Quantum papers — 2026-09-15

Today's work centers on understanding how quantum local differential privacy interacts with entanglement, which is important because many useful quantum protocols depend on having entangled resources. We found that for a channel with a d-dimensional input, every epsilon-QLDP channel becomes entanglement-breaking when epsilon is at most d over d minus one. This means that if the privacy requirement is not too strict relative to the input dimension, the channel loses its ability to preserve entanglement.

We also showed an approximate version of this result for (epsilon, delta)-QLDP, meaning channels in a similar high-privacy regime are close in diamond norm to an entanglement-breaking channel. Furthermore, we established a composition result for private quantum channels that have entangled inputs and global measurements when they are in this high-privacy regime. This connects directly to our work on private quantum learning theory, where we proved that certain learning protocols using arbitrary quantum memory can be simulated by simpler protocols under specific noise conditions.

In parallel, there is progress in applying parameter-efficient quantum machine learning to natural language tasks, where a 10-qubit hybrid circuit achieved strong performance on paraphrase detection benchmarks like Quora Question Pairs. This work showed that multi-qubit entanglement was the main driver of performance across different circuit variants during this task.

Another area involves benchmarking quantum architecture search for molecular ground-state estimation, where we introduced a structure-aware benchmark to show that energy accuracy alone is insufficient for comparing different quantum methods. We found that local entropy profiles helped distinguish inaccurate outputs, suggesting that entangling-gate counts do not always reflect the actual entanglement present in the state.

Finally, we are exploring the limits of quantum pseudorandomness by showing a unitary oracle separation between pseudorandom function-like states and pseudorandom unitaries. This distinction suggests that quantum pseudorandomness behaves quite differently from classical notions, indicating fundamental differences between randomness in states versus randomness in operations.

The most significant finding relates to QSTAR, which shows that using selective routing allows the quantum branch to play a useful role by only engaging it for low-confidence samples rather than replacing the entire classical classifier. This is important because it clarifies when and how variational quantum circuits provide an advantage over fixed heads.

The work on QSTAR compared manually designed heads, KetGPT-designed heads, and parameter-matched classical baselines on Fashion-MNIST data. While a standard QTL head peaked at fifty seven point zero percent accuracy, the strongest KetGPT head achieved seventy eight point five percent accuracy and a zero point seven eight five F1-score. This suggests that architecture searching for quantum heads is beneficial when they act as targeted fallbacks for uncertain inputs.

Furthermore, on low-confidence samples, KetGPT number one eighty improved accuracy over a parameter matched MLP fallback by six point eight two, four point three one, and three point zero three percentage points across thresholds of zero point seven zero and zero point nine zero. This demonstrates the selective routing mechanism's effectiveness in boosting performance for difficult cases.

This adaptive approach ultimately led to Adaptive KetGPT-QTL reaching eighty point nine percent accuracy and a zero point eight zero seven F1-score, which surpassed the adaptive classical baseline. A separate compact circuit ablation showed that KetGPT number one sixty was a stronger fixed head candidate, achieving eighty one point nine percent accuracy with only ten quantum parameters.

The cost of certifying these quantum models is also being examined, focusing on measurement correlation rather than just parameter count. The cost to certify an empirical Fisher matrix under coordinate-wise parameter shift costs scales with the square of the parameter count and inversely with epsilon squared, where V and G are measured readout variance and gradient norm. This scaling suggests that a cubic cost is a finite-size window determined by whether the readout light cone grows with the register size.

The work on proving geometry theorems on a superconducting quantum processor also shows that automated logical reasoning is viable for near-term quantum processors. The framework implements Wu's algebraic elimination method using quantum pseudo-division and another approach via backward symbolic reasoning guided by a hybrid strategy. These experiments successfully proved the perpendicularity of square diagonals and a nineteen seventy eight International Mathematical Olympiad problem.

Today's papers

The papers

Important terms

Quantum Local Differential Privacy (QLDP)
This concept deals with how privacy is maintained in quantum channels while preserving entanglement. The research found that if privacy is not too strict relative to the input dimension, the channel loses its ability to keep entanglement.
Entanglement-Breaking Channel
A channel that destroys quantum entanglement. The study showed that for QLDP channels, this happens when the privacy parameter epsilon is less than or equal to d over d minus one, meaning high privacy limits entanglement preservation.
Parameter-Efficient Quantum Machine Learning (PEQML)
This involves using smaller quantum circuits to perform machine learning tasks. A 10-qubit hybrid circuit showed strong performance on paraphrase detection benchmarks, highlighting multi-qubit entanglement's role.
Selective Routing in QSTAR
A technique where a quantum branch is only used for low-confidence samples instead of the whole classical classifier. This adaptive approach significantly boosted accuracy by targeting uncertain inputs.