quantum software engineers

Abstract: Selecting an effective quantum compiler configuration requires coordinated decisions over both hardware targets and compiler settings, with the ultimate goal of improving circuit execution fidelity. Existing SOTA approaches typically decompose this problem into two sequential stages: a device is chosen first, after which compiler options are tuned on that device through RL-based search. This bottom-up strategy can be fundamentally limited by its initial device decision, since a poorly matched backend may constrain the best fidelity achievable regardless of how effectively later compiler options are optimized. In contrast to classical compiler tuning, where the search space is often prohibitively large, the configuration space of quantum compilers remains manageable enough to support exhaustive search. Consequently, rather than repeatedly searching from candidate configurations, one can derive reusable configuration knowledge from offline oracle results and apply it directly to new circuits. In this paper, we introduce a top-down configuration-selection paradigm and build QuOPTBench, an exhaustively searched benchmark containing oracle configurations for 268 quantum circuits. We first study whether LLMs can directly infer suitable configurations and evaluate ten representative LLMs. The results reveal that vanilla LLMs remain far from the oracle. We then employ an LLM to extract transferable rules from sampled circuits governing configuration selection. Using these rules together with predictors trained on the enumerated configuration data of the sampled circuits, we design QuTOP, a rule-guided ML framework that performs fast configuration selection without iterative online search. Across our evaluation, the distilled rules consistently strengthen LLM-based selection, while QuTOP provides the strongest overall balance between solution quality and selection latency among the baselines.

Abstract: Fault-tolerant quantum applications depend on both decoded measurement information and a continuing supply of magic states. While an operation waits for either, its logical data require protection that produces more syndrome data and decoding work. Architects must provision the quantum and classical parts of the machine together, before complete systems are available to measure. FTWeave is a system-level simulator for this architectural exploration. It accepts OpenQASM 2/3 circuits, CUDA-Q Logical compiler artifacts, Stim circuits, and provider-derived physical inputs through adapters that preserve operation and measurement dependencies. Users bind these inputs to quantum resources, classical processors, memory, communication, and factory configurations. One event timeline determines application progress, resource ownership, and continuing protection. This supplies the system model needed to connect circuit and decoder evidence to application performance. Controlled demand studies and complete multiplier and Ising circuits show why the coupling changes provisioning decisions. A fixed-work approximation predicts a 3.55x multiplier speedup from additional factories where the coupled model gives almost none. Explicit ownership also changes useful capacity: increasing decoder workers alone has no benefit in a storage-constrained case, while increasing workers and feedback entries together gives 4.93x speedup. Selected color and hypergraph-product code mappings take 53-90% longer under decoder service variability, despite an unchanged mean. These comparisons identify useful resource combinations and distinguish protection work from the elapsed lifetime of quantum data.

Abstract: Quantum processors are increasingly used as accelerators inside high-performance computing (HPC) workflows. A workflow runtime decides which quantum circuits to run, how to group them into provider jobs, and what to repeat after a failed attempt. Many search problems split into independent parts, but the runtime can use that structure only when the workflow exposes the parts and a validity check for each one. SemQBench measures what a runtime gains from this visibility. It compares seven execution policies for the same search problem, including two controls without amplitude amplification. The policies change one runtime choice at a time: whether to amplify, whether partial results may be combined across runs, whether the parts share one circuit, and what a retry keeps. We run them on the 20-qubit IQM Garnet processor using 106 distinct circuits in three jobs, and report circuit executions, active device time, and provider jobs separately before combining them in a cost model. Amplifying the problem as one whole circuit shows no statistically clear gain over random sampling and uses 6.7-104$\times$ more active device time. Exposing the parts and collecting valid partial results across a fixed batch of runs cuts the executions needed for 95% completion confidence by 2.20-4.00$\times$, and this policy is never worse than the other amplified policies in executions, device time, or jobs; it is selected in 99 of 108 overhead settings. Fewer executions do not always mean less device time: on one workload, executions fall from thirteen to four while active device time rises from 7.44 to 9.81 $μ$s. Exposing problem structure therefore gives the runtime a strong default policy and the measurements needed to decide when the simpler unamplified option is cheaper.

