arXiv subjects

Stefan Kühn

Publications and source records attributed to Stefan Kühn.

At least 37 records · Page 2Linked to original sources

arXiv2024

Gaussian boson sampling for binary optimization

Binary optimization is a fundamental area in computational science, with wide-ranging applications from logistics to cryptography, where the tasks are often formulated as Quadratic or Polynomial Unconstrained Binary Optimization problems (QUBO/PUBO). In this work, we propose to use a parametrized Gaussian Boson Sampler (GBS) with threshold detectors to address such problems. We map general PUBO instance onto a quantum Hamiltonian and optimize the Conditional Value-at-Risk of its energy with respect to the GBS ansatz. In particular, we observe that, when the algorithm reduces to standard Variational Quantum Eigensolver, the cost function is analytical. Therefore, it can be computed efficiently, along with its gradient, for low-degree polynomials using only classical computing resources. Numerical experiments on 3-SAT and Graph Partitioning problems show significant performance gains over random guessing, providing a first proof of concept for our proposed approach.

quant-ph↗

arXiv2024

Small-scale Hamiltonian optimization of interpolating operators for Lagrangian lattice quantum field theory

Lattice quantum field theory calculations may potentially combine the advantages of Hamiltonian formulations with the scalability and control of conventional Lagrangian frameworks. However, such hybrid approaches need to consider (1) the differences in renormalized coupling values between the two formulations, and (2) finite-volume and discretization effects when the Hamiltonian component of the calculation is characterized by a smaller volume or coarser lattice spacing than the Lagrangian component. This work investigates the role of both factors in the application of Hamiltonian-optimized interpolating operator constructions for the conventional Lagrangian framework. The numerical investigation is realized for the pseudoscalar meson in the Schwinger model, using tensor-network and Monte-Carlo calculations. It is demonstrated that tensor-network-optimized constructions are robust to both (1) and (2). In particular, accurate optimized constructions for the pseudoscalar meson can be obtained from calculations with a smaller number of Hamiltonian lattice sites, even when the meson mass itself receives significant finite-volume corrections. To the extent that these results generalize to theories with more complicated spectra, the method holds promise for near-term applications in large-scale calculations of lattice quantum field theory.

hep-lat↗

arXiv2024

Hybrid Oscillator-Qubit Quantum Processors: Simulating Fermions, Bosons, and Gauge Fields

We develop a hybrid oscillator-qubit processor framework for quantum simulation of strongly correlated fermions and bosons that avoids the boson-to-qubit mapping overhead encountered in qubit hardware. This framework gives exact decompositions of particle interactions such as density-density terms and gauge-invariant hopping, as well as approximate methods based on the Baker-Campbell Hausdorff formulas including the magnetic field term for the $U(1)$ quantum link model in $(2+1)$D. We use this framework to show how to simulate dynamics using Trotterisation, perform ancilla-free partial error detection using Gauss's law, measure non-local observables, estimate ground state energies using a oscillator-qubit variational quantum eigensolver as well as quantum signal processing, and we numerically study the influence of hardware errors in circuit QED experiments. To show the advantages over all-qubit hardware, we perform an end-to-end comparison of the gate complexity for the gauge-invariant hopping term and find an improvement of the asymptotic scaling with the boson number cutoff $S$ from $\mathcal{O}(\log(S)^2)$ to $\mathcal{O}(1)$ in our framework as well as, for bosonic matter, a constant factor improvement of better than $10^4$. We also find an improvement from $\mathcal{O}(\log(S))$ to $\mathcal{O}(1)$ for the $U(1)$ magnetic field term. While our work focusses on an implementation in superconducting hardware, our framework can also be used in trapped ion, and neutral atom hardware. This work establishes digital quantum simulation with hybrid oscillator-qubit hardware as a viable and advantageous method for the study of qubit-boson models in materials science, chemistry, and high-energy physics.

quant-ph↗

arXiv2024

Benchmarking Variational Quantum Algorithms for Combinatorial Optimization in Practice

