arXiv subjects

Frank K. Wilhelm

Publications and source records attributed to Frank K. Wilhelm.

At least 19 recordsLinked to original sources

arXiv2026

Analytical Series Expansion for Efficient Gradient Evaluation in Multi-Qubit Optimal Control

The open-loop optimization of quantum dynamics using gradient-based quantum optimal control methods involves calculating the time-ordered propagator and its gradient. In this Letter, we present a unifying framework for gradient-based quantum optimal control with respect to any general pulse parameterization by deriving the formal solution from first principles. For the case of unitary propagators, we derive a series expansion involving time-independent commutators and time-dependent coefficients, significantly reducing the number of matrix exponentials needed to compute the gradient. The expansion highlights the connection between derivatives of the propagator and operator evolution in the Heisenberg picture. The method is particularly suited for simulating optimal control tasks in quantum systems with local interactions, which is a common situation in large multi-qubit platforms. We compare the computational cost required for the series with the Gradient Optimization of Analytic conTrols (GOAT) method, and, focusing on the problem of preparation of a GHZ state, demonstrate more than an order of magnitude speedup for a qubit ladder and a chain geometry.

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arXiv2026

Quantum Simulation of Strongly Correlated Fermion-Phonon Models in Circuit QED

Gate-based digital quantum simulations offer an exciting new paradigm for studying the many-body physics of strongly correlated systems. In this context, electron-phonon models are challenging for qubit-only quantum simulators, as bosonic degrees of freedom require costly finite-dimensional encodings. Here, we elaborate on an alternative approach based on a digital-analog circuit QED architecture, where fermions are encoded in transmon qubits while bosons are represented directly by microwave resonators. The central building block of this framework is a qubit-resonator Rabi gate that emulates strong electron-phonon coupling and can be implemented through a sequence of resonant Jaynes-Cummings gates interleaved with layers of single-qubit rotations. Using this Rabi gate as the fundamental unitary operation, we construct quantum circuits for the Hubbard-Holstein and Yukawa-Sachdev-Ye-Kitaev models, which describe, respectively, strongly correlated electrons coupled to phonons and phonon-mediated interactions among Majorana fermions. We further demonstrate how nonclassical phonon physics and signatures of quantum chaos in these models can be probed through circuit simulations, and develop measurement and variational protocols tailored to near-term superconducting quantum hardware.

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arXiv2026

Control Protocols for Entangling Gates for Group-IV Color-Centers in Diamond

Accurately controlling entangling gates remains a major challenge for quantum technology applications with solid-state spin qubits. Here, we study a group-IV color-center with a strongly-coupled nuclear spin and approach the problem from a quantum control perspective. We show that there are three different types of entangling gates where the entanglement is mediated by the parallel hyperfine-coupling component, the orthogonal one or both. We derive the respective quantum speed limits (QSL) and show by means of dynamical decoupling, resonant driving of single- and double-quantum transitions, quantum optimal control and algebraic gate decomposition how these gates can be realized. We finally discuss the experimental applicability.

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arXiv2026

Self gravity decoheres quantum systems

We study the effects of self gravity on the quantum state of a massive and static particle that initially contains quantum coherence between two positions. We employ linearized quantum gravity to obtain the self-interacting dynamics of the particle mediated by gravitons, and find that the effective evolution of the particle's state can be viewed as a quantum channel composed of a unitary, dephasing, depolarizing, and erasure part. Depolarization drives the state towards maximal mixedness while depolarization and dephasing decrease its quantum coherence. Crucially, the intrinsic diffusion and dephasing timescales of the problem determine a relation between the mass and size of the particle that naturally identifies the transition between its classical and quantum regime. Our work therefore provides an explanation for the observational difference between the quantum behavior of small and light systems and the classical behavior of larger and heavier ones.

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arXiv2026

Benchmarking Optimization Algorithms for Automated Calibration of Quantum Devices

We present the results of a comprehensive study of optimization algorithms for the calibration of quantum devices. As part of our ongoing efforts to automate bring-up, tune-up, and system identification procedures, we investigate a broad range of optimizers within a simulated environment designed to closely mimic the challenges of real-world experimental conditions. Our benchmark includes widely used algorithms such as Nelder-Mead and the state-of-the-art Covariance Matrix Adaptation Evolution Strategy (CMA-ES). We evaluate performance in both low-dimensional settings, representing simple pulse shapes used in current optimal control protocols with a limited number of parameters, and high-dimensional regimes, which reflect the demands of complex control pulses with many parameters. Based on our findings, we recommend the CMA-ES algorithm and provide empirical evidence for its superior performance across all tested scenarios.

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arXiv2026

Optimal Two-Qubit Gates for Group-IV Color-Centers in Diamond

Color centers associated with group-IV dopants in diamond with long-lived nuclear spins have emerged as major candidates for distributed quantum computing nodes and quantum repeaters. Several proof-of-principle experiments have already been demonstrated. A key operation for long-distance entanglement-distribution protocols are fast and robust gates between the electron spin and a nuclear spin. Here, we investigate numerically for an existing experimental platform of a Germanium-vacancy (GeV) center with a strongly-coupled ${}^{13}$C spin, how such gates can be implemented via quantum optimal control. In the presence of realistic noise we investigate different parameter regimes and gate operations and obtain robust two-qubit gates with fidelities exceeding $99.9 \%$. The framework provides a scalable strategy for group-IV quantum nodes and can be adapted to related architectures.

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arXiv2026

Exploring the Fidelity of Flux Qubit Measurement in Different Bases via the Quantum Flux Parametron

High-fidelity qubit readout is a fundamental requirement for practical quantum computing systems. In this work, we investigate methods to enhance the measurement fidelity of flux qubits via a quantum flux parametron-mediated readout scheme. Through theoretical modeling and numerical simulations, we analyze the impact of different measurement bases on fidelity in single-qubit and coupled two-qubit systems. For single-qubit systems, we show that energy bases consistently outperform flux bases in achieving higher fidelity. In coupled two-qubit systems, we explore two measurement models: sequential and simultaneous measurements, both aimed at reading out a single target qubit. Our results indicate that the highest fidelity can be achieved either by performing sequential measurement in a dressed basis over a longer duration or by conducting simultaneous measurement in a bare basis over a shorter duration. Importantly, the sequential measurement model consistently yields more robust and higher fidelity readouts compared to the simultaneous approach. These findings quantify achievable fidelities and provide valuable guidance for optimizing measurement protocols in emerging quantum computing architectures.

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arXiv2026

Data-Efficient Quantum Noise Modeling via Machine Learning

Maximizing the computational utility of near-term quantum processors requires predictive noise models that inform robust, noise-aware compilation and error mitigation. Conventional models often fail to capture the complex error dynamics of real hardware or require prohibitive characterization overhead. We introduce a data-efficient framework that first constructs a physically motivated, parameterized noise model, and subsequently employs machine learning-driven Bayesian optimization to identify its parameters. Our approach circumvents costly characterization protocols by estimating algorithm- and hardware-specific error parameters directly from readily available experimental data derived from existing application and benchmark circuit executions. The generality and robustness of the framework are demonstrated across diverse algorithms and superconducting devices, yielding high-fidelity predictions by estimating an independent parameter set tailored to each specific algorithm-hardware context. Crucially, we show that a model calibrated exclusively on small-scale circuits accurately predicts the behavior of larger validation circuits. Our data-efficient approach achieves up to a 65% improvement in model fidelity quantified by the Hellinger distance between predicted and experimental circuit output distributions, compared to standard noise models derived from device properties. This work establishes a practical paradigm for application-aware noise characterization, enabling compilation and error-mitigation strategies tailored to the specific interplay between quantum algorithms and device-specific noise dynamics.

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arXiv2026

Quantum Deep Learning: A Comprehensive Review

Quantum deep learning (QDL) explores the use of both quantum and quantum-inspired resources to determine when deep learning's core capabilities, such as expressivity, generalization, and scalability, can be enhanced based on specific resource constraints. Distinct from broader quantum machine learning, QDL emphasizes compositional depth at the pipeline level and the integration of quantum or quantum-inspired components within end-to-end workflows. This review provides an operational definition of QDL and introduces a taxonomy comprising four primary paradigms: hybrid quantum-classical models, quantum deep neural networks, quantum algorithms for deep learning primitives, and quantum-inspired classical algorithms. Theoretical principles are connected to advanced architectures, software toolchains, and experimental demonstrations across superconducting, trapped-ion, photonic, semiconductor spin, and neutral-atom systems, as well as quantum annealers. Claims of quantum advantage are critically assessed by distinguishing provable complexity-theoretic separations from empirical observations. The analysis characterizes trade-offs between model expressivity, trainability, and classical simulability, while systematically detailing the bottlenecks imposed by optimization landscapes, input-output access models, and hardware constraints. Applications are surveyed in domains encompassing image classification, natural language processing, scientific discovery, quantum data processing, and quantum optimal control, underscoring fair benchmarking against optimized classical counterparts and a comprehensive assessment of resource requirements. This review serves as a tutorial entry point for graduate students while guiding readers to specialized literature. It concludes with a verification-aware roadmap to transition QDL from near-term demonstrations to scalable and fault-tolerant implementations.

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arXiv2025

A mathematical justification to apply the secular approximation to the Redfield equation

Quantum master equations are widely used to describe the dynamics of open quantum systems. All these different master equations rely on specific approximations that may or may not be justified. Starting from a microscopic model, applying the standard Born and Markov approximations results in the Redfield equation that does not guarantee to preserve positivity. The latter is typically achieved by additionally applying the secular approximation resulting in a quantum master equation in Lindblad form. There are other ways to obtain an equation in Lindblad form, one of which is the recently proposed Universal Lindblad Equation. It has been shown that it is in the same equivalence class of approximations as the Redfield master equation although avoiding the heuristic secular approximation [arXiv:2004.01469]. In this work, we prove that the solutions of the master equation obtained by applying the secular approximation are also obtained by an approximation of the same order as the one performed to obtain the Redfield equation. We hereby provide a mathematical justification for the secular approximation. We show that the result of applying the secular approximation is obtained naturally by applying a self-consistency argument. This shows that the resulting master equation is also in the same equivalence class of approximations as the Redfield master equation and the Universal Lindblad Equation. We furthermore compare it to the Universal Lindblad Equation numerically and show numerical evidence that the master equation obtained through the secular approximation yields more accurate solutions.

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arXiv2025

End-to-End Quantum Algorithm for Topology Optimization in Structural Mechanics

Topology optimization is a key methodology in engineering design for finding efficient and robust structures. Due to the enormous size of the design space, evaluating all possible configurations is typically infeasible. In this work, we present an end-to-end, fault-tolerant quantum algorithm for topology optimization that operates on the exponential Hilbert space representing the design space. We demonstrate the algorithm on the two-dimensional Messerschmitt-Bölkow-Blohm (MBB) beam problem. By restricting design variables to binary values, we reformulate the compliance minimization task as a combinatorial satisfiability problem solved using Grover's algorithm. Within Grover's oracle, the compliance is computed through the finite-element method (FEM) using established quantum algorithms, including block-encoding of the stiffness matrix, Quantum Singular Value Transformation (QSVT) for matrix inversion, Hadamard test, and Quantum Amplitude Estimation (QAE). The complete algorithm is implemented and validated using classical quantum-circuit simulations. A detailed complexity analysis shows that the method evaluates the compliance of exponentially many structures in quantum superposition in polynomial time. In the global search, our approach maintains Grover's quadratic speedup compared to classical unstructured search. Overall, the proposed quantum workflow demonstrates how quantum algorithms can advance the field of computational science and engineering.

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arXiv2025

Towards Quantum Algorithms for the Optimization of Spanning Trees: The Power Distribution Grids Use Case

Optimizing the topology of networks is an important challenge across engineering disciplines. In energy systems, network reconfiguration can substantially reduce losses and costs and thus support the energy transition. Unfortunately, many related optimization problems are NP hard, restricting practical applications. In this article, we address the problem of minimizing losses in radial networks, a problem that routinely arises in distribution grid operation. We show that even the computation of approximate solutions is computationally hard and propose quantum optimization as a promising alternative. We derive two quantum algorithmic primitives based on the Quantum Alternating Operator Ansatz (QAOA) that differ in the sampling of network topologies: a tailored sampling of radial topologies and simple sampling with penalty terms to suppress non-radial topologies. We show how to apply these algorithmic primitives to distribution grid reconfiguration and quantify the necessary quantum resources.

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arXiv2025

Digital-Analog Simulations of Schrödinger Cat States in the Dicke-Ising Model

The Dicke-Ising model, one of the few paradigmatic models of matter-light interaction, exhibits a superradiant quantum phase transition above a critical coupling strength. However, in natural optical systems, its experimental validation is hindered by a "no-go theorem''. Here, we propose a digital-analog quantum simulator for this model based on an ensemble of interacting qubits coupled to a single-mode photonic resonator. We analyze the system's free energy landscape using field-theoretical methods and develop a digital-analog quantum algorithm that disentangles qubit and photon degrees of freedom through a parity-measurement protocol. This disentangling enables the emulation of a photonic Schrödinger cat state, which is a hallmark of the superradiant ground state in finite-size systems and can be unambiguously probed through the Wigner tomography of the resonator's field.

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arXiv2025

Post-processing noisy quantum computations utilizing N-representability constraints

We propose and analyze a method for improving quantum chemical energy calculations on a quantum computer impaired by decoherence and shot noise. The error mitigation approach relies on the fact that the one- and two-particle reduced density matrices (1- and 2-RDM) of a chemical system need to obey so-called N-representability constraints. We post-process the result of an RDM measurement by projecting it into the subspace where certain N-representability conditions are fulfilled. Furthermore, we utilize that such constraints also hold in the hole and particle-hole sector and perform projections in these sectors as well. We expand earlier work by conducting a careful analysis of the method's performance in the context of quantum computing. Specifically, we consider typical decoherence channels (dephasing, damping, and depolarizing noise) as well as shot noise due to a finite number of projective measurements. We provide analytical considerations and examine numerically three example systems, \ch{H2}, \ch{LiH}, and \ch{BeH2}. From these investigations, we derive our own practical yet effective method to best employ the various projection options. Our results show the approach to significantly lower energy errors and measurement variances of (simulated) quantum computations.

