based algorithm that efficiently updates the cut rank when two vertices swap sides across a bipartition, such that computing the new cut rank from scratch, which would be much more expensive, is not necessary. We show that the approach is highly effective for determining qubit assignments in distributed MBQC by testing it on grid graphs and the measurement-based Quantum Approximate Optimization Algorithm (QAOA).

quant-ph↗

arXiv2025

Efficient Preparation of Resource States for Hamiltonian Simulation and Universal Quantum Computation

The direct compilation of algorithm-specific graph states in measurement-based quantum computation (MBQC) can lead to resource reductions in terms of circuit depth, entangling gates, and even the number of physical qubits. In this work, we extend previous studies on algorithm-tailored graph states to periodic sequences of generalized Pauli rotations, which commonly appear in, e.g., Trotterized Hamiltonian simulation. We first implement an enhanced simulated-annealing-based algorithm to find optimal periodic graph states within local-Clifford equivalent MBQC resources. In addition, we derive a novel scheme for the preparation of resource states based on a graph state and a ladder of CNOT gates, which we term anticommutation-based MBQC, since it uncovers a direct relationship between the graph state and the anticommutation matrix for the set of Hamiltonians generating the computation. We also deploy our two approaches to derive universal resource states from minimal universal sets of generating Hamiltonians. Finally, we demonstrate and compare both of our methods based on various examples from condensed matter physics and universal quantum computation.

quant-ph↗

arXiv2025

Reduced Sampling Overhead for Probabilistic Error Cancellation by Pauli Error Propagation

Quantum error mitigation is regarded as a possible path to near-term quantum utility. The methods under the quantum error mitigation umbrella term, such as probabilistic error cancellation (PEC), zero-noise extrapolation (ZNE) or Clifford data regression (CDR) are able to significantly reduce the error for the estimation of expectation values, although at an exponentially scaling cost, i.e., in the sampling overhead. In this work, we present a method to reduce the sampling overhead of PEC through Pauli error propagation combined with classical preprocessing. Our findings indicate that this method significantly reduces sampling overheads for Clifford circuits, leveraging the well-defined interaction between the Clifford group and Pauli noise. Additionally, we show that the method is applicable to non-Clifford circuits, though with more limited effectiveness, primarily constrained by the number of non-Clifford gates present in the circuit. We further provide examples of Clifford sub-circuits commonly encountered in relevant calculations, such as resource state generation in measurement-based quantum computing.

quant-ph↗

arXiv2025

Exploring Quantum Annealing for Coarse-Grained Protein Folding

We explore the potential application of quantum annealing to address the protein structure problem. To this end, we compare several proposed ab initio protein folding models for quantum computers and analyze their scaling and performance for classical and quantum heuristics. Furthermore, we introduce a novel encoding of coordinate based models on the tetrahedral lattice, based on interleaved grids. Our findings reveal significant variations in model performance, with one model yielding unphysical configurations within the feasible solution space. Furthermore, we conclude that current quantum annealing hardware is not yet suited for tackling problems beyond a proof-of-concept size, primarily due to challenges in the embedding. Nonetheless, we observe a scaling advantage over our in-house simulated annealing implementation, which, however, is only noticeable when comparing performance on the embedded problems.

quant-ph↗

arXiv2025

Fully numerical Hartree-Fock calculations for atoms and small molecules with quantics tensor trains

We present a fully numerical framework for the optimization of molecule-specific quantum chemical basis functions within the quantics tensor train format using a finite-difference scheme. The optimization is driven by solving the Hartree-Fock equations (HF) with the density-matrix renormalization group (DMRG) algorithm on Cartesian grids that are iteratively refined. In contrast to the standard way of tackling the mean-field problem by expressing the molecular orbitals as linear combinations of atomic orbitals (LCAO) our method only requires as much basis functions as there are electrons within the system. Benchmark calculations for atoms and molecules with up to ten electrons show excellent agreement with LCAO calculations with large basis sets supporting the validity of the tensor network approach. Our work therefore offers a promising alternative to well-established HF-solvers and could pave the way to define highly accurate, fully numerical, molecule-adaptive basis sets, which, in the future, could lead to benefits for post-HF calculations.