Abstract: Together with a right-handed neutrino, the fermions of one generation of the Standard Model are labelled by five bits, a combinatorial structure tied to anomaly cancellation. We make this precise. Anomaly cancellation is the vanishing of a cubic form, the defining property of triorthogonal codes, the quantum error-correcting codes behind magic state distillation. Removing the right-handed neutrino gives a $[[15,1,3]]_p$ code for every prime $p$, including the Bravyi-Kitaev code for $p = 2$. For qutrits it is the unique shortest distance-three triorthogonal code.

Abstract: Quantum federated learning trains a quantum neural network (QNN) across nodes that hold quantum data, such as the states of quantum sensors. To forget data, unlearning methods for quantum models replay them, and federated unlearning from stored updates removes whole nodes only. Quantum data cannot be replayed, since a state is consumed when measured and cannot be cloned. We propose Shadow-based Data Erasure (SHADE), in which each node records a classical shadow of every training state, a few randomized single-qubit measurements taken at training time. The gradient and curvature of a QNN on a state are expectations of observables, so SHADE estimates them for the forget data from the shadows at any later parameters and removes their effect by a federated Newton correction. Only classical estimates cross the network. We prove that the shadow size needed for a target unlearning error grows exponentially in the size of the backward light cone of the measured observable and not in the number of qubits. In simulation with 50 nodes and on edge boards, SHADE matches the forget accuracy of retraining within 0.5 points, without replay and in under 0.2 s.

Abstract: Quantum computing introduces specialized software stacks and programming interfaces that are often tightly coupled to specific ecosystems and hardware backends, limiting interoperability and software reuse. For HPCQC application developers, this complicates the integration of quantum accelerators into existing applications. Existing quantum frameworks also use ecosystem-specific circuit representations and compilation pipelines, hindering integration with established heterogeneous compiler infrastructures. We propose OpenMQPI, an MLIR-based OpenMP extension for quantum programming that leverages OpenMP's standardized target offloading infrastructure to integrate quantum resources into HPC applications. OpenMQPI introduces QPIR, a lightweight MLIR dialect for representing quantum circuits within OpenMP target regions, and a compiler pipeline that performs quantum-specific optimizations and lowers circuits to executables compatible with OpenMP offloading. At runtime, an MQSS plugin enables the generated executable to offload quantum circuits to quantum hardware through the OpenMP target offloading model. We evaluate OpenMQPI using the VQE, QFT, and Deutsch-Jozsa algorithms with 5, 10, 15, and 20 qubits, comparing execution times against Qiskit and CUDA Quantum. OpenMQPI achieves the lowest average VQE execution time across all tested qubit configurations. At 20 qubits, it requires 5.18 s, compared with 5.83 s for Qiskit and 7.39 s for CUDA Quantum. For QFT and Deutsch-Jozsa, OpenMQPI achieves execution times comparable to Qiskit and lower than those of CUDA Quantum.

Abstract: Large language models (LLMs) have shown strong results in classical code generation and are increasingly used to write the unit tests that safeguard that code. Whether they can do the same for quantum software is less clear, because quantum programs are probabilistic, depend on numerical tolerances, and are judged by domain-specific checkers, so a well-formed test can still disagree with the benchmark's verdict. Existing quantum benchmarks measure whether a model produces a correct solution, but not whether its tests can distinguish correct implementations from faulty ones. We introduce QTestBench, a framework that evaluates LLM-generated quantum test suites against independent benchmark checkers, never treating the tests themselves as ground truth. For each task, QTestBench prompts models to produce syntactic, semantic, and behavioral tests, injects candidate solutions at runtime, and compares each test verdict with the checker's label under three validation cohorts, each answering a distinct diagnostic question. We benchmark five LLMs on eight PennyLane QHack challenges and ten Qiskit HumanEval tasks. Generated suites almost always execute, but discrimination lags behind: the best generator reaches a test quality of 0.71 on QHack and 0.34 on Qiskit HumanEval, so executability alone overstates test quality. Oracle-verified synthetic mutants stabilize bug-detection estimates when natural faulty solutions are scarce, as on three of ten Qiskit tasks that yield none. QTestBench offers a reproducible, cross-framework benchmark for the trustworthiness of LLM-generated quantum tests.

