arXiv subjects

Jonas Stein

Publications and source records attributed to Jonas Stein.

At least 19 recordsLinked to original sources

arXiv2026

The Organization of Environmental Coupling Shapes What Quantum Reservoirs Remember

For an open quantum reservoir, how the system forgets is part of how it computes. Quantum reservoir computing processes input streams with fixed quantum dynamics and trains only a linear readout. Dissipation can make old inputs fade, but prior studies commonly fix the environmental process and tune only its strength. Here we show numerically that the coupling pattern, meaning whether transitions connect to separate or shared environmental channels, changes which parts of the input history remain accessible. Paired simulations of finite spin reservoirs keep the Hamiltonian, inputs, measurements, and readout fixed. The tested patterns produce distinct task profiles, with no universal winner. Shared relaxation preserves more recent input history than independent local loss, and the retained memory changes when the qubits contribute with different relative phases to the shared decay channel. This ordering recurs across system sizes, Hamiltonians, input protocols, and targeted controls. Environmental coupling is therefore more than a damping parameter: it is a design layer that shapes not only how quickly information fades, but which input history remains available for computation.

quant-ph↗

arXiv2026

Implicit Differentiation for Measurement-Efficient Bilevel Quantum-Classical Optimization

Quantum optimization has shown promising results for quadratic unconstrained binary optimization (QUBO) problems. Real-world applications, however, often involve polynomial coefficients that depend on tunable external factors - such as demand forecasts or risk preferences - giving rise to bilevel optimization structures. We show how variational quantum algorithms (VQAs) can efficiently handle such parametric problems, making three contributions. First, we propose a bilevel optimization model for diagonal cost Hamiltonians where coefficients depend on a tunable outer parameter: an outer loop adjusts this parameter - reshaping the cost landscape - while an inner VQA optimizes circuit variables. Second, since derivative-free probing methods incur a multiplicative overhead when each outer evaluation requires a complete inner solve, we develop correlator-reuse implicit differentiation (CR-ID), which obtains outer gradients by reusing quantum measurements already collected during inner energy estimation, requiring essentially no additional circuit executions. Experiments across three coefficient families show that CR-ID consistently improves budget-normalized efficiency by ~4\% in 1D and over 14\% in multi-dimensional settings, showing a significant performance advantage compared to finite-difference methods. Third, we show that this property is architecture-dependent: VQE admits exact reuse gradients, whereas QAOA introduces a state-dependent term that creates a cost-bias trade-off.

quant-ph↗

arXiv2026

Exploiting Symmetry in Quantum Reservoir Computing

Quantum reservoir computing (QRC) uses a quantum processor without training it. The input is encoded into a quantum state, a fixed random circuit evolves it, selected observables are measured, and only a simple linear readout is trained on the measured values. We study QRC for forecasting on a ring of sensors, such as weather stations around a circle of latitude. On such a ring, the same physical rule governs every position, so a model that respects this symmetry can learn one shared local rule from all sensors at once instead of a separate rule per sensor. This is especially valuable when data is scarce. Because the readout sees only the measured numbers, the symmetry can be lost even when the quantum state respects it. We show how to preserve the symmetry by measuring every observable together with all its shifted copies and by using one shared rule for encoding, circuit, and readout, and we prove that this construction is sufficient. In a controlled audit the aligned design consistently outperforms misaligned alternatives, and the advantage persists in noisy simulations, on IBM hardware, and on real weather data.

quant-ph↗

arXiv2026

Symmetry Alone Is Not an Ansatz: Task-Aligned Interactions in Equivariant Quantum Circuits

The success of variational quantum learning models crucially depends on choosing parametrizations that reflect the structure of the problem at hand. Symmetries provide one of the clearest such structures: whenever transformations of the input leave the desired outcome unchanged, this invariance should be built into the model rather than discovered during training. However, imposing a symmetry does not by itself determine a useful ansatz. Even within the symmetry-preserving space, one must decide where the trainable degrees of freedom should be placed. In this work, we study this remaining design freedom in equivariant variational quantum circuits. Building on symmetry-based parameter sharing, we disentangle two architectural choices: how much symmetry should be enforced, and which symmetry-respecting interactions should be trainable. Using Tic-Tac-Toe as a fully enumerable and structurally transparent test case, we find that suitable subgroups preserve most of the generalization benefit. By contrast, the dominant gains arise from gates acting directly on decisive task motifs. Thus, symmetry defines the admissible design space, while effective ans\"atze require an additional task-informed choice of trainable interactions.

