# Quantum Machine Learning

After porting the quantum-chemistry pipeline of a generative model writing circuits, a quantum sampler drawing bitstrings, classical repair expanding them and a classical solver picking the best, to maximum weighted independent set, a preregistered held-out test returns a negative answer: tabu search reaches repair-basin mass 0.82–0.94 and simulated annealing comes second, while every quantum sampler and a matched learned classical policy trails both at every size. An earlier positive-looking result came from picking the best of 50 configurations per instance, an upper bound rather than a deployable method; under random configurations, oracle QAOA reaches only 0.014 at n=28.

After porting the quantum-chemistry pipeline of a generative model writing circuits, a quantum sampler drawing bitstrings, classical repair expanding them and a classical solver picking the best, to maximum weighted independent set, a preregistered held-out test returns a negative answer: tabu search reaches repair-basin mass 0.82–0.94 and simulated annealing comes second, while every quantum sampler and a matched learned classical policy trails both at every size. An earlier positive-looking result came from picking the best of 50 configurations per instance, an upper bound rather than a deployable method; under random configurations, oracle QAOA reaches only 0.014 at n=28.

Quantum DeepONet ensembles cut the hidden-layer cost of operator learning from the quadratic cost of dense layers to near-linear, and add a finite-sample, distribution-free lower bound on query-averaged coverage. Previously quantum operator learning returned only noisy point predictions, while Bayesian networks and Monte Carlo dropout offered no distribution-free guarantee. The approach replaces dense hidden layers with quantum orthogonal neural networks and applies split conformal calibration to the mean and standard deviation of independently trained ensembles. On synthetic antiderivative and advection benchmarks, relative L2 errors are 0.46% and 2.28%, with 8-model ensemble coverage of 92.13% and 88.99% against a 90% target.

Quantum DeepONet ensembles cut the hidden-layer cost of operator learning from the quadratic cost of dense layers to near-linear, and add a finite-sample, distribution-free lower bound on query-averaged coverage. Previously quantum operator learning returned only noisy point predictions, while Bayesian networks and Monte Carlo dropout offered no distribution-free guarantee. The approach replaces dense hidden layers with quantum orthogonal neural networks and applies split conformal calibration to the mean and standard deviation of independently trained ensembles. On synthetic antiderivative and advection benchmarks, relative L2 errors are 0.46% and 2.28%, with 8-model ensemble coverage of 92.13% and 88.99% against a 90% target.

HyperQ attaches a quantum residual branch in parallel inside every transformer block of a frozen 1.1-billion-parameter masked-diffusion language model (LLaDA-1.1B), where a lightweight circuit hypernetwork continuously emits each token's own IQP circuit coordinates (rotation angles, coupling strengths and measurement axes) from that token's hidden state, executes them on a fixed ring-plus-chord edge set, and adds the measured expectation values back into the query-key-value tensors through a low-rank residual; because the expectation values of this restricted two-body IQP family have an exact closed form whose evaluation cost grows linearly with qubit count, circuits of 16, 32 and 64 qubits can be trained inside that backbone, raising the six-benchmark average from 47.65 to 52.

HyperQ attaches a quantum residual branch in parallel inside every transformer block of a frozen 1.1-billion-parameter masked-diffusion language model (LLaDA-1.1B), where a lightweight circuit hypernetwork continuously emits each token's own IQP circuit coordinates (rotation angles, coupling strengths and measurement axes) from that token's hidden state, executes them on a fixed ring-plus-chord edge set, and adds the measured expectation values back into the query-key-value tensors through a low-rank residual; because the expectation values of this restricted two-body IQP family have an exact closed form whose evaluation cost grows linearly with qubit count, circuits of 16, 32 and 64 qubits can be trained inside that backbone, raising the six-benchmark average from 47.65 to 52.