Variational quantum algorithms and, in particular, variants of the varational quantum eigensolver have been proposed to address combinatorial optimization (CO) problems. Using only shallow ansatz circuits, these approaches are deemed suitable for current noisy intermediate-scale quantum hardware. However, the resources required for training shallow variational quantum circuits often scale superpolynomially in problem size. In this study we numerically investigate what this scaling result means in practice for solving CO problems using Max-Cut as a benchmark. For fixed resources, we compare the average performance of training a shallow variational quantum circuit, sampling with replacement, and a greedy algorithm starting from the same initial point as the quantum algorithm. We identify a minimum problem size for which the quantum algorithm can consistently outperform sampling and, for each problem size, characterize the separation between the quantum algorithm and the greedy algorithm. Furthermore, we extend the average case analysis by investigating the correlation between the performance of the algorithms by instance. Our results provide a step towards meaningful benchmarks of variational quantum algorithms for CO problems for a realistic set of resources.

quant-ph↗

arXiv2024

Concurrent VQE for Simulating Excited States of the Schwinger Model

This work explores the application of the concurrent variational quantum eigensolver (cVQE) for computing excited states of the Schwinger model. By designing suitable ansatz circuits utilizing universal SO(4) or SO(8) qubit gates, we demonstrate how to efficiently obtain the lowest two, four, and eight eigenstates with one, two, and three ancillary qubits for both vanishing and non-vanishing background electric field cases. Simulating the resulting quantum circuits classically with tensor network techniques, we demonstrate the capability of our approach to compute the two lowest eigenstates of systems with up to $\mathcal{O}(100)$ qubits. Given that our method allows for measuring the low-lying spectrum precisely, we also present a novel technique for estimating the additive mass renormalization of the lattice based on the energy gap. As a proof-of-principle calculation, we prepare the ground and first-excited states with one ancillary and four physical qubits on quantum hardware, demonstrating the practicality of using the cVQE to simulate excited states.

quant-ph↗

arXiv2024

Towards determining the (2+1)-dimensional Quantum Electrodynamics running coupling with Monte Carlo and quantum computing methods

In this paper, we examine a compact $U(1)$ lattice gauge theory in $(2+1)$ dimensions and present a strategy for studying the running coupling and extracting the non-perturbative $Λ$-parameter. To this end, we combine Monte Carlo simulations and quantum computing, where the former can be used to determine the numerical value of the lattice spacing $a$, and the latter allows for reaching the perturbative regime at very small values of the bare coupling and, correspondingly, small values of $a$. The methodology involves a series of sequential steps (i.e., the step scaling function) to bridge results from small lattice spacings to non-perturbative large-scale lattice calculations. Focusing on the pure gauge case, we demonstrate that these quantum circuits, adapted to gauge degrees of freedom, are able to capture the relevant physics by studying the expectation value of the plaquette operator, for matching with corresponding Monte Carlo simulations. We also present results for the static potential and static force, which can be related to the renormalized coupling. The procedure outlined in this work can be extended to Abelian and non-Abelian lattice gauge theories with matter fields and might provide a way towards studying lattice quantum chromodynamics utilizing both quantum and classical methods.

hep-lat↗

arXiv2024

Physics-Informed Bayesian Optimization of Variational Quantum Circuits

In this paper, we propose a novel and powerful method to harness Bayesian optimization for Variational Quantum Eigensolvers (VQEs) -- a hybrid quantum-classical protocol used to approximate the ground state of a quantum Hamiltonian. Specifically, we derive a VQE-kernel which incorporates important prior information about quantum circuits: the kernel feature map of the VQE-kernel exactly matches the known functional form of the VQE's objective function and thereby significantly reduces the posterior uncertainty. Moreover, we propose a novel acquisition function for Bayesian optimization called Expected Maximum Improvement over Confident Regions (EMICoRe) which can actively exploit the inductive bias of the VQE-kernel by treating regions with low predictive uncertainty as indirectly ``observed''. As a result, observations at as few as three points in the search domain are sufficient to determine the complete objective function along an entire one-dimensional subspace of the optimization landscape. Our numerical experiments demonstrate that our approach improves over state-of-the-art baselines.

cs.LG↗

arXiv2024

First-Order Phase Transition of the Schwinger Model with a Quantum Computer

We explore the first-order phase transition in the lattice Schwinger model in the presence of a topological $θ$-term by means of the variational quantum eigensolver (VQE). Using two different fermion discretizations, Wilson and staggered fermions, we develop parametric ansatz circuits suitable for both discretizations, and compare their performance by simulating classically an ideal VQE optimization in the absence of noise. The states obtained by the classical simulation are then prepared on the IBM's superconducting quantum hardware. Applying state-of-the art error-mitigation methods, we show that the electric field density and particle number, observables which reveal the phase structure of the model, can be reliably obtained from the quantum hardware. To investigate the minimum system sizes required for a continuum extrapolation, we study the continuum limit using matrix product states, and compare our results to continuum mass perturbation theory. We demonstrate that taking the additive mass renormalization into account is vital for enhancing the precision that can be obtained with smaller system sizes. Furthermore, for the observables we investigate we observe universality, and both fermion discretizations produce the same continuum limit.

hep-lat↗

arXiv2023

Gaussian Boson Sampling for binary optimization

In this study, we consider a Gaussian Boson Sampler for solving a Flight Gate Assignment problem. We employ a Variational Quantum Eigensolver approach using the Conditional Value-at-risk cost function. We provide proof of principle by carrying out numerical simulations on randomly generated instances.

quant-ph↗

arXiv2023

Studying the phase diagram of the three-flavor Schwinger model in the presence of a chemical potential with measurement- and gate-based quantum computing

We propose an ansatz quantum circuit for the variational quantum eigensolver (VQE), suitable for exploring the phase structure of the multi-flavor Schwinger model in the presence of a chemical potential. Our ansatz is capable of incorporating relevant model symmetries via constrains on the parameters, and can be implemented on circuit-based as well as measurement-based quantum devices. We show via classical simulation of the VQE that our ansatz is able to capture the phase structure of the model, and can approximate the ground state to a high level of accuracy. Moreover, we perform proof-of-principle simulations on superconducting, gate-based quantum hardware. Our results show that our approach is suitable for current gate-based quantum devices, and can be readily implemented on measurement-based quantum devices once available.

hep-lat↗

arXiv2023

Computing the Mass Shift of Wilson and Staggered Fermions in the Lattice Schwinger Model with Matrix Product States

Simulations of lattice gauge theories with tensor networks and quantum computing have so far mainly focused on staggered fermions. In this paper, we use matrix product states to study Wilson fermions in the Hamiltonian formulation and present a novel method to determine the additive mass renormalization. Focusing on the single-flavor Schwinger model as a benchmark model, we investigate the regime of a nonvanishing topological $θ$-term, which is inaccessible to conventional Monte Carlo methods. We systematically explore the dependence of the mass shift on the volume, the lattice spacing, the $θ$-parameter, and the Wilson parameter. This allows us to follow lines of constant renormalized mass, and therefore to substantially improve the continuum extrapolation of the mass gap and the electric field density. For small values of the mass, our continuum results agree with the theoretical prediction from mass perturbation theory. Going beyond Wilson fermions, our technique can also be applied to staggered fermions, and we demonstrate that the results of our approach agree with a recent theoretical prediction for the mass shift at sufficiently large volumes.

hep-lat↗

arXiv2023

Mass Renormalization of the Schwinger Model with Wilson and Staggered Fermions in the Hamiltonian Lattice Formulation

Lattice computations in the Hamiltonian formulation have so far mainly focused on staggered fermions. In these proceedings, we study Wilson fermions in the Hamiltonian formulation and propose a new method to determine the resulting mass shift. As a benchmark study, we examine the one-flavour Schwinger model with Wilson fermions and a topological $θ$-term using matrix product states. Wilson fermions explicitly break chiral symmetry; thus, the bare mass of the lattice model receives an additive renormalization. In order to measure this mass shift directly, we develop a method that is suitable for the Hamiltonian formulation, which relies on the fact that the vacuum expectation value of the electric field density vanishes when the renormalized mass is zero. We examine the dependence of the mass shift on the lattice spacing, the lattice volume, the $θ$-parameter, and the Wilson parameter. Using the mass shift, we then perform the continuum extrapolation of the electric field density and compare the resulting mass dependence to the analytical predictions of mass perturbation theory. We demonstrate that incorporating the mass shift significantly improves the continuum extrapolation. Finally, we apply our method to the same model using staggered fermions instead of Wilson fermions and compare the resulting mass shift to recent theoretical predictions.

hep-lat↗

arXiv2023

Simulating gauge theories with variational quantum eigensolvers in superconducting microwave cavities