quant-ph↗

arXiv2026

Where a Quantum Reservoir Works: A Transferable Operating Band

In quantum reservoir computing, a fixed quantum system transforms an input signal, while learning reduces to training a simple linear readout on its measured outputs. Since the quantum dynamics themselves are never optimized, the method is well suited to today's hardware. Yet these dynamics must still be chosen carefully, because their settings remain fixed throughout training and inference. It therefore remains open whether useful dynamics occupy a task-transferable region of control space and whether that region can be found without target-task tuning. We address this question for a dissipative reservoir by mapping performance over three central physical controls: the strength of the input drive, the coupling between neighboring qubits, and the rate of dissipation. Good performance concentrates in a well-defined operating band of this control space. This region transfers across tasks and reservoir initializations, and the same regime persists under an architectural change. It is also mechanistically grounded, since it disappears whenever any of the mechanisms that create it is removed. Finally, the region can be located cheaply before any task is run, using a simple memory diagnostic.

quant-ph↗

arXiv2026

Parity Supervision as a Driver of Generalization in Quantum Generative Modeling

Generative models learn probability distributions in order to produce new samples beyond a finite training set. Their usefulness therefore depends on assigning probability to valid but previously unseen states. In a controlled benchmark, we test whether parity-based training provides an inductive bias for this kind of generalization in instantaneous quantum polynomial-time (IQP) circuit Born machines. We compare the same IQP circuit trained with parity supervision and coordinate-wise mean-squared error (MSE), together with classical controls. Parity supervision improves exact distributional fit and recovery of unseen high-value states over IQP-MSE. A circuit-free spectral reconstruction shows that the matched parity moments already transfer evidence from observed samples to structurally compatible unseen states, while the IQP circuit further refines this structure. These results identify parity supervision as both a tractable training signal and a generalization mechanism when the target distribution, training objective, and circuit architecture are spectrally aligned.

quant-ph↗

arXiv2026

Architecture Shape Governs QNN Trainability: Jacobian Null Space Growth and Parameter Efficiency

Variational quantum circuits with angle encoding implement truncated Fourier series, and architectures arranging $N$ qubits with $L$ encoding layers each -- sharing encoding budget $E = NL$ -- generate identical frequency spectra, identical frequency redundancy, and require the same minimum parameter count for coefficient control. Despite this equivalence, trainability varies substantially with architecture shape $(N,L)$ at fixed $E$. We identify structural rank deficiency of the coefficient matching Jacobian $J$ as the mechanism responsible. For serial single-qubit architectures, we prove $\mathrm{rank}(J) \leq 2L+1$ regardless of parameter count $P$, with $\dim(\ker J) \geq P-(2L+1)$ growing without bound -- a phenomenon we term \emph{structural gradient starvation}: a growing fraction of parameters become structurally decoupled from the loss as $P$ increases at fixed $L$. Parallel architectures avoid this via independent phase trajectories, ensuring $\sigma_{\min}(J^{(\mathrm{par})}) > 0$ generically for $P \leq 2E+1$, so no parameter lies in $\ker J$. For practitioners, we further show that the two natural routes to increasing parameter count have fundamentally different effects: adding feature map (FM) layers monotonically strengthens the Jacobian QFIM eigenvalue spectrum and achieves $R^2 \geq 0.95$ with $1.6$--$2.2\times$ fewer parameters than adding trainable blocks across all tested architectures, while trainable blocks improve training only through the classical interpolation mechanism with no quantum-specific benefit.

quant-ph↗

arXiv2026

From Quantum Shots to Training Data: Reorganizing Measurement Records in Quantum Machine Learning

Between keeping every shot as a noisy training example and averaging all shots into one clean feature lies an entire spectrum of data organizations that quantum machine learning usually leaves implicit. Shot grouping makes this choice explicit by partitioning a fixed measurement record into disjoint groups and averaging within each group, tuning smoothly between the two conventions with a single validated parameter and no additional quantum executions. We evaluate the method on chaotic synthetic benchmarks and on real-world data under strict execution budgets. At the balanced allocation, intermediate grouping lowers mean error across the evaluated tasks, with supported improvements on every task. Matched controls show that the gain acts as correctly scaled regularization of the classical readout. Unmitigated runs on two superconducting processors show positive mean differences on every task. Shot grouping therefore offers a practical way to improve finite-shot quantum learning at no added quantum cost.

quant-ph↗

arXiv2026

Quantum Optimization Methods for the Generalized Traveling Salesman Problem

This paper studies quantum optimization baselines for the Generalized Traveling Salesman Problem (GTSP), a clustered routing problem that naturally models variant selection and sequencing problems under discrete alternatives. We propose a novel GTSP QUBO formulation focused on maintaining feasible solutions for quantum annealing, as well as a hardware-executable gate-based pipeline utilizing the Quantum Approximate Optimization Algorithm (QAOA). We implement a constrained QAOA variant using an XY-mixer, which preserves the stepwise Hamming weight in the ideal circuit model, while feasibility with respect to the full GTSP constraints is tracked explicitly during post-processing. We compare the two quantum optimization paradigms on problem instances from GTSPLIB, an established benchmark dataset, and validate against classical state-of-the-art solvers. To mitigate current quantum hardware size limitations, we further extend a preprocessing method to reduce the node count in instance clusters, constructing new NISQ-friendly instances from reduced subsets. Across all tested instances, quantum solvers often produce competitive solution quality when tested on smaller graphs, but exhibit higher runtimes and a sharp degradation in feasibility and scalability as instance size grows. Our evaluation highlights where quantum optimizers can already succeed and which algorithmic bottlenecks, like sampling rates, runtime issues, and other practical failure modes, remain as open problems.

quant-ph↗

arXiv2026

Free Information Disrupts Even Bayesian Crowds

A core tenet underpinning the conception of contemporary information networks, such as social media platforms, is that users should not be constrained in the amount of information they can freely and willingly exchange with one another about a given topic. By means of a computational agent-based model, we show how even in groups of truth-seeking and cooperative agents with perfect information-processing abilities, unconstrained information exchange may lead to detrimental effects on the correctness of the group's beliefs. If unconstrained information exchange can be detrimental even among such idealized agents, it is prudent to assume it can also be so in practice. We therefore argue that constraints on information flow should be carefully considered in the design of communication networks with substantial societal impact, such as social media platforms.

cs.MA↗

arXiv2026

Constrained Quantum Optimization via Iterative Warm-Start XY-Mixers

The Quantum Approximate Optimization Algorithm (QAOA) is a leading hybrid heuristic for combinatorial optimization, but efficiently handling hard constraints remains a significant challenge. XY-mixers successfully confine quantum state evolution to a feasible subspace, such as the Hamming-weight-1 sector for one-hot constraints. On the contrary, warm-starting biases the search toward promising regions based on preliminary solutions. Combining these two techniques requires maintaining the essential alignment between the initial state and the mixer Hamiltonian to preserve convergence guarantees. Previous work demonstrated warm-starting with XY-mixers via a biased initial state, but relying only on standard mixer Hamiltonians. Consequently, the initial state is no longer a ground state of the mixer. In this work, we overcome these limitations by formulating a warm-started XY-mixer Hamiltonian for one-hot constraints and proving its ground-state properties. Furthermore, we provide a shallow circuit implementation suitable for NISQ implementations. We embed the warm-starting into a classical heuristic that iteratively updates the bias based on previous samples, called Iterative Warm-Starting (IWS). Extensive numerical simulations on Max-$k$-Cut and Traveling Salesperson Problem instances demonstrate that IWS-QAOA significantly accelerates the solution-finding process, increasing the probability of sampling optimal solutions by orders of magnitude compared to standard XY-QAOA. Finally, we validate our approach on the ibm_boston QPU using hardware-tailored 144-qubit problem instances. By coupling IWS-QAOA with a greedy steepest-descent post-processing strategy to repair infeasible measurements caused by hardware noise, we successfully identify optimal solutions on actual quantum devices.

quant-ph↗

arXiv2026

Long Range Frequency Tuning for QML

Angle-encoded variational quantum circuits admit a truncated Fourier series representation of their output, but approximating functions with maximum frequency $\omega_{\max}$ using fixed unary encoding requires $\mathcal{O}(\omega_{\max})$ encoding gates. Trainable-frequency (TF) circuits promise a reduction by learning the data-encoding prefactors alongside the ansatz parameters, adapting the accessible frequency spectrum to the target during training. We identify a practical barrier that prevents this promise from being realized: the prefactor gradient is suppressed by the spectral gap between the circuit's accessible frequencies and the target spectrum, independently of the ansatz parameters, confining gradient-driven prefactor movement to a narrow neighborhood of initialization. We propose \emph{ternary grid initialization} -- setting prefactors to $\{1, 3, 9, \ldots, 3^{k-1}\}$ -- which ensures every target frequency within $[-\omega_{\max}, \omega_{\max}]$ lies within $\tfrac{1}{2}$ unit of the accessible spectrum at initialization, so that the spectral-gap bound no longer constrains the target-driven gradient to be small. This is a necessary condition for reliable convergence, whose sufficiency we establish empirically. On a synthetic benchmark with target frequencies shifted well beyond the standard initialization range, ternary initialization achieves median $R^2 = 0.997$ versus $0.18$ for unary initialization, with $100\%$ of runs achieving $R^2 > 0.95$ against $0\%$. CMA-ES with $20\times$ the evaluation budget reaches only $25\%$ success, confirming the limitation is a property of the optimization landscape rather than of gradient-based optimization specifically. Real-world validation on two benchmark datasets demonstrates consistent advantages over both fixed and trainable unary baselines.

cs.LG↗

arXiv2026

Illustration of Barren Plateaus in Quantum Computing

Variational Quantum Circuits (VQCs) have emerged as a promising paradigm for quantum machine learning in the NISQ era. While parameter sharing in VQCs can reduce the parameter space dimensionality and potentially mitigate the barren plateau phenomenon, it introduces a complex trade-off that has been largely overlooked. This paper investigates how parameter sharing, despite creating better global optima with fewer parameters, fundamentally alters the optimization landscape through deceptive gradients -- regions where gradient information exists but systematically misleads optimizers away from global optima. Through systematic experimental analysis, we demonstrate that increasing degrees of parameter sharing generate more complex solution landscapes with heightened gradient magnitudes and measurably higher deceptiveness ratios. Our findings reveal that traditional gradient-based optimizers (Adam, SGD) show progressively degraded convergence as parameter sharing increases, with performance heavily dependent on hyperparameter selection. We introduce a novel gradient deceptiveness detection algorithm and a quantitative framework for measuring optimization difficulty in quantum circuits, establishing that while parameter sharing can improve circuit expressivity by orders of magnitude, this comes at the cost of significantly increased landscape deceptiveness. These insights provide important considerations for quantum circuit design in practical applications, highlighting the fundamental mismatch between classical optimization strategies and quantum parameter landscapes shaped by parameter sharing.

cs.LG↗

arXiv2026

Quantum Generator Kernels

Quantum kernel methods offer significant theoretical benefits by rendering classically inseparable features separable in quantum space. Yet, the practical application of Quantum Machine Learning (QML), currently constrained by the limitations of Noisy Intermediate-Scale Quantum (NISQ) hardware, necessitates effective strategies to compress and embed large-scale real-world data like images into the constrained capacities of existing quantum devices or simulators. To this end, we propose Quantum Generator Kernels (QGKs), a generator-based approach to quantum kernels, comprising a set of Variational Generator Groups (VGGs) that merge universal generators into a parameterizable operator, ensuring scalable coverage of the available quantum space. Thereby, we address shortcomings of current leading strategies employing hybrid architectures, which might prevent exploiting quantum computing's full potential due to fixed intermediate embedding processes. To optimize the kernel alignment to the target domain, we train a weight vector to parameterize the projection of the VGGs in the current data context. Our empirical results demonstrate superior projection and classification capabilities of the QGK compared to state-of-the-art quantum and classical kernel approaches and show its potential to serve as a versatile framework for various QML applications.