Abstract: We study byte-level autoregressive language models whose hidden state is a small quantum register, whose transitions are learned token-conditioned quantum channels, and whose next-byte probabilities come directly from Born-rule measurements without a learned classical vocabulary projection or softmax. In the fixed-width recurrent setting, unitary dynamics cannot contract or reset stored distinctions; experimentally, unitary recurrence loses to its retrained one-token control in every tested variant. Introducing learned dissipation, then token-conditioned dissipative gating, yields useful memory beyond one token. The gated model improves test negative log-likelihood by 0.20 +/- 0.03 nats/byte over retrained parameter-matched one-token controls at context length 12, and by 0.29-0.33 at longer contexts, but never beats retrained two-token controls. A key-value recall benchmark shows a width-dependent threshold: one stored pair meets the pre-registered accuracy bar at 4-5 memory qubits, two pairs at 6-7, and three pairs remain unsolved. This is consistent with, but does not establish, a capacity explanation for the short effective memory horizon. As a secondary result, one-qubit models reach lower stationary memory entropy than a heuristically optimized classical predictive frontier at matched error in 9/9 seeds. On IBM Heron hardware, computational-basis memory-register distributions show signal against a uniform null in 12/12 circuits across prefixes of up to 12 tokens, next-bit probabilities pass pre-registered accuracy bars at four-token prefixes, and bytes are generated autoregressively by sampling physically measured bit probabilities. The tested models are classically simulable and substantially worse than classical n-gram baselines. We claim no computational quantum advantage.

Abstract: Flow models generate trajectories from an initial distribution to a target distribution by solving an ordinary differential equation defined by a velocity field. Flow matching learns this velocity field by modeling the transport dynamics between the two distributions. Wavefunction flow establishes a formal connection between flow models and quantum dynamics by introducing a continuity Hamiltonian, which drives the Schrödinger evolution of quantum states. In this paper, we investigate accurate and efficient quantum simulation of the wavefunction flow, thereby realizing the efficient implementation of flow models on quantum computers. We first leverage a quantum read-only memory (QROM)-based phase kickback framework for the wavefunction flow simulation, generating probability densities that closely match those produced by the corresponding conventional flow model. To address the high circuit-resource cost, we further incorporate a trained quantum neural network (QNN) into the phase kickback framework, replacing QROM for data encoding. Numerical experiments demonstrate that our proposed method implements flow models on quantum computers more efficiently, since it maintains the accuracy of wavefunction flow simulation compared with the QROM-based framework, and significantly reduces the circuit resources.

Abstract: Variational quantum algorithms are often limited by barren plateaus: gradients vanish as circuit size and depth increase, making quantum neural networks difficult to train. We propose Q-Capsule, a localized capsule-based quantum neural architecture that mitigates this problem through register partitioning, local readout, sparse inter-capsule coupling, trainable data re-uploading, and Quantum Fisher Information Matrix (QFIM)-guided adaptive depth growth. By restricting the dominant support of each observable to a small capsule and controlling inter-capsule entanglement, Q-Capsule preserves useful gradient signals while retaining communication between local quantum representations. As the register width increases, Q-Capsule consistently maintains stable gradient variance, whereas globally entangling baselines exhibit exponential suppression with a log-gradient-variance slope near -ln 2 per qubit. Q-Capsule also produces more structured optimization landscapes, higher parameter efficiency, improved robustness to depolarizing noise, and lower measurement requirements. Its adaptive policy achieves 98.1% accuracy on binary classification and 97.7% on four-class classification, while using approximately 73% fewer two-qubit gates than the fixed-deep model on the multiclass task.

Abstract: Quantum compilers synthesize high-level operations, such as the quantum Fourier transform and multi-controlled X gates, into gate-level circuits. Across compilation stages, a circuit may be serialized, exchanged as OpenQASM, converted between compilers, or lowered to gates. These representation changes can preserve computation while removing the high-level operation itself, leaving the receiving compiler unable to apply a requested synthesis method. We call this loss synthesis availability. We study synthesis availability in Qiskit, TKET, and Cirq through controlled experiments, repository analysis, circuits captured from project tests, and a Munich Quantum Toolkit pipeline. Synthesis availability survives serialization when deserialization restores the high-level operation and survives compiler conversion only when the receiving compiler supports that operation. It does not survive the evaluated OpenQASM routes. After a direct OpenQASM 3 round trip, requested synthesis has no effect in all 360 delivered conditions even though compilation succeeds. In the MQT pipeline, OpenQASM 2 interchange increases the two-qubit gate count by 37.2 percent for an eight-qubit Grover circuit. We also introduce Verified, which records high-level operations before a representation change and reconstructs them only when a check confirms that the record still matches the delivered circuit. Verified restores requested synthesis in all 830 recovery runs, with median verification times from 2.0 to 638 ms per operation family. The check rejects every stale record but also some valid records. These results show that preserving functional equivalence alone is insufficient when later synthesis choices depend on retained high-level structure.