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arXiv2025

Quantum computing and artificial intelligence: status and perspectives

This white paper discusses and explores the various points of intersection between quantum computing and artificial intelligence (AI). It describes how quantum computing could support the development of innovative AI solutions. It also examines use cases of classical AI that can empower research and development in quantum technologies, with a focus on quantum computing and quantum sensing. The purpose of this white paper is to provide a long-term research agenda aimed at addressing foundational questions about how AI and quantum computing interact and benefit one another. It concludes with a set of recommendations and challenges, including how to orchestrate the proposed theoretical work, align quantum AI developments with quantum hardware roadmaps, estimate both classical and quantum resources - especially with the goal of mitigating and optimizing energy consumption - advance this emerging hybrid software engineering discipline, and enhance European industrial competitiveness while considering societal implications.

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arXiv2025

Calculating response functions of coupled oscillators using quantum phase estimation

We study the problem of estimating frequency response functions of systems of coupled, classical harmonic oscillators using a quantum computer. The functional form of these response functions can be mapped to a corresponding eigenproblem of a Hermitian matrix $H$, thus suggesting the use of quantum phase estimation. Our proposed quantum algorithm operates in the standard $s$-sparse, oracle-based query access model. For a network of $N$ oscillators with maximum norm $\lVert H \rVert_{\mathrm{max}}$, and when the eigenvalue tolerance $\varepsilon$ is much smaller than the minimum eigenvalue gap, we use $\mathcal{O}(\log(N s \lVert H \rVert_{\mathrm{max}}/\varepsilon)$ algorithmic qubits and obtain a rigorous worst-case query complexity upper bound $\mathcal{O}(s \lVert H \rVert_{\mathrm{max}}/(δ^2 \varepsilon) )$ up to logarithmic factors, where $δ$ denotes the desired precision on the coefficients appearing in the response functions. Crucially, our proposal does not suffer from the infamous state preparation bottleneck and can as such potentially achieve large quantum speedups compared to relevant classical methods. As a proof-of-principle of exponential quantum speedup, we show that a simple adaptation of our algorithm solves the random glued-trees problem in polynomial time. We discuss practical limitations as well as potential improvements for quantifying finite size, end-to-end complexities for application to relevant instances.

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arXiv2025

Truncated Variational Hamiltonian Ansatz: efficient quantum circuit design for quantum chemistry and material science

Quantum computing has the potential to revolutionize quantum chemistry and material science by offering solutions to complex problems unattainable with classical computers. However, the development of efficient quantum algorithms that are efficient under noisy conditions remains a major challenge. This paper introduces the truncated Variational Hamiltonian Ansatz (tVHA), a novel circuit design for conducting quantum calculations on Noisy Intermediate-Scale Quantum (NISQ) devices. tVHA provides a promising approach for a broad range of applications by utilizing principles from the adiabatic theorem in solid state physics. Our proposed ansatz significantly reduces the parameter count and can decrease circuit size substantially, with a trade-off in accuracy. Thus, tVHA facilitates easier convergence within the variational quantum eigensolver framework compared to state-of-the-art ansätze such as Unitary Coupled Cluster (UCC) and Hardware-Efficient Ansatz (HEA). While this paper concentrates on the practical applications of tVHA in quantum chemistry, demonstrating its suitability for both weakly and strongly correlated systems and its compatibility with active space calculations, its underlying principles suggest a wider applicability extending to the broader field of material science computations on quantum computing platforms.

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arXiv2025

Bounding the rotating wave approximation for coupled harmonic oscillators

In this work we study the validity of the rotating wave approximation of an ideal system composed of two harmonic oscillators evolving with a quadratic Hamiltonian and arbitrarily strong interaction. We prove its validity for arbitrary states by bounding the error introduced. We then restrict ourselves to the dynamics of Gaussian states and are able to fully quantify the deviation of arbitrary pure Gaussian states that evolve through different dynamics from a common quantum state. We show that this distance is fully determined by the first and second moments of the statistical distribution of the number of excitations created from the vacuum during an appropriate effective time-evolution. We use these results to completely control the dynamics for this class of states, therefore providing a toolbox to be used in quantum optics and quantum information. Applications and potential physical implementations are also discussed.

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