Monitored quantum circuits exhibit a measurement-induced phase transition between volume-law and area-law entanglement as a function of the measurement rate $p$. Prior work places measurements at random locations and treats the rate as the control parameter. We instead fix the measurement budget and vary the placement process, comparing random placement against hand-designed and learned policies in brickwork random Clifford circuits at matched budget. First, placement geometry matters more than placement information. A deterministic contiguous sweep cuts the half-cut entropy by a factor of 3.4 relative to random placement, while equal-coverage unstructured placement and a greedy policy with full state access do far worse. The effect is carried by spatial order alone: measuring the $k$ least recently measured sites gives $4.14 \pm 0.06$ bits with random tie-breaking and $1.29 \pm 0.04$ bits with position-ordered tie-breaking. Second, the sweep eliminates the transition rather than shifting it. Tripartite mutual information crossings recede as $p^* \propto 1/L$, the steady-state entropy saturates at an $L$-independent ceiling near $0.46/p$, and data for $64 \le L \le 512$ collapse onto the form $S = p^{-1} f(pL)$ predicted by a ballistic regrowth argument. Third, in stabilizer dynamics every outcome is deterministic or a fair coin flip, so the record's Shannon entropy is exactly countable; the sweep dominates the entropy-versus-record-cost frontier while paying the same roughly one bit per measurement as random placement. Policies trained by cross-entropy and proximal policy optimization do not find the sweep: score-based policies parameterize which sites to measure, not the order in which degenerate scores are resolved, and the effect lives in that order. The phase diagram of monitored dynamics is a property of the placement process, not only of the measurement rate.
Parameterized quantum circuits (PQCs) are increasingly used as policies and value functions in quantum reinforcement learning, yet it remains unclear when and why quantum policies generalize. We give a PAC-Bayesian account in which generalization is governed not by the raw number of circuit parameters, but by the effective dimension of the Fisher geometry induced by the circuit. This quantity is inflated by entanglement, making entangling connectivity an independent axis of complexity.In controlled experiments that fix the number of trainable rotations and vary only entanglement, we find that circuits with larger Fisher effective dimension exhibit larger train-test gaps, while parameter count is a weak predictor. The resulting bound acts primarily as a ranking certificate: it correctly orders circuits with identical parameter count, which parameter-counting bounds cannot do. We validate this mechanism across supervised classification, quantum contextual bandits, and value-function generalization, where entangled circuits consistently generalize worse than non-entangled circuits of equal parameter count, with gaps shrinking as sample size increases.Our strongest evidence comes from low-variance decision models, including single-observable classifiers, value heads, and one-step policies. In end-to-end multi-step policy learning, entanglement effects remain statistically significant but high return variance leaves the full ordering only partially resolved. Partial-correlation analysis shows that Fisher effective dimension screens off entangling pattern, and controls for training accuracy, readout, and optimizer rule out major optimization confounders. The effect also persists on an IBM Heron quantum processor under real noise. Overall, our results reframe quantum policy design around an entanglement--generalization trade-off rather than expressivity alone.
In the literate human brain, reading and writing doubly dissociate: a ventral decoding route (pure alexia) and a fronto-parietal encoding route (pure agraphia), sharing a partial orthographic core. A decoder-only large language model (LLM) drives both from one autoregressive path optimized on text (a \emph{cultural} invention, not an evolved instinct). We ask how entangled it is, comparing an input-side ``reading code'' $\mathbf{W}_{E}$ with an output-side ``writing code'' $\mathbf{W}_{U}$ via an index $\mathcal{E}\in[0,1]$ (CKA, Procrustes residual, mutual $k$-NN) calibrated against an independent-init floor and tied ceiling. On GPT-2, OPT and Pythia (14M--1.4B), untied models hold one \emph{coupled but sub-ceiling} code ($\mathcal{E}=0.23$--$0.35$, far above floor) on a non-monotonic couple-then-differentiate trajectory, $\mathbf{W}_{U}$ drifting $\sim$3.2$\times$ farther than $\mathbf{W}_{E}$ in every decile. Equally informative is a negative: the matching behavioural test, that comprehension and production fail together rather than dissociate, cannot be run. For minimal pairs the alexia analogue is empty by theorem: greedy production implies a vocabulary-wide argmax, so it wins the pairwise ranking. Differential-damage indices are not scale-identified: heavy-tailed damage makes linear standardizations collapse onto their larger term, and the rank transform fixing this is bounded, so its null saturates. Both scores also contain the target's log-probability, which alone explains most of their variance and manufactures the apparent coupling. We withdraw a coupling statistic, a cross-level bridge and a separation measure. In a model reading and writing off one next-token distribution, no output-side pair isolates either ability: entanglement needing no index to see. By analogy, not homology, this situates LLMs in the space of possible minds.
Aspen Erlandsson Brisebois, Luis Pablo Gonzalez Dominguez, Shivansi Prajapati +8quant-ph cs.LG q-bio.BM
Parameterized quantum circuits (PQCs) provide a flexible substrate for hybrid quantum machine learning (QML), but their practical value on Noisy Intermediate-Scale Quantum (NISQ) devices remains an empirical question, especially because training depth and scale can introduce optimization challenges such as barren plateaus. Here we study how the number and topology of two-qubit entangling gates in the feature-map stage influence a fixed hybrid QNN workflow for classifying strong versus weak epitope-receptor binding in Porcine Reproductive and Respiratory Syndrome (PRRS) vaccine design. The dataset consists of docking-derived binding affinities for N=80 9-mer epitopes, labeled as Strong or Weak binding, and partitioned into training, validation, and test subsets using a 40:30:30 split. We compare a classical CNN benchmark with a hybrid Embedding-QNN architecture under four feature-map configurations: a non-entangling Z feature map, an all-to-all high-entanglement ZZ feature map, and two interleaved nearest-neighbour entanglement patterns of low and high depth. Among the configurations tested, the high-entanglement ZZ feature map is seen to provide the strongest evidence of reduced training-set overfit, with a lower training area under the accuracy curve (AUAC) and the highest test/training AUAC ratio, while preserving competitive test-set accuracy. These results do not establish a general QML advantage, but they suggest that feature-map entanglement topology is a meaningful design variable for sparse biological screening tasks and warrants further evaluation with additional metrics, larger datasets, and noise-aware or hardware-based experiments.