arXiv subjects

Lena Funcke

Publications and source records attributed to Lena Funcke.

At least 55 records · Page 3Linked to original sources

arXiv2022

Impact of quantum noise on the training of quantum Generative Adversarial Networks

Current noisy intermediate-scale quantum devices suffer from various sources of intrinsic quantum noise. Overcoming the effects of noise is a major challenge, for which different error mitigation and error correction techniques have been proposed. In this paper, we conduct a first study of the performance of quantum Generative Adversarial Networks (qGANs) in the presence of different types of quantum noise, focusing on a simplified use case in high-energy physics. In particular, we explore the effects of readout and two-qubit gate errors on the qGAN training process. Simulating a noisy quantum device classically with IBM's Qiskit framework, we examine the threshold of error rates up to which a reliable training is possible. In addition, we investigate the importance of various hyperparameters for the training process in the presence of different error rates, and we explore the impact of readout error mitigation on the results.

quant-ph↗

arXiv2022

Studying quantum algorithms for particle track reconstruction in the LUXE experiment

The LUXE experiment (LASER Und XFEL Experiment) is a new experiment in planning at DESY Hamburg, which will study Quantum Electrodynamics (QED) at the strong-field frontier. In this regime, QED is non-perturbative. This manifests itself in the creation of physical electron-positron pairs from the QED vacuum. LUXE intends to measure the positron production rate in this unprecedented regime by using, among others, a silicon tracking detector. The large number of expected positrons traversing the sensitive detector layers results in an extremely challenging combinatorial problem, which can become computationally very hard for classical computers. This paper presents a preliminary study to explore the potential of quantum computers to solve this problem and to reconstruct the positron trajectories from the detector energy deposits. The reconstruction problem is formulated in terms of a quadratic unconstrained binary optimisation. Finally, the results from the quantum simulations are discussed and compared with traditional classical track reconstruction algorithms.

hep-ex↗

arXiv2022

Applications of Machine Learning to Lattice Quantum Field Theory

There is great potential to apply machine learning in the area of numerical lattice quantum field theory, but full exploitation of that potential will require new strategies. In this white paper for the Snowmass community planning process, we discuss the unique requirements of machine learning for lattice quantum field theory research and outline what is needed to enable exploration and deployment of this approach in the future.

hep-lat↗

arXiv2021

Dimensional Expressivity Analysis, best-approximation errors, and automated design of parametric quantum circuits

The design of parametric quantum circuits (PQCs) for efficient use in variational quantum simulations (VQS) is subject to two competing factors. On one hand, the set of states that can be generated by the PQC has to be large enough to contain the solution state. Otherwise, one may at best find the best approximation of the solution restricted to the states generated by the chosen PQC. On the other hand, the PQC should contain as few parametric quantum gates as possible to minimize noise from the quantum device. Thus, when designing a PQC one needs to ensure that there are no redundant parameters. The dimensional expressivity analysis discussed in these proceedings is a means of addressing these counteracting effects. Its main objective is to identify independent and redundant parameters in the PQC. Using this information, superfluous parameters can be removed and the dimension of the space of states that are generated by the PQC can be computed. Knowing the dimension of the physical state space then allows us to deduce whether or not the PQC can reach all physical states. Furthermore, the dimensional expressivity analysis can be implemented efficiently using a hybrid quantum-classical algorithm. This implementation has relatively small overhead costs both for the classical and quantum part of the algorithm and could therefore be used in the future for on-the-fly circuit construction. This would allow for optimized circuits to be used in every loop of a VQS rather than the same PQC for the entire VQS. These proceedings review and extend work in [1, 2].

quant-ph↗

arXiv2021

CP-violating Dashen phase transition in the two-flavor Schwinger model: a study with matrix product states