Abstract: Variational quantum algorithms (VQAs) generally rely on classical optimization to train parameterized quantum circuits. This training seeks to minimize an objective function, and its efficiency is central to the practical success of these algorithms. However, globally minimizing such training objectives over the circuit parameters is known to be $\mathsf{NP}$-hard, limiting the prospect of general guarantees for efficient training. In this Letter, we prove that even the weaker task of finding a local minimum of such VQA training objectives is strongly $\mathsf{NP}$-hard, including when the objective admits efficient classical evaluation. Moreover, we show that this hardness persists even for the task of finding a parameter vector within $\ell_p$-distance strictly less than $π/2$ of some local minimizer, for every $p\geq 1$. Our central technical result is that approximating a local minimizer of a Hermitian trigonometric polynomial is strongly $\mathsf{NP}$-hard. By explicitly constructing quantum circuits whose training objectives reproduce these hard instances, we obtain a polynomial-time reduction to VQA training. Our results establish a fundamental computational barrier to variational quantum training: even reaching the vicinity of a local minimum remains hard in the worst case.

Abstract: Transducers (Belovs, Jeffery and Yolcu, 2024) are a quantum computing framework describing a quantum algorithm as a unitary converting an input state into a target state using a catalyst, an auxiliary vector that is left unchanged. They are a powerful tool in quantum algorithm design, especially in the context of quantum query complexity: feasible points of the (dual) adversary semidefinite program directly translate into transducers and the optimal transduction complexity is equal to the adversary bound, i.e. the Las Vegas complexity, which is known to characterize bounded-error quantum query complexity. Moreover, contrary to bounded-error algorithms, transducers compose exactly, which limits overheads due to controlling errors in algorithms constructed by composition. Constructing efficient, let alone optimal, transducers in terms of quantum query complexity nevertheless remains a hard task since it still requires solving the adversary SDP and constructing the unitary to obtain an explicit algorithm. In this paper, we show how using the symmetry group of state-conversion problems simplifies both steps. First, using a symmetrization argument, we prove an optimal catalyst can always be chosen covariant under a representation of the symmetry group. Second, we prove that the transducer intertwines two different representations of the group and can thus be chosen block diagonal in the isotypic decomposition of the Hilbert space. Using those methods, we then derive optimal transducers, with optimal constants, for different widely used quantum algorithmic primitives, such as unstructured search, amplitude amplification and amplitude estimation. Our approach extends previous work on the use of representation theory to compute adversary lower bounds (Høyer, Lee, and {\v S}palek, 2007; Ambainis, Magnin, Roetteler and Roland, 2011) to the systematic construction of optimal algorithms.

Abstract: Random Clifford operators have numerous applications in quantum computing, including randomized benchmarking, classical shadows, and quantum authentication. However, sampling and implementing uniformly random $n$-qubit Clifford incur near-quadratic complexity due to the size of Clifford group. We introduce a cryptographic way to overcome these barriers: trapdoored Clifford operator distributions whose samples are computationally indistinguishable from uniformly random Cliffords, yet implementing them can be much faster given the trapdoor. We construct a distribution of trapdoored Clifford operators whose elements can be sampled and implemented in near-linear time under a variant of the learning parity with noise assumption. Our constructions allow fast tableau action on Pauli labels for classical simulation, and also can be optimized to admit polylogarithmic-depth implementation. Along the way, we construct trapdoored matrices over finite fields that support efficient multiplication by both a matrix and its inverse, resolving an open question left by Vaikuntanathan and Zamir [SODA'26]. We use these constructions to obtain faster protocols based on random Cliffords. We also explore their applications to the worst-case to average-case reductions for matrix and Clifford problems including the iterated matrix multiplication and Clifford circuit synthesis. In particular, we show the hardness of batching Clifford circuits: synthesizing circuits that apply the same Clifford to multiple registers is at least as hard as worst-case matrix multiplication, even when synthesis succeeds on a small constant fraction of random Cliffords. This extends to approximate implementations by general quantum circuits.

Abstract: We construct protocols for classically verifiable quantum advantage and classical verification of $\mathsf{BQP}$ computations using \emph{quantum indistinguishability obfuscation} (qiO). Specifically, given qiO and assuming a slightly stronger version of $\mathsf{BQP}\neq\mathsf{BPP}$, we construct a two-message quantum-advantage protocol that is efficiently and publicly verifiable. Our result can be viewed as a rigorous cryptographic foundation for the heuristic quantum advantage proposals based on \emph{peaked random circuit sampling} of Aaronson and Zhang (arXiv:2404.14493). We also construct two simple protocols for classically verifying arbitrary $\mathsf{BQP}$ computations. The first protocol is privately verifiable and assumes only the existence of qiO. This gives a rare example of a nontrivial cryptographic application of (quantum) iO that does not make additional computational hardness assumptions. The second protocol additionally assumes post-quantum one-way functions and is \emph{publicly verifiable}. To our knowledge, this is the first publicly verifiable protocol for classical verification of $\mathsf{BQP}$ computations under computational assumptions in the standard model. We show that all our results hold when qiO is assumed only for ancilla-free unitary circuits. As evidence supporting this assumption, we prove a worst-to-average-case reduction for obfuscating such circuits. This reduction extends the local-mixing framework of Canetti, Chamon, Mucciolo and Ruckenstein (TCC 2024) under quantum analogues of their assumptions.

Abstract: We present an efficient quantum algorithm for the non-uniform Chebyshev transform. It is defined as the projection of a function onto Chebyshev polynomials sampled at given nodes that are uniform in $x\in[-1,1]$, and hence non-uniform in the angle $θ=\arccos x$, a setting that QFT-based quantum Chebyshev transforms cannot handle. Our construction is based on an improvement of an existing Non-uniform Quantum Fourier Transform (NUQFT) whereby we remove the conditioning from non-uniform node sampling. Hence, error bounds are independent of the geometry-dependent parameter $κ$ of prior work. We use the fact that Chebyshev transform matrix is the average of two Type-II non-uniform DFTs, which we implement with a single controlled NUQFT circuit. We provide explicit oracle constructions, including the row-access oracle previously left as an assumption. The resulting $\varepsilon$-accurate block encoding has $O(1)$ normalization and uses $O(L)$ qubits and $\widetilde O(L^2)$ gates, where $L=\log N+\log(1/\varepsilon)$. We give an end-to-end implementation with complexity analysis, including the success probability and output-state error.

Abstract: Constructing explicit codes matching the parameters of random codes has been a central and largely elusive question in coding theory. The quantum setting is even more challenging since it is highly desirable that the quantum code be an LDPC code. Local coordinate-wise linear (LCL) [Levi, Mosheiff, and Shagrithaya, FOCS 2025] witnesses provide a unifying language for many coding-theoretic properties, from distance to list decoding and list recovery. In particular, it provides a framework to study properties of random linear codes, which achieve optimal parameters for many properties of linear codes. For CSS quantum codes, however, a local witness has two distinct ranks: its physical rank before quotienting by stabilizers and its logical rank after quotienting. We develop a quantum version of the LCL framework for nested spaces $S \subseteq C$, in which local constraints are imposed on physical representatives while independence is measured in the logical quotient $C/S$. The resulting theory gives a threshold theorem for random CSS codes, and as a consequence shows that the per-sector rate threshold is equal to the classical rate threshold. We also define a quantum analogue of subspace design [Guruswami and Xing, STOC 2013] and show that they can be described in a natural manner within the quantum-LCL framework. Finally, we give explicit constructions for arbitrary folded quantum-LCL properties, in a manner similar to the LCL derandomization of [Jeronimo and Shagrithaya, STOC 2026]. As a consequence, we obtain the first explicit constructions of quantum list-decodable codes and list-recoverable codes that have optimal list sizes, in addition to explicit quantum subspace design codes. We note that all our explicit constructions are qLDPC codes, an important property for quantum error-correcting codes.

Abstract: Quantum software is critical for improving the efficiency and reliability of scarce quantum hardware. However, its design still relies heavily on ad-hoc, handcrafted heuristics that are often suboptimal and quickly become obsolete as quantum hardware evolves. LLM-guided evolutionary search offers a promising way to automatically explore complex software designs, but existing search frameworks lack the quantum-specific support needed for efficient evolution: verification is expensive, feedback is sparse, and heterogeneous quantum programs require different optimization objectives. In this paper, we present QSA, a quantum-aware harness for LLM-guided evolutionary search toward automating quantum software design. QSA equips the search with three forms of quantum-specific guidance: an evolution-hardness-guided coreset and approximate scoring to reduce verification cost, static and snapshot analyses to provide fine-grained execution context, and task-specific rewards for compiler passes and runtime policies. We evaluate QSA on the IBM Quantum platform across three benchmark suites. For multiprogramming, QSA improves QPU utilization by 4.2%-9.5% and Hellinger fidelity by 15.2%-19.5% over the state of the art. For error mitigation, QSA reduces mitigation time by at least 96.8% while achieving comparable or better fidelity. These gains require only $6.9 in LLM API cost over 11.3 hours.

Abstract: High Performance Computing (HPC) and Quantum Computing (QC) systems are increasingly converging towards unified High Performance Computing-Quantum Computing (HPCQC) infrastructures, driven by a growing need to bridge classical and quantum workflows, which affects all levels of the system stack, from the hardware to compilers and runtimes, all the way to applications. However, today's QC devices are still in the Noisy Intermediate-Scale Quantum (NISQ) era, are error-prone and resource-limited, and therefore require specialized optimizations and topology mappings to achieve sufficient fidelity. This places special emphasis on proper compilation and optimization within the overall quantum software stack. Many existing stacks remain fragmented, with separate components responsible for device selection, compiler-pass optimization, and job queue scheduling. This paper proposes a unified, learning-based selector that integrates these disparate stages into a cohesive framework. Our proposed selector scheme leverages reinforcement learning and deep learning models that can be extended to simultaneously optimize multiple objectives -- such as fidelity, compilation time, and scheduling latency -- while dynamically adapting to circuit characteristics and device conditions.

Abstract: Quantum circuit optimization is critical for mitigating the noise inherent in current quantum hardware. Quantum compilers typically sequentially apply multiple optimizations (also called ``optimization passes'') to improve the circuit. The impact of the order in which these passes are executed has yet been largely unexplored. This paper investigates the significance of the order of optimization passes within quantum circuit compilation, specifically analyzing interactions between different optimization methods and quantifying their mutual influences. Using Qiskit's compiler, we systematically evaluate pairwise combinations of 16 selected optimization passes, measuring circuit depth and gate count across various benchmark circuits. Our findings indicate dependencies between certain optimization passes, demonstrating that the order of the passes affects the optimization quality. In some cases, the worse performing sequence can be corrected through repeated pass application. %such that they are as good as the best performing one by extending the sequence. Experiments on multi-pass sequences show that more than two optimization passes may have an impact on each other but that this always links to the previously found pairwise effects. We observe that it is important to initially choose the best order of optimization passes to get the best possible optimization for the given circuit. The experiments reveal some factors which are important to choose the best, or at least a good, order; among those, the resulting optimization sequence depends the most on the native gate set.

Abstract: Interactive Quantum Classifiers (IQCs) constitute a family of quantum machine learning models inspired by open quantum systems, in which the interaction between a target qubit and an environment is described by a Hamiltonian. Previous works introduced alternative Hamiltonian parameterizations and showed empirically that they can improve classification performance, but the role of these parameters in the resulting classifier remains poorly understood. In this work, we derive a closed-form expression for the reduced quantum channel generated by a parametrized IQC with a single target qubit. The analytical solution explicitly reveals how the Hamiltonian parameters control the constant, sine, and cosine components of the classifier output, establishing a Fourier interpretation of the induced feature map. This analysis motivates a generalized family of Hamiltonian encodings, including matrix-parameterized environmental Hamiltonians whose Fourier components depend on linear combinations of input features, thereby enabling non-separable Fourier structures. Numerical experiments on synthetic and real-world datasets show that the proposed models can improve classification performance on several nonlinear benchmarks. The generalized matrix encoding achieves the strongest aggregate performance in the evaluated benchmark, while a simpler four-parameter extension often attains comparable performance with substantially fewer trainable parameters. We additionally characterize the generated state ensembles using the standard fidelity-based expressibility measure, finding that global expressibility does not directly predict classification performance. Our results provide an analytical characterization of parametrized Hamiltonians in Interactive Quantum Classifiers and establish Fourier analysis as a useful framework for understanding and designing open-system-inspired quantum learning models.