Quantum-enhanced computing methods are promising candidates to solve currently intractable problems. We consider here a variational quantum eigensolver (VQE), that delegates costly state preparations and measurements to quantum hardware, while classical optimization techniques guide the quantum hardware to create a desired target state. In this work, we propose a bosonic VQE using superconducting microwave cavities, overcoming the typical restriction of a small Hilbert space when the VQE is qubit based. The considered platform allows for strong nonlinearities between photon modes, which are highly customisable and can be tuned in situ, i.e. during running experiments. Our proposal hence allows for the realization of a wide range of bosonic ansatz states, and is therefore especially useful when simulating models involving degrees of freedom that cannot be simply mapped to qubits, such as gauge theories, that include components which require infinite-dimensional Hilbert spaces. We thus propose to experimentally apply this bosonic VQE to the U(1) Higgs model including a topological term, which in general introduces a sign problem in the model, making it intractable with conventional Monte Carlo methods.

quant-ph↗

arXiv2023

Simulating the flight gate assignment problem on a trapped ion quantum computer

We study the flight gate assignment problem on IonQ's Aria trapped ion quantum computer using the variational quantum eigensolver. Utilizing the conditional value at risk as an aggregation function, we demonstrate that current trapped ion quantum hardware is able to obtain good solutions for this combinatorial optimization problem with high probability. In particular, we run the full variational quantum eigensolver for small instances and we perform inference runs for larger systems, demonstrating that current and near-future quantum hardware is suitable for addressing combinatorial optimization problems.

quant-ph↗

arXiv2023

A qubit-ADAPT Implementation for H$_2$ Molecules using an Explicitly Correlated Basis

With the recent advances in the development of devices capable of performing quantum computations, a growing interest in finding near-term applications has emerged in many areas of science. In the era of non-fault tolerant quantum devices, algorithms that only require comparably short circuits accompanied by high repetition rates are considered to be a promising approach for assisting classical machines with finding solution on computationally hard problems. The ADAPT approach previously introduced in Nat. Commun. 10, 3007 (2019) extends the class of variational quantum eigensolver (VQE) algorithms with dynamically growing ansätze in order to find approximations to ground and excited state energies of molecules. In this work, the ADAPT algorithm has been combined with a first-quantized formulation for the hydrogen molecule in the Born-Oppenheimer approximation, employing the explicitly correlated basis functions introduced in J. Chem. Phys. 43, 2429 (1965). By the virtue of their explicit electronic correlation properties, it is shown in classically performed simulations that relatively short circuits yield chemical accuracy ($< 1.6$ mHa) for ground and excited state potential curves that can compete with second quantized approaches such as Unitary Coupled Cluster.

quant-ph↗

arXiv2023

Exploring the CP-violating Dashen phase in the Schwinger model with tensor networks

We numerically study the phase structure of the two-flavor Schwinger model with matrix product states, focusing on the (1+1)-dimensional analog of the CP-violating Dashen phase in QCD. We simulate the two-flavor Schwinger model around the point where the positive mass of one fermion flavor corresponds to the negative mass of the other fermion flavor, which is a sign-problem afflicted regime for conventional Monte Carlo techniques. Our results indicate that the model undergoes a CP-violating Dashen phase transition at this point, which manifests itself in abrupt changes of the average electric field and the analog of the pion condensate in the model. Studying the scaling of the bipartite entanglement entropy as a function of the volume, we find clear indications that this transition is not of first order.

hep-lat↗

arXiv2023

Review on Quantum Computing for Lattice Field Theory

In these proceedings, we review recent advances in applying quantum computing to lattice field theory. Quantum computing offers the prospect to simulate lattice field theories in parameter regimes that are largely inaccessible with the conventional Monte Carlo approach, such as the sign-problem afflicted regimes of finite baryon density, topological terms, and out-of-equilibrium dynamics. First proof-of-concept quantum computations of lattice gauge theories in (1+1) dimensions have been accomplished, and first resource-efficient quantum algorithms for lattice gauge theories in (1+1) and (2+1) dimensions have been developed. The path towards quantum computations of (3+1)-dimensional lattice gauge theories, including Lattice QCD, requires many incremental steps of improving both quantum hardware and quantum algorithms. After reviewing these requirements and recent advances, we discuss the main challenges and future directions.

hep-lat↗

arXiv2023

Quantum algorithms for charged particle track reconstruction in the LUXE experiment

The LUXE experiment is a new experiment in planning in Hamburg, which will study Quantum Electrodynamics at the strong-field frontier. 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 expensive for classical computers. This paper investigates the potential future use of gate-based quantum computers for pattern recognition in track reconstruction. Approaches based on a quadratic unconstrained binary optimisation and a quantum graph neural network are investigated in classical simulations of quantum devices and compared with a classical track reconstruction algorithm. In addition, a proof-of-principle study is performed using quantum hardware.

quant-ph↗