We numerically study the Hamiltonian lattice formulation of the two-flavor Schwinger model using matrix product states. Keeping the mass of the first flavor at a fixed positive value, we tune the mass of the second flavor through a range of negative values, thus exploring a regime where conventional Monte Carlo methods suffer from the sign problem and may run into instabilities due to zero modes. Our results indicate a phase transition at the point where the absolute value of the second flavor mass approaches the first flavor mass. The phase transition is accompanied by the formation of a fermion condensate, a steep drop of the average electric field, and a peak in the bipartite entanglement entropy. Our data hints at a second order transition, which is the 1+1D analog of the CP-violating Dashen phase transition in QCD.

hep-lat↗

arXiv2021

Lattice QCD results for the topological up-quark mass contribution: too small to rescue the $m_u=0$ solution to the strong CP problem

A vanishing Yukawa coupling of the up quark could in principle solve the strong CP problem. To render this solution consistent with current algebra results, the up quark must receive an alternative mass contribution that conserves CP symmetry. Such a contribution could be provided by QCD through non-perturbative topological effects, including instantons. In this talk, we present the first direct lattice computation of this topological mass contribution, using gauge configurations generated by the Extended Twisted Mass collaboration. We use the Iwasaki gauge action, Wilson twisted mass fermions at maximal twist, and dynamical up, down, strange and charm quarks. Our result for the topological mass contribution is an order of magnitude too small to account for the phenomenologically required up-quark mass. This rules out the "massless" up-quark solution to the strong CP problem, in accordance with previous results relying on $χ$PT fits to lattice data. The talk is based on [Alexandrou et al., PRL 125, 232001 (2020)], where more details can be found.

hep-lat↗

arXiv2021

3+1D $θ$-Term on the Lattice from the Hamiltonian Perspective

Quantum and tensor network simulations have emerged as prominent sign-problem free approaches to lattice gauge theories. Unlike conventional Markov chain Monte Carlo methods, they are based on the Hamiltonian formulation. In this talk, we fill a gap in the literature and present the first derivation of the Hamiltonian 3+1D $θ$-term -- which is an important sign-problem afflicted term -- for Abelian and non-Abelian lattice gauge theories. Furthermore, we perform exact diagonalization for a 3+1D U(1) lattice gauge theory including the $θ$-term on a unit periodic cube. Our numerical results reveal a novel phase transition at fixed values of $θ$ in the strong-coupling regime. The transition is evidenced by an avoided level crossing in the ground state energy, as well as sudden changes in the plaquette expectation value, the electric energy density, and the topological charge density. Extensions of our work to larger lattices can be readily performed using state-of-the-art tensor network simulations. Moreover, our work provides a concrete starting point for an eventual quantum simulation of the $θ$-dependent phase structure and dynamics of lattice gauge theories in 3+1D. This talk is mainly based on [1]. We expand beyond [1] by including a derivation of the (non-)Abelian fixed-length Higgs term in the Hamiltonian formulation for future studies of (non-)Abelian-Higgs models with a $θ$-term.

hep-lat↗

arXiv2021

Model-Independent Error Mitigation in Parametric Quantum Circuits and Depolarizing Projection of Quantum Noise

Finding ground states and low-lying excitations of a given Hamiltonian is one of the most important problems in many fields of physics. As a novel approach, quantum computing on Noisy Intermediate-Scale Quantum (NISQ) devices offers the prospect to efficiently perform such computations and may eventually outperform classical computers. However, current quantum devices still suffer from inherent quantum noise. In this work, we propose an error mitigation scheme suitable for parametric quantum circuits. This scheme is based on projecting a general quantum noise channel onto depolarization errors. Our method can efficiently reduce errors in quantum computations, which we demonstrate by carrying out simulations both on classical and IBM's quantum devices. In particular, we test the performance of the method by computing the mass gap of the transverse-field Ising model using the variational quantum eigensolver algorithm.

