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Coherent Floquet quantum reservoirs for molecular property prediction

Luofei Wang, Da Zhang, Congren Wang, Yiming Li, Yuxiao Yang, Xuan Zhang, Xuefeng Cui, Zhang-Qi Yin

arXiv:2609.11071v1quant-phcs.LG

TL;DR

Molecular property prediction needs compact representations that preserve useful relations across local graph events and time-dependent observations. This paper builds a fixed DTC-QRC with coherent Floquet processing, controlled reset, and endpoint readout, and reports stronger performance than matched ESNs on the studied graph and ethene forecasting tasks. The results support a common reservoir framework for molecular screening and time-resolved prediction, while hardware tests indicate task-information retention under device noise.

  • Problem

    Molecular graph and trajectory streams require fixed-width representations that retain distributed chemical relations and relevant history across successive observations.

  • Method

    A fixed DTC-QRC processes successive graph events and surface-hopping frames with coherent Floquet evolution, controlled reset, endpoint observables, and a trained classical decoder.

  • Results

    At matched input lengths and readout widths, DTC-QRC outperforms ESNs on long-prefix graph classification and the studied ethene gap forecasts; dephasing lowers performance in both applications.

  • Takeaways & Limitations

    The architecture provides a common framework for molecular screening and time-resolved property prediction, with reset strength matched to the retained history of the target.

Abstract

from arXiv · show

Quantum reservoir computing (QRC) uses quantum dynamics to represent input histories for prediction through a trained classical readout. Discrete time crystals (DTCs) exhibit robust subharmonic responses under periodic driving, and previous work has used their dynamics to construct DTC-QRC. Here we construct a DTC-based reservoir architecture to predict molecular properties from structural and dynamical observations. Coherent Floquet evolution processes local molecular graph events and surface-hopping frames, while controlled reset regulates the contribution of earlier inputs. Measurements at the end of each input sequence yield a feature vector of fixed dimension. Trained classical decoders use this vector for inhibitor-activity and blood--brain-barrier permeability classification and electronic-gap forecasting, while the reservoir parameters remain fixed during training. With matched input lengths and output widths, DTC-QRC outperforms echo-state networks on long-prefix graph classification and the studied ethene gap forecasting tasks. Dephasing lowers performance in both applications, consistent with a role for coherent propagation. Experiments on the Quafu superconducting quantum cloud platform show that pair observables retain task information under device noise. The architecture provides a common framework for molecular screening and time-resolved property prediction using quantum reservoir computing.

I. INTRODUCTION

Molecular prediction requires compact representations that retain relations across local graph observations and successive trajectory frames. This work introduces a fixed DTC-QRC with controlled reset and endpoint observables for structural and dynamical molecular prediction.

  • Motivation: Molecular event streams require fixed-width states that retain distributed chemical relations and relevant history across successive observations.Graph structure can separate related chemical groups across several bonds, while trajectory prediction may depend on earlier frames when current inputs are similar.
  • Approach: DTC-QRC injects successive molecular events into fixed Floquet dynamics, uses controlled reset to regulate earlier-input contributions, and decodes endpoint observables with a trained classical readout.Reservoir parameters remain fixed during decoder training.
  • Approach: The architecture processes BFS graph events for inhibitor-activity and BBB permeability classification and surface-hopping frames for future electronic-gap forecasting.Graph events encode local atoms, bonds, rings, and depth; trajectory inputs describe nuclear motion for gap prediction.
  • Results: At matched input lengths and readout widths, DTC-QRC outperforms ESNs on long-prefix graph classification and the studied ethene gap forecasts.The architecture uses the same framework while adjusting retained history for structural screening versus time-resolved prediction.
  • Results: Hardware experiments show that second-order correlations retain task information in the DTC regime under device noise, with the transition edge giving the highest mean classification performance among sampled drives.The result identifies a trade-off between information mixing and noise resilience for hardware tuning.

A. Molecular event encoding

The method converts molecular structures and trajectories into fixed-width Hamiltonian inputs, then processes them with repeated Floquet evolution and reset-controlled history weighting. Endpoint observables provide the decoder representation while the reservoir dynamics remain fixed.

  • A. Molecular event encoding: BFS traversal converts canonical molecular graphs into fixed-width event sequences containing atom, bond, ring-closure, and traversal-depth information.The first T events form X_T(G), with each event retaining 3Q entries for a Q-qubit reservoir.
  • A. Molecular event encoding: Surface-hopping frames provide standardized, clipped interatomic distances and backward-difference radial velocities as 15-dimensional inputs for Q = 15.Each sample contains T = 20 events spaced by 0.5 fs, with distance mapped to X and radial velocity to Z.
  • A. Molecular event encoding: Endpoint Z and ZZ observables expose relations between events without requiring intermediate-state measurements, producing the fixed-width features used by the decoder.The architecture also supports temporal-multiplexed endpoint continuations for trajectory processing.
  • B. Floquet dynamics and controlled reset: Each event undergoes an input rotation followed by L Floquet cycles, where noncommuting pulse, disorder, and conditional-phase operations propagate dependence on earlier events.The simulations use L = 3, while graph and trajectory interfaces differ in qubit count and reset placement.
  • B. Floquet dynamics and controlled reset: The reset channel mixes the evolved state with the all-zero state, with graph streams resetting after every event and trajectories resetting only between physical frames.The graph application fixes p = 0.10; hopping reset is selected by validation MAE within each target, sampling scheme, and decoder family.
  • B. Floquet dynamics and controlled reset: Unrolling the recurrence yields a geometric reset-induced event-age kernel in which influences crossing ℓ resets carry weight (1 − p)^ℓ.This kernel controls relative history weights, while Floquet dynamics, measurements, and the decoder determine which event relations support prediction.

C. Readout and temporal multiplexing

The readout forms fixed-width endpoint features from one-body and pairwise observables, with temporal multiplexing extending the feature bank for surface-hopping regression. These measurements can expose relations among successive inputs while keeping the reservoir dynamics fixed.

  • Readout: The final-state representation contains every one-body and pairwise computational-basis observable.A single computational-basis sample set estimates all D_Q entries.
  • Readout: Endpoint Z + ZZ observables expose relations between successive events because later inputs act on states containing earlier-event effects.The paper defines a relation as readable when a decoder can recover it from measured coordinates.
  • Temporal multiplexing: TM3 concatenates endpoint Z + ZZ measurements after zero, one, and two additional Floquet cycles for surface-hopping regression.During the continuation cycles, no new inputs or reset are applied.
  • Temporal multiplexing: For Q = 15, final-state sampling exposes 120 coordinates, whereas TM3 exposes 360 and requires separate hardware executions at its three depths.Graph classification uses final-state sampling; surface-hopping regression uses both final-state sampling and TM3.
  • Feature banks: The same feature bank can serve multiple classical prediction heads when inputs, reservoir, reset, and sampling remain fixed.Changing the reset parameter p requires a different feature bank, while longer streams increase circuit depth despite bounded final-state width.

D. Classical decoding and baselines

Classical decoders convert fixed reservoir features into classification or regression outputs, while matched echo-state-network comparisons test recurrent processing under aligned inputs, widths, splits, and seeds.

  • Classical decoding: An affine head fits linear scores, whereas RBF-SVR fits nonlinear decision boundaries and regression functions.Decoder choice determines how measured reservoir information is converted into predictions.
  • Classical decoding: RBF-SVR provides the primary nonlinear decoder for both classification and regression, with classification evaluated using ROC-AUC.BACE and BBBP tune C, gamma, and epsilon by validation AUC followed by log loss and accuracy tie-breakers.
  • ESN baseline: The ESN baseline uses the same T × 3Q token array, decoder grid, data split, and random seed as the corresponding QRC comparison.On graph tasks, it exposes 78 recurrent coordinates, matching D_12.
  • ESN baseline: The matched ESN comparison isolates recurrent processing of the same local event stream, unlike full-graph message passing and chemical fingerprints.The broader structural methods use the full molecular structure rather than the matched local-event input.

E. Statistical analysis and dephasing

The analysis estimates uncertainty from paired multi-seed comparisons and scans reset settings for graph and hopping tasks. Dephasing is evaluated against coherent evolution under fixed task-specific protocols.

  • Statistical analysis: Graph curves report six-seed means and standard deviations, with 20,000 percentile-bootstrap draws resampling paired QRC–ESN differences.Hopping intervals independently resample seeds and trajectories while preserving method pairing.
  • Reset analysis: Hopping reset values are selected by six-seed mean validation MAE, with ties resolved toward smaller p.The candidate set contains 27 reset values.
  • Reset analysis: The graph reset scan fixes Q = 12 and compares complete response curves across T ∈ {6, 12, 20, 30} against the closed reservoir.Each reset value is evaluated at the same sequence length as its closed-reservoir comparison.
  • Dephasing: Dephasing is applied after every event using λ = 0.5 or 1, with λ = 0 as the exact coherent reference.The analysis averages eight or 32 Pauli trajectories per input sample and suffix while retaining exact reset weights.
  • Dephasing: Dephasing conditions use final-state Z + ZZ sampling and RBF-SVR under the original split and decoder-selection rules.BACE uses Q = 12, T = 30, while hopping uses Q = 15, T = 20.

III. MOLECULAR GRAPH CLASSIFICATION

DTC-QRC processes molecular graph events into fixed-width measurements for BACE and BBBP classification, with fixed reservoir parameters and matched ESN comparisons. On long prefixes, dissipative DTC-QRC outperforms the ESN, while decoder choice and reset strength affect the recovered predictive information.

  • Each molecule drives a 12-qubit reservoir with the first T BFS events, producing 78 final-state Z + ZZ measurement coordinates for decoding.The reservoir parameters remain fixed while the decoder learns molecular labels; comparisons use matched input lengths, output widths, and protocols.
  • At T = 30, BACE AUC reaches 0.798 for dissipative DTC-QRC versus 0.762 for the matched ESN.All six paired seeds favor QRC on both datasets at T = 24 and 30, and Table I reports the long-prefix comparison.
  • Weak reset improves mean RBF-SVR AUC over the closed reservoir at the longest graph prefix in both datasets.The result makes history weighting relevant to accumulating molecular structure.
  • At T = 30 and p = 0.10, BACE AUC rises from 0.656 with affine decoding to 0.798 with RBF-SVR.BBBP follows the same pattern, while weak reset slightly lowers affine-decoder AUC relative to p = 0.
  • Fixed quantum dynamics combine event history, while the classical decoder learns how the measured representation relates to the molecular label.The decoder therefore determines how much predictive information can be recovered from the fixed-width observables.

V. EFFECTS OF CONTROLLED DISSIPATION

Controlled reset tunes how much molecular history contributes to prediction: weak reset benefits longer graph prefixes, whereas trajectory forecasts favor stronger, target-dependent forgetting.

  • Graph classification: Weak reset improves several longer graph prefixes, while stronger reset can remove structural context needed for classification.The clearest gains occur for longer BBBP prefixes; short prefixes change little or incur small losses.
  • Surface-hopping forecasting: Trajectory forecasts favor stronger reset, with the preferred history weighting depending on the prediction target, decoder, and sampling choice.Nearest-future gaps emphasize recent motion, while longer-horizon errors rise as reset approaches completeness.
  • Surface-hopping forecasting: Complete reset retains local endpoint motion but removes earlier encoded frames, lowering the 5-fs error by about 0.14 eV while barely changing the mean 1-fs error.The p = 1 limit removes reservoir memory between events, while final distances and radial velocities remain available.
  • Interpretation: The two applications therefore require different uses of reservoir history: weak reset accumulates graph chemistry, whereas stronger reset emphasizes recent nuclear motion.The survival weight (1−p)^ℓ provides direct physical control over this distinction while Floquet parameters remain fixed.

VI. FLOQUET-DRIVE DEPENDENCE

Floquet-drive scans show nonmonotonic ethene-gap error and identify a common low-error operating window near the DTC transition, even when reservoir memory is removed.

  • Drive scan: The two scan criteria favor g = 0.88 and g = 0.86, identifying g ≃0.86–0.88 as a common low-error operating window across targets and reset strengths.The window keeps errors close to each configuration’s scanned minimum.
  • Drive scan: At g = 0.84, 17 of 20 dissipative configurations lie within 5% of their own scanned minima, supporting a near-optimal fixed operating point.This setting lies close to the related-system DTC transition reference gc ≃0.84.
  • Mechanism: The favorable drive region reflects both input-history treatment and how Floquet evolution transforms molecular inputs into decoder-useful observables.At complete reset, the 1-fs MAE falls from 1.403 eV at g = 0 to 0.722 eV at g = 0.84.

VII. DEPHASING EFFECTS

Dephasing reduces predictive performance in both molecular applications, supporting a role for coherent propagation in forming useful final representations.

  • Performance under dephasing: At λ = 0.5 and k = 8, BACE AUC falls from 0.783 to 0.504, and dephasing lowers classification performance at both trajectory counts.Weak reset reduces the observed AUC loss, but does not remove the degradation.
  • Performance under dephasing: Gap-forecast target-balanced MAE ratios exceed unity under dephasing for both reset settings and trajectory counts relative to coherent evolution.The penalty persists when history weighting is held fixed.
  • Mechanism: Dephasing suppresses off-diagonal density-matrix elements that later Floquet cycles can convert into populations and correlations used by final Z + ZZ measurements.The observed losses are consistent with coherent propagation contributing to molecular representations.
  • Hardware demonstration: On Quafu, full Z + ZZ readout reaches its highest sampled mean hardware AUC at g = 0.84, with 0.585 across three Shenglian batches.Connected-ZZ readout exceeds Z-only readout at the two higher-g points, while its relative value depends on drive regime and noise survival.
  • Hardware caveat: Cross-drive hardware differences are associative rather than causal because the g = 0.84 batches were acquired one day earlier.Refitting the affine head measures retained task information despite coordinate changes between ideal and hardware domains.

IX. CONCLUSION AND OUTLOOK

DTC-QