arXiv subjects

Markus Baumann

Publications and source records attributed to Markus Baumann.

13 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

Emergent Problem-Graph Alignment in RL-Discovered Entanglement Topologies for QAOA

In the Quantum Approximate Optimization Algorithm (QAOA), the entanglement topology, where qubit pairs are connected by two-qubit gates, is conventionally set equal to the edge set of the problem graph. This coupling ties circuit design to explicit problem knowledge and may not yield the most trainable circuit under limited optimization budgets. We investigate whether a reinforcement learning (RL) agent can discover more effective entanglement topologies for QAOA-based MaxCut optimization without direct access to the problem graph. A Masked Proximal Policy Optimization agent sequentially places IsingZZ gates to construct a circuit topology, while a variational inner loop optimizes the resulting QAOA parameters and returns the approximation ratio as a sparse terminal reward. The agent's observation contains only the edges placed so far and the current approximation ratio; graph structure can only be inferred indirectly through the optimization reward. On Erd\H{o}s--R\'{e}nyi instances with up to $10$~qubits, the agent consistently converges to topologies that are strict subsets of the problem graph, achieving overlap ratios approaching $1.0$, despite receiving no explicit information about the graph structure in its observations. These sparse, problem-aligned topologies outperform the full graph topology and several structural baselines when the optimization budget is limited ($50$~gradient steps), but are overtaken by denser topologies given sufficient optimization budget. Our results reveal a trainability--expressibility trade-off governed by topology density and suggest that the variational optimization landscape implicitly encodes structural information about the problem Hamiltonian.

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

Detrimental Agnostic Entanglement: The Case Against Hardware-Efficient Ans\"atze for Combinatorial Optimization

Variational quantum algorithms (VQAs) for combinatorial optimization routinely employ entangling gates as a default design choice, yet the role of entanglement, in its amount and structure, remains poorly understood. This gap is particularly consequential for problems governed by diagonal Hamiltonians, whose ground states are classical product states and therefore require no entanglement in principle, raising the fundamental question of whether and how entangling gates help or hinder the variational search. We investigate this question for MaxCut by introducing two complementary control mechanisms that provide smooth, monotonic control over hardware-efficient ansatz (HEA) entanglement as quantified by the Meyer-Wallach measure $Q$, and by benchmarking against QAOA as a problem-structured reference. Tracking the entanglement trajectory $Q(t)$ throughout VQA training reveals that when the ansatz grants the optimizer indirect control over entanglement through its parameters, it consistently drives entanglement down. In line with this tendency, a fully separable ansatz outperforms all entangled hardware-efficient configurations, establishing a monotonic relationship: less problem-agnostic entanglement yields better performance. In contrast, QAOA, whose entanglement is structurally derived from the problem Hamiltonian, maintains high entanglement yet achieves competitive solution quality, demonstrating that entanglement structure, not merely quantity, determines its utility. These findings suggest that HEAs for diagonal Hamiltonians are inappropriate and that variational approaches to combinatorial optimization should prioritize problem-structured circuit designs.

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

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↗

arXiv2025

Topology-Guided Quantum GANs for Constrained Graph Generation

Quantum computing (QC) promises theoretical advantages, benefiting computational problems that would not be efficiently classically simulatable. However, much of this theoretical speedup depends on the quantum circuit design solving the problem. We argue that QC literature has yet to explore more domain specific ansatz-topologies, instead of relying on generic, one-size-fits-all architectures. In this work, we show that incorporating task-specific inductive biases -- specifically geometric priors -- into quantum circuit design can enhance the performance of hybrid Quantum Generative Adversarial Networks (QuGANs) on the task of generating geometrically constrained K4 graphs. We evaluate a portfolio of entanglement topologies and loss-function designs to assess their impact on both statistical fidelity and compliance with geometric constraints, including the Triangle and Ptolemaic inequalities. Our results show that aligning circuit topology with the underlying problem structure yields substantial benefits: the Triangle-topology QuGAN achieves the highest geometric validity among quantum models and matches the performance of classical Generative Adversarial Networks (GAN). Additionally, we showcase how specific architectural choices, such as entangling gate types, variance regularization and output-scaling govern the trade-off between geometric consistency and distributional accuracy, thus emphasizing the value of structured, task-aware quantum ansatz-topologies.

quant-ph↗

arXiv2025

From Classical Data to Quantum Advantage -- Quantum Policy Evaluation on Quantum Hardware

Quantum policy evaluation (QPE) is a reinforcement learning (RL) algorithm which is quadratically more efficient than an analogous classical Monte Carlo estimation. It makes use of a direct quantum mechanical realization of a finite Markov decision process, in which the agent and the environment are modeled by unitary operators and exchange states, actions, and rewards in superposition. Previously, the quantum environment has been implemented and parametrized manually for an illustrative benchmark using a quantum simulator. In this paper, we demonstrate how these environment parameters can be learned from a batch of classical observational data through quantum machine learning (QML) on quantum hardware. The learned quantum environment is then applied in QPE to also compute policy evaluations on quantum hardware. Our experiments reveal that, despite challenges such as noise and short coherence times, the integration of QML and QPE shows promising potential for achieving quantum advantage in RL.

quant-ph↗