quant-ph↗

arXiv2021

Machine Learning of Thermodynamic Observables in the Presence of Mode Collapse

Estimating the free energy, as well as other thermodynamic observables, is a key task in lattice field theories. Recently, it has been pointed out that deep generative models can be used in this context [1]. Crucially, these models allow for the direct estimation of the free energy at a given point in parameter space. This is in contrast to existing methods based on Markov chains which generically require integration through parameter space. In this contribution, we will review this novel machine-learning-based estimation method. We will in detail discuss the issue of mode collapse and outline mitigation techniques which are particularly suited for applications at finite temperature.

hep-lat↗

arXiv2021

Investigating the variance increase of readout error mitigation through classical bit-flip correction on IBM and Rigetti quantum computers

Readout errors are among the most dominant errors on current noisy intermediate-scale quantum devices. Recently, an efficient and scaleable method for mitigating such errors has been developed, based on classical bit-flip correction. In this talk, we compare the performance of this method for IBM's and Rigetti's quantum devices, demonstrating how the method improves the noisy measurements of observables obtained on the quantum hardware. Moreover, we examine the variance amplification to the data after applying of our mitigation procedure, which is common to all mitigation strategies. We derive a new expression for the variance of the mitigated Pauli operators in terms of the corrected expectation values and the noisy variances.Our hardware results show good agreement with the theoretical prediction, and we demonstrate that the increase of the variance due to the mitigation procedure is only moderate.

quant-ph↗

arXiv2021

Reconstruction of the neutrino mass as a function of redshift

We reconstruct the neutrino mass as a function of redshift, z, from current cosmological data using both standard binned priors and linear spline priors with variable knots. Using cosmic microwave background temperature, polarization and lensing data, in combination with distance measurements from baryonic acoustic oscillations and supernovae, we find that the neutrino mass is consistent with $\sum m_ν(z)$ = const. We obtain a larger bound on the neutrino mass at low redshifts coinciding with the onset of dark energy domination, $\sum m_ν(z = 0)$ < 1.46 eV (95% CL). This result can be explained either by the well-known degeneracy between $\sum m_ν$ and $Ω_Λ$ at low redshifts, or by models in which neutrino masses are generated very late in the Universe. We finally convert our results into cosmological limits for models with non-relativistic neutrino decay and find $\sum m_ν$ < 0.21 eV (95% CL), which would be out of reach for the KATRIN experiment.

astro-ph.CO↗

arXiv2021

Investigating a (3+1)D Topological $θ$-Term in the Hamiltonian Formulation of Lattice Gauge Theories for Quantum and Classical Simulations

Quantum technologies offer the prospect to efficiently simulate sign-problem afflicted regimes in lattice field theory, such as the presence of topological terms, chemical potentials, and out-of-equilibrium dynamics. In this work, we derive the (3+1)D topological $θ$-term for Abelian and non-Abelian lattice gauge theories in the Hamiltonian formulation, paving the way towards Hamiltonian-based simulations of such terms on quantum and classical computers. We further study numerically the zero-temperature phase structure of a (3+1)D U(1) lattice gauge theory with the $θ$-term via exact diagonalization for a single periodic cube. In the strong coupling regime, our results suggest the occurrence of a phase transition at constant values of $θ$, as indicated by an avoided level-crossing and abrupt changes in the plaquette expectation value, the electric energy density, and the topological charge density. These results could in principle be cross-checked by the recently developed (3+1)D tensor network methods and quantum simulations, once sufficient resources become available.

hep-lat↗

arXiv2021

Towards Quantum Simulations in Particle Physics and Beyond on Noisy Intermediate-Scale Quantum Devices

We review two algorithmic advances that bring us closer to reliable quantum simulations of model systems in high energy physics and beyond on noisy intermediate-scale quantum (NISQ) devices. The first method is the dimensional expressivity analysis of quantum circuits, which allows for constructing minimal but maximally expressive quantum circuits. The second method is an efficient mitigation of readout errors on quantum devices. Both methods can lead to significant improvements in quantum simulations, e.g., when variational quantum eigensolvers are used.