cs.LG↗

arXiv2026

Quantum Computing -- Strategic Recommendations for the Industry

This whitepaper surveys the current landscape and short- to mid-term prospects for quantum-enabled optimization and machine learning use cases in industrial settings. Grounded in the QCHALLenge program, it synthesizes hardware trajectories from different quantum architectures and providers, and assesses their maturity and potential for real-world use cases under a standardized traffic-light evaluation framework. We provide a concise summary of relevant hardware roadmaps, distinguishing superconducting and ion-trap technologies, their current states, modalities, and projected scaling trajectories. The core of the presented work are the use case evaluations in the domains of optimization problems and machine learning applications. For the conducted experiments, we apply a consistent set of evaluation criteria (model formulation, scalability, solution quality, runtime, and transferability) which are assessed in a shared system of three categories, ranging from optimistic (solutions produced by quantum computers are competitive with classical methods and/or a clear path to a quantum advantage is shown) to pessimistic (significant hurdles prevent practical application of quantum solutions now and potentially in the future). The resulting verdicts illuminate where quantum approaches currently offer promise, where hybrid classical-quantum strategies are most viable, and where classical methods are expected to remain superior.

quant-ph↗

arXiv2025

Quantum Optimization Algorithms

Quantum optimization allows for up to exponential quantum speedups for specific, possibly industrially relevant problems. As the key algorithm in this field, we motivate and discuss the Quantum Approximate Optimization Algorithm (QAOA), which can be understood as a slightly generalized version of Quantum Annealing for gate-based quantum computers. We delve into the quantum circuit implementation of the QAOA, including Hamiltonian simulation techniques for higher-order Ising models, and discuss parameter training using the parameter shift rule. An example implementation with Pennylane source code demonstrates practical application for the Maximum Cut problem. Further, we show how constraints can be incorporated into the QAOA using Grover mixers, allowing to restrict the search space to strictly valid solutions for specific problems. Finally, we outline the Variational Quantum Eigensolver (VQE) as a generalization of the QAOA, highlighting its potential in the NISQ era and addressing challenges such as barren plateaus and ansatz design.

quant-ph↗

arXiv2025

Evaluating Variational Quantum Circuit Architectures for Distributed Quantum Computing

Scaling quantum computers, i.e., quantum processing units (QPUs) to enable the execution of large quantum circuits is a major challenge, especially for applications that should provide a quantum advantage over classical algorithms. One approach to scale QPUs is to connect multiple machines through quantum and classical channels to form clusters or even quantum networks. Using this paradigm, several smaller QPUs can collectively execute circuits that each would not be able on its own. However, communication between QPUs is costly as it requires generating and maintaining entanglement, and hence it should be used wisely. In this paper, we evaluate the architectures, and in particular the entanglement patterns, of variational quantum circuits in a distributed quantum computing (DQC) setting. That is, using Qiskit, we simulate the execution of an eight qubit circuit using four QPUs each with two computational and two communication qubits where non-local CX-gates are performed using the remote-CX protocol. We compare the performance of various circuits on a binary classification task where training is executed under ideal and testing under noisy conditions. The study provides initial results on suitable VQC architectures for the DQC paradigm, and indicates that a standard VQC baseline is not always the best choice, and alternative architectures that use entanglement between QPUs sparingly deliver better results under noise.

quant-ph↗

arXiv2025

Evolutionary-Based Circuit Optimization for Distributed Quantum Computing

In this work, we evaluate an evolutionary algorithm (EA) to optimize a given circuit in such a way that it reduces the required communication when executed in the Distributed Quantum Computing (DQC) paradigm. We evaluate our approach for a state preparation task using Grover circuits and show that it is able to reduce the required global gates by more than 89% while still achieving high fidelity as well as the ability to extract the correct solution to the given problem. We also apply the approach to reduce circuit depth and number of CX gates. Additionally, we run experiments in which a circuit is optimized for a given network topology after each qubit has been assigned to specific nodes in the network. In these experiments, the algorithm is able to reduce the communication cost (i.e., number of hops between QPUs) by up to 19%.

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