physics.chem-ph↗

arXiv2024

Digital Quantum Simulation of Scalar Yukawa Coupling

Motivated by the revitalized interest in the digital simulation of medium- and high-energy physics phenomena, we investigate the dynamics following a Yukawa-interaction quench on IBM Q. Adopting the zero-dimensional version of the scalar Yukawa-coupling model as our point of departure, we design low-depth quantum circuits emulating its dynamics with up to three bosons. In the one-boson case we demonstrate circuit compression, i.e., a constant-depth circuit containing only two controlled-NOT (CNOT) gates. In the more complex three-boson case, we design a circuit in which one Trotter step entails $8$ CNOTs. Using an analogy with the traveling-salesman problem, we also provide a CNOT-cost estimate for higher boson-number truncations. Based on these circuits, we quantify the system dynamics by evaluating the expected boson number at an arbitrary time after the quench and the survival probability of the initial vacuum state (the Loschmidt echo). We also utilize these circuits to drive adiabatic transitions and compute the energies of the ground- and first-excited states of the considered model. Finally, through error mitigation -- i.e, zero-noise extrapolation -- we demonstrate a good agreement of our results with a numerically-exact classical benchmark.

quant-ph↗

arXiv2023

Deterministic Ansätze for the Measurement-based Variational Quantum Eigensolver

Measurement-based quantum computing (MBQC) is a promising approach to reducing circuit depth in noisy intermediate-scale quantum algorithms such as the Variational Quantum Eigensolver (VQE). Unlike gate-based computing, MBQC employs local measurements on a preprepared resource state, offering a trade-off between circuit depth and qubit count. Ensuring determinism is crucial to MBQC, particularly in the VQE context, as a lack of flow in measurement patterns leads to evaluating the cost function at irrelevant locations. This study introduces MBVQE-ansätze that respect determinism and resemble the widely used problem-agnostic hardware-efficient VQE ansatz. We evaluate our approach using ideal simulations on the Schwinger Hamiltonian and $XY$-model and perform experiments on IBM hardware with an adaptive measurement capability. In our use case, we find that ensuring determinism works better via postselection than by adaptive measurements at the expense of increased sampling cost. Additionally, we propose an efficient MBQC-inspired method to prepare the resource state, specifically the cluster state, on hardware with heavy-hex connectivity, requiring a single measurement round, and implement this scheme on quantum computers with $27$ and $127$ qubits. We observe notable improvements for larger cluster states, although direct gate-based implementation achieves higher fidelity for smaller instances.

quant-ph↗

arXiv2023

Mapping quantum circuits to shallow-depth measurement patterns based on graph states

The paradigm of measurement-based quantum computing (MBQC) starts from a highly entangled resource state on which unitary operations are executed through adaptive measurements and corrections ensuring determinism. This is set in contrast to the more common quantum circuit model, in which unitary operations are directly implemented through quantum gates prior to final measurements. In this work, we incorporate concepts from MBQC into the circuit model to create a hybrid simulation technique, permitting us to split any quantum circuit into a classically efficiently simulatable Clifford-part and a second part consisting of a stabilizer state and local (adaptive) measurement instructions, a so-called standard form, which is executed on a quantum computer. We further process the stabilizer state with the graph state formalism, thus enabling a significant decrease in circuit depth for certain applications. We show that groups of fully commuting operators can be implemented using fully-parallel, i.e., non-adaptive, measurements within our protocol. In addition, we discuss how such circuits can be implemented in constant quantum depths by employing quantum teleportation. Finally, we demonstrate the utility of our technique on two examples of high practical relevance: the Quantum Approximate Optimization Algorithm (QAOA) and the Variational Quantum Eigensolver (VQE).

quant-ph↗

arXiv2022

Mixed QCD-electroweak corrections to dilepton production at the LHC in the high invariant mass region

We compute mixed QCD-electroweak corrections to the neutral-current Drell-Yan production of a pair of massless leptons in the high invariant mass region. Our computation is fully differential with respect to the final state particles. At relatively low values of the dilepton invariant mass, $m_{\ell \ell} \sim 200$ GeV, we find unexpectedly large mixed QCD-electroweak corrections at the level of -1%. At higher invariant masses, $m_{\ell \ell} \sim 1$ TeV, we observe that these corrections can be well approximated by the product of QCD and electroweak corrections. Hence, thanks to the well-known Sudakov enhancement of the latter, they increase at large invariant mass and reach e.g. -3% at $m_{\ell \ell} = 3$ TeV. Finally, we note that the inclusion of mixed corrections reduces the theoretical uncertainty related to the choice of electroweak input parameters to below the percent level.

hep-ph↗

arXiv2021

Soft-photon radiative corrections to the $e^- p \to e^- p l^- l^+$ process

We calculate the leading-order QED radiative corrections to the process $e^- p\rightarrow e^- p l^- l^+ $ in the soft-photon approximation, in two different energy regimes which are of relevance to extract nucleon structure information. In the low-energy region, this process is studied to better constrain the hadronic corrections to precision muonic Hydrogen spectroscopy. In the high-energy region, the beam-spin asymmetry for double virtual Compton scattering allows to directly access the Generalized Parton Distributions. We find that the soft-photon radiative corrections have a large impact on the cross sections and are therefore of paramount importance to extract the nucleon structure information from this process. For the forward-backward asymmetry the radiative corrections are found to affect the asymmetry only around or below the 1\% level, whereas the beam-spin asymmetry is not affected at all in the soft-photon approximation, which makes them gold-plated observables to extract nucleon structure information in both the low- and high-energy regimes.