quant-ph↗

arXiv2021

Domestic Axion

We attempt to identify a phenomenologically viable solution to the strong $CP$ problem in which the axion is composed entirely out of Standard Model fermion species. The axion consists predominantly of the $η'$ meson with a minuscule admixture of a pseudoscalar bilinear composite of neutrinos, $η_ν$. The Peccei-Quinn symmetry is an axial symmetry that acts on the up quark and the neutrino species and is spontaneously broken by the QCD condensate of quarks as well as the condensate of neutrinos triggered by chiral gravitational anomaly. The up-quark mass is spontaneously generated by the neutrino condensate which plays the role of an additional composite Higgs doublet with the compositeness scale of the order of the neutrino masses. Such a scenario is highly economical: it solves the strong $CP$ problem, generates the up-quark and neutrino masses from fermion condensates and simultaneously protects the axion shift symmetry against gravitational anomaly. The phenomenology is different from the standard hidden axion case. One of the experimental signatures is the existence of a gravity-competing isotope-dependent attractive force among nucleons at (sub)micron distances.

hep-ph↗

arXiv2021

Best-approximation error for parametric quantum circuits

In Variational Quantum Simulations, the construction of a suitable parametric quantum circuit is subject to two counteracting effects. The number of parameters should be small for the device noise to be manageable, but also large enough for the circuit to be able to represent the solution. Dimensional expressivity analysis can optimize a candidate circuit considering both aspects. In this article, we will first discuss an inductive construction for such candidate circuits. Furthermore, it is sometimes necessary to choose a circuit with fewer parameters than necessary to represent all relevant states. To characterize such circuits, we estimate the best-approximation error using Voronoi diagrams. Moreover, we discuss a hybrid quantum-classical algorithm to estimate the worst-case best-approximation error, its complexity, and its scaling in state space dimensionality. This allows us to identify some obstacles for variational quantum simulations with local optimizers and underparametrized circuits, and we discuss possible remedies.

quant-ph↗

arXiv2021

Dimensional Expressivity Analysis of Parametric Quantum Circuits

Parametric quantum circuits play a crucial role in the performance of many variational quantum algorithms. To successfully implement such algorithms, one must design efficient quantum circuits that sufficiently approximate the solution space while maintaining a low parameter count and circuit depth. In this paper, we develop a method to analyze the dimensional expressivity of parametric quantum circuits. Our technique allows for identifying superfluous parameters in the circuit layout and for obtaining a maximally expressive ansatz with a minimum number of parameters. Using a hybrid quantum-classical approach, we show how to efficiently implement the expressivity analysis using quantum hardware, and we provide a proof of principle demonstration of this procedure on IBM's quantum hardware. We also discuss the effect of symmetries and demonstrate how to incorporate or remove symmetries from the parametrized ansatz.

quant-ph↗

arXiv2021

Ruling Out the Massless Up-Quark Solution to the Strong CP Problem by Computing the Topological Mass Contribution with Lattice QCD

The infamous strong CP problem in particle physics can in principle be solved by a massless up quark. In particular, it was hypothesized that topological effects could substantially contribute to the observed nonzero up-quark mass without reintroducing CP violation. Alternatively to previous work using fits to chiral perturbation theory, in this Letter, we bound the strength of the topological mass contribution with direct lattice QCD simulations, by computing the dependence of the pion mass on the dynamical strange-quark mass. We find that the size of the topological mass contribution is inconsistent with the massless up-quark solution to the strong CP problem.

hep-lat↗

arXiv2021

Estimation of Thermodynamic Observables in Lattice Field Theories with Deep Generative Models

In this work, we demonstrate that applying deep generative machine learning models for lattice field theory is a promising route for solving problems where Markov Chain Monte Carlo (MCMC) methods are problematic. More specifically, we show that generative models can be used to estimate the absolute value of the free energy, which is in contrast to existing MCMC-based methods which are limited to only estimate free energy differences. We demonstrate the effectiveness of the proposed method for two-dimensional $ϕ^4$ theory and compare it to MCMC-based methods in detailed numerical experiments.

hep-lat↗