Late fusion is an efficient, noise-robust, self-characterizing alternative to reconstruction for circuit-cutting QML and claims advantage over classical machine learning - consistent with recent benchmarking, quantum offers no accuracy edge on these datasets.
Abstract
Circuit cutting lets a large quantum neural network (QNN) run as independent subcircuits on small devices, but rebuilding its outputs by reconstruction carries a classical sampling overhead exponential in the number of cuts - the dominant runtime cost in prior work. We ask whether, for machine-learning tasks, this step is necessary, and replace it with late fusion: each subcircuit is trained and measured independently, and a small classical head combines their outputs - a linear-cost, decision-level combination borrowed from multimodal learning. To characterize the trade-off we introduce a quantumness dial $Q$, a tunable reconstruction budget interpolating from pure fusion to full reconstruction, and a cut-entanglement diagnostic that indicates how much reconstruction a task needs (Spearman $\rho=0.59$ over $104$ runs). Across synthetic and standard datasets, independently trained late fusion matches full reconstruction accuracy within $0.04$ at every point of the controlled sweep and on every classical benchmark, at exponentially lower cost; it is also markedly more robust to shot and device noise. Controlled entangled-data experiments locate the boundary where fusion must fail. We do not claim advantage over classical machine learning - consistent with recent benchmarking, quantum offers no accuracy edge on these datasets. Late fusion is thus an efficient, noise-robust, self-characterizing alternative to reconstruction for circuit-cutting QML.
The unitary brick-wall is proposed: a $k-particle fermionic architecture for nearest-neighbor hardware, combining Reconfigurable Beam Splitter gates with interleaved single-qubit phase gates and a non-Gaussian magic-state encoding.
Variational quantum circuits have been central to many proposed near-term applications of quantum computing, but a growing body of evidence suggests that trainability and quantum advantage are fundamentally at odds: ans\"atze expressive enough to resist efficient classical simulation tend to exhibit barren plateaus, while structures that provably rule out barren plateaus typically render them classically simulable. We propose a stacked linear combination of unitaries (S-LCU) as a variational ansatz which provides a tunable trade-off between barren plateaus and classical simulability. Using a diagrammatic analysis, we bound the loss-landscape variance of the Free Fermion S-LCU, whose elements are fermionic Gaussian unitaries. We prove a variance lower bound of $\Omega(1/(n k^{3l}))$, with a simulation cost of $O(k^{2l} n^3)$ using the best known classical algorithm, compared to a quantum gate complexity of only $O(lkn^2)$. The number of layers $l$ serves as a single dial that trades computational complexity against the rate of cost concentration. This offers practitioners a systematic method for constructing ans\"atze with a complexity-trainability trade-off that best suits their application and hardware.
Quantum reservoirs offer a hardware-friendly route to quantum machine learning, replacing trainable circuits with fixed random dynamics and a classical readout. Because the reservoir is not optimized, performance depends entirely on the choice of reservoir family, yet existing diagnostics demand resources that grow exponentially with system size. We introduce a scalable, hardware-agnostic framework built on two complementary quantities. The first is a task-independent order-statistics (ORS) expressivity score, which compares only the largest output probabilities of a reservoir ensemble against an analytical Haar baseline. It never reconstructs the full output distribution, is cost-independent of Hilbert-space dimension, and admits a closed-form depolarizing noise correction, making it directly usable on hardware. The second is the task-dependent effective rank $R_{\mathrm{eff}}$ of the feature matrix, which measures how much input-dependent information reaches the readout. We validate the ORS score against established complexity diagnostics and confirm it remains informative under simulated noise and on IBM quantum hardware. Across synthetic and real quantum extreme learning machine and quantum reservoir computing benchmarks, ORS captures the intrinsic expressivity hierarchy of reservoir families while $R_{\mathrm{eff}}$ determines when that expressivity becomes usable predictive information.
L. Domingo, Oriol Balló-Gimbernat, Fernando Vilariño· 0 citations
Quantum algorithms are conventionally presented with their input state supplied for free. When the input is classical data, this convention conceals a cost that is frequently larger than the algorithm it precedes. We review what the three standard encodings, such as basis encoding, amplitude encoding, and Grover--Rudolph distribution loading, actually cost once transpiled to a hardware gate set, and argue that the resulting $\Theta(N)$ bound is a counting theorem rather than an engineering limitation that improved hardware will remove. Measured gate counts for a representative loading task are reported: an optimal library implementation requires $247$ CNOT gates at $n=8$ qubits and doubles with each additional qubit, while the classical preprocessing that produces the rotation angles requires reading the entire input vector. We show how this cost eliminates the quadratic advantage of quantum amplitude estimation for Monte Carlo integration, and argue that the same accounting constrains quantum machine learning more broadly: the strong input models that make quantum algorithms fast on classical data also enable classical dequantization, and quantum kernel methods carry a $\Theta(M^2)$ state-preparation cost for the Gram matrix that does not amortize. We explain that the efficiently preparable states, device-generated distributions, variationally learned loading, and amortized preparation are required to get advantage from quantum machine learning and close with a checklist for evaluating input-dependent advantage claims. Executable notebooks reproducing every construction and measurement discussed here are available.
This paper invalidates the algorithm-relative exponential-cost conclusion for the supervised two-body readout, without affecting the gradient-variance, barren-plateau, parameter-shift, or sampling-hardness results.
Parametrized quantum circuits (PQCs) form the computational backbone of variational quantum algorithms, yet their practical utility is increasingly constrained by optimisation failures as circuit depth grows. Gradient signals decay rapidly under standard random initialisation, and existing structured approaches abandon inter-layer coordination the moment independent optimisation begins. In this work, we introduce a depthconditioned parameterisation that preserves this coordination throughout training by generating all circuit parameters from a low-dimensional Fourier model over normalised depth, anchored by a task-adapted shallow-circuit prior and augmented with perlayer residuals that retain full expressivity. Gradient information from all layers is aggregated into a compact set of shared weights, providing a principled mechanism for sustaining training signals at depth. Numerically, the proposed method achieves reliable convergence in regimes where all baseline strategies fail or succeed only sporadically, reducing final validation error twoto ten-fold and reaching convergence thresholds up to 2.6 times faster, with $\mathcal{O}\left(d_{\theta}\right)$ overhead independent of circuit depth.
Thi Thuy Nga Nguyen, John Le, T. Vu et al.· 2026 IEEE International Conf...· 0 citations