hep-ph↗

arXiv2021

Planar two-loop integrals for $\mathbf{μe}$ scattering in QED with finite lepton masses

We present analytic results for one of two types of planar QED two-loop integrals for $μe$ scattering including finite lepton masses. No approximations are made, such that the results are valid not only in the limit of a small electron mass. The results are expressed in terms of multiple polylogarithms with algebraic function arguments in a representation which allows for fast numerical evaluation in the physical phase-space.

hep-ph↗

arXiv2021

MultivariateApart: Generalized Partial Fractions

We present a package to perform partial fraction decompositions of multivariate rational functions. The algorithm allows to systematically avoid spurious denominator factors and is capable of producing unique results also when being applied to terms of a sum separately. The package is designed to work in Mathematica, but also provides interfaces to the Form and Singular computer algebra systems.

cs.SC↗

arXiv2020

Leading-order QED radiative corrections to timelike Compton scattering on the proton

We evaluate the leading-order QED radiative corrections to the timelike Compton scattering (TCS) process $γp \to l^- l^+ p$. We study these corrections in two energy regimes using different models for the TCS amplitude. In the low-energy regime we calculate the contribution due to the proton and its lowest-energy excitation, the $Δ(1232)$ resonance. In the high-energy near-forward kinematical regime we calculate the TCS amplitude in a handbag approach in terms of Generalized Parton Distributions (GPDs). On the level of cross sections we find the QED radiative corrections to be in the $5 -10\%$ range in the low-energy regime and around $20\%$ in the high-energy regime. We show that in both the di-lepton forward-backward asymmetry as well as in the photon beam helicity asymmetry these corrections nearly cancel out, making them gold-plated observables to extract the real and imaginary parts of the TCS amplitude. We demonstrate in particular the sensitivity of these asymmetries on GPD parameterizations for a recent CLAS12@JLab TCS experiment.

hep-ph↗

arXiv2020

Mixed EW-QCD two-loop amplitudes for $q\bar{q} \to \ell^+\ell^-$ and $γ_5$ scheme independence of multi-loop corrections

We perform a dedicated study of the $q \bar{q}$-initiated two-loop electroweak-QCD Drell-Yan scattering amplitude in dimensional regularization schemes for vanishing light quark and lepton masses. For the relative order $α$ and $α_s$ one-loop Standard Model corrections, details of our comparison to the original literature are given. The infrared pole terms of the mixed two-loop amplitude are governed by a known generalization of the dipole formula and we show explicitly that exactly the same two-loop polarized hard scattering functions are obtained in both the standard 't Hooft-Veltman-Breitenlohner-Maison $γ_5$ scheme and Kreimer's anticommuting $γ_5$ scheme.

hep-ph↗

arXiv2020

Multiple polylogarithms with algebraic arguments and the two-loop EW-QCD Drell-Yan master integrals

We consider Feynman integrals with algebraic leading singularities and total differentials in $ε\,\mathrm{d}\ln$ form. We show for the first time that it is possible to evaluate integrals with singularities involving unrationalizable roots in terms of conventional multiple polylogarithms, by either parametric integration or matching the symbol. As our main application, we evaluate the two-loop master integrals relevant to the $αα_s$ corrections to Drell-Yan lepton pair production at hadron colliders. We optimize our functional basis to allow for fast and stable numerical evaluations in the physical region of phase space.

hep-th↗

arXiv2019

Mixed QCD-EW two-loop corrections to Drell-Yan production

The Drell-Yan production of charged lepton pairs is one of the key processes measured at hadron colliders. The QCD corrections to the cross section are known to order $α_s^2$ and electroweak corrections are known to order $α$. The next important step for a better theoretical understanding is the complete calculation of the mixed QCD-EW corrections of order $α_sα$. In my talk, I report on the first complete calculation of the virtual two-loop corrections of order $αα_s$ to the lepton-pair production cross section. The calculation is carried out analytically using tensor reduction, integration-by-parts relations and the method of differential equations. We validate a previous calculation of the subset of mixed QCD-QED corrections and show how the jet and soft functions of that reference can be used to subtract the infrared divergences of the complete mixed QCD-electroweak virtual corrections.

hep-ph↗