arXiv subjects
Publications and source records attributed to Karl Jansen.
In this proceeding contribution we discuss how to define canonical momenta for SU(N) lattice gauge theories in the Hamiltonian formalism in a basis where the gauge field operators are diagonal. For an explicit discretisation of SU(2) we construct the momenta and check the violation of the fundamental commutation relations.
LUXE (Laser Und XFEL Experiment) is a proposed experiment at DESY which will study Quantum Electrodynamics (QED) in the strong-field regime, where QED becomes non-perturbative. Measuring the rate of created electron-positron pairs using a silicon pixel tracking detector is an essential ingredient to study this regime. Precision tracking of positrons traversing the four layers of the tracking detector becomes very challenging at high laser intensities due to the high rates, which can be computationally expensive for classical computers. In this work, we update our previous study of the potential of using quantum computing to reconstruct positron tracks. The reconstruction task is formulated as a quadratic unconstrained binary optimisation and is solved using simulated quantum computers and a hybrid quantum-classical algorithm, namely the variational quantum eigensolver. Different ansatz circuits and optimisers are studied. The results are discussed and compared with classical track reconstruction algorithms using a graph neural network and a combinatorial Kalman filter.
We study two different SU(2) gauge-scalar theories in 3 and 4 spacetime dimensions. Firstly, we focus on the 3 dimensional SU(2) theory with multiple Higgs fields in the adjoint representation, that can be mapped to cuprate systems in condensed matter physics which host a rich phase diagram including high-Tc superconductivity. It has been proposed that the theory with 4 adjoint Higgs fields can be used to explain the physics of hole-doped cuprates for a wide range of parameters. We show exploratory results on the phase diagram of the theory. On the other hand, we are interested in the 4 dimensional theory with 2 sets of fundamental scalar (Higgs) fields, which is relevant to the 2 Higgs Doublet Model (2HDM), a proposed extension to the Standard Model of particle physics. The goal is to understand the particle spectrum of the theory at zero temperature and the electroweak phase transition at finite temperature. We present exploratory results on scale setting and the multi-parameter phase diagram of this theory.
We present a calculation of the Mellin moments of the nucleon transverse quark spin densities extracted from the unpolarized and transversity generalized form factors. We use three $N_F=2+1+1$ ensembles of twisted mass fermions with quark masses tuned to their physical values and lattice spacings $a\sim 0.08$~fm, $a\sim 0.07$~fm and $a\sim 0.06$~fm and extrapolate the form factors to the continuum limit. Besides isovector densities we also include results for the tensor charge for each quark flavor using the ensemble with $a\sim 0.08$~fm for which we include the disconnected contributions.
We develop a classical bit-flip correction method to mitigate measurement errors on quantum computers. This method can be applied to any operator, any number of qubits, and any realistic bit-flip probability. We first demonstrate the successful performance of this method by correcting the noisy measurements of the ground-state energy of the longitudinal Ising model. We then generalize our results to arbitrary operators and test our method both numerically and experimentally on IBM quantum hardware. As a result, our correction method reduces the measurement error on the quantum hardware by up to one order of magnitude. We finally discuss how to pre-process the method and extend it to other errors sources beyond measurement errors. For local Hamiltonians, the overhead costs are polynomial in the number of qubits, even if multi-qubit correlations are included.
We numerically study the phase structure of the CP(1) model in the presence of a topological $θ$-term, a regime afflicted by the sign problem for conventional lattice Monte Carlo simulations. Using a bond-weighted tensor renormalization group method, we compute the free energy for inverse couplings ranging from $0\leq β\leq 1.1$ and find a CP-violating, first-order phase transition at $θ=π$. In contrast to previous findings, our numerical results provide no evidence for a critical coupling $β_c<1.1$ above which a second-order phase transition emerges at $θ=π$ and/or the first-order transition line bifurcates at $θ\neqπ$. If such a critical coupling exists, as suggested by Haldane's conjecture, our study indicates that is larger than $β_c>1.1$.
Lattice field theory is a very powerful tool to study Feynman's path integral non-perturbatively. However, it usually requires Euclidean background metrics to be well-defined. On the other hand, a recently developed regularization scheme based on Fourier integral operator $ζ$-functions can treat Feynman's path integral non-pertubatively in Lorentzian background metrics. In this article, we formally $ζ$-regularize lattice theories with Lorentzian backgrounds and identify conditions for the Fourier integral operator $ζ$-function regularization to be applicable. Furthermore, we show that the classical limit of the $ζ$-regularized theory is independent of the regularization. Finally, we consider the harmonic oscillator as an explicit example. We discuss multiple options for the regularization and analytically show that they all reproduce the correct ground state energy on the lattice and in the continuum limit. Additionally, we solve the harmonic oscillator on the lattice in Minkowski background numerically.
Condensed matter physics of gauge theories coupled to fermions can exhibit a rich phase structure, but are nevertheless very difficult to study in Monte Carlo simulations when they are afflicted by a sign problem. As an alternate approach, we use tensor network methods to explore the finite density physics of Abelian gauge theories without dynamical matter. As a concrete example, we consider the U(1) gauge invariant quantum link ladder with spin-1/2 gauge fields in an external electric field which cause the winding electric fluxes to condense in the ground state. We demonstrate how the electric flux tubes arrange themselves in the bulk giving rise to crystalline patterns, whose period can be controlled by tuning the external field. We propose observables to detect the transitions in ground state properties not only in numerical experiments, but also in future cold-atom realizations. A systematic procedure for reaching the thermodynamic limit, as well as extending the studies from ladders to extended geometries is outlined.
We propose to utilize NISQ-era quantum devices to compute short distance quantities in $(2+1)$-dimensional QED and to combine them with large volume Monte Carlo simulations and perturbation theory. On the quantum computing side, we perform a calculation of the mass gap in the small and intermediate regime, demonstrating, in the latter case, that it can be resolved reliably. The so obtained mass gap can be used to match corresponding results from Monte Carlo simulations, which can be used eventually to set the physical scale. In this paper we provide the setup for the quantum computation and show results for the mass gap and the plaquette expectation value. In addition, we discuss some ideas that can be applied to the computation of the running coupling. Since the theory is asymptotically free, it would serve as a training ground for future studies of QCD in $(3+1)$-dimensions on quantum computers.
Barren plateaus appear to be a major obstacle to using variational quantum algorithms to simulate large-scale quantum systems or replace traditional machine learning algorithms. They can be caused by multiple factors such as expressivity, entanglement, locality of observables, or even hardware noise. We propose classical splitting of ansätze or parametrized quantum circuits to avoid barren plateaus. Classical splitting is realized by splitting an $N$ qubit ansatz to multiple ansätze that consists of $\mathcal{O}(\log N)$ qubits. We show that such an ansatz can be used to avoid barren plateaus. We support our results with numerical experiments and perform binary classification on classical and quantum datasets. Then, we propose an extension of the ansatz that is compatible with variational quantum simulations. Finally, we discuss a speed-up for gradient-based optimization and hardware implementation, robustness against noise and parallelization, making classical splitting an ideal tool for noisy intermediate scale quantum (NISQ) applications.
We present an error mitigation scheme which corrects readout errors on Noisy Intermediate-Scale Quantum (NISQ) computers [1,2]. After a short review of applying the method to one qubit, we proceed to discuss the case when correlations between different qubits occur. We demonstrate how the readout error can be mitigated in this case. By performing experiments on IBMQ hardware, we show that such correlations do not have a strong effect on the results, justifying to neglect them.
We report on our computation of the pion transition form factor ${\cal F}_{P\rightarrow γ^*γ^*}$ from twisted mass lattice QCD in order to determine the numerically dominant light pseudoscalar pole contribution in the hadronic light-by-light scattering contribution to the anomalous magnetic moment of the muon $a_μ=(g-2)_μ$. The pion transition form factor is computed directly at the physical point. We present first results for our estimate of the pion-pole contribution with kinematic setup for the pion at rest.
We explore ideas for generating sounds and eventually music by using quantum devices in the NISQ era using quantum circuits. In particular, we first consider a concept for a "qeyboard", i.e. a quantum keyboard, where the real-time behaviour of expectation values using a time evolving quantum circuit can be associated to sound features like intensity, frequency and tone. Then, we examine how these properties can be extracted from physical quantum systems, taking the Ising model as an example. This can be realized by measuring physical quantities of the quantum states of the system, e.g. the energies and the magnetization obtained via variational quantum simulation techniques.
Quantum computing offers a new paradigm for advancing high-energy physics research by enabling novel methods for representing and reasoning about fundamental quantum mechanical phenomena. Realizing these ideals will require the development of novel computational tools for modeling and simulation, detection and classification, data analysis, and forecasting of high-energy physics (HEP) experiments. While the emerging hardware, software, and applications of quantum computing are exciting opportunities, significant gaps remain in integrating such techniques into the HEP community research programs. Here we identify both the challenges and opportunities for developing quantum computing systems and software to advance HEP discovery science. We describe opportunities for the focused development of algorithms, applications, software, hardware, and infrastructure to support both practical and theoretical applications of quantum computing to HEP problems within the next 10 years.
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.
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.
In this work, we perform a lattice QCD study of the intrinsic, rapidity-independent soft function within the framework of large momentum effective theory. The computation is carried out using a gauge ensemble of $N_f=2+1+1$ clover-improved twisted mass fermion. After applying an appropriate renormalization procedure and the removal of significant higher-twist contamination, we obtain the intrinsic soft function that is comparable to the one-loop perturbative result at large external momentum. The determination of the nonperturbative soft function from first principles is crucial to sharpen our understanding of the processes with small transverse momentum such as the Drell-Yan production and the semi-inclusive deep inelastic scattering. Additionally, we calculate the Collins-Soper evolution kernel using the quasi-transverse-momentum-dependent wave function as input.
We present the first calculation of the $x$-dependence of the isovector transversity generalized parton distributions (GPDs) for the proton within lattice QCD. We compute the matrix elements with non-local operators containing a Wilson line. The calculation implements the Breit symmetric frame. The proton momenta are chosen as $0.83,\,1.25,\,1.67$ GeV, and the values of the momentum transfer squared are $0.69,\,1.02$ GeV$^2$. These combinations include cases with zero and nonzero skewness. The calculation is performed using one ensemble of two degenerate-mass light, a strange and a charm quark of maximally twisted mass fermions with a clover term. The lattice results are renormalized non-perturbatively and finally matched to the light-cone GPDs using one-loop perturbation theory within the framework of large momentum effective theory. The final GPDs are given in the $\overline{\rm MS}$ scheme at a scale of 2 GeV. In addition to the individual GPDs, we form the combination of the transversity GPDs that is related to the transverse spin structure of the proton. Finally, we extract the lowest two moments of GPDs and draw a number of important qualitative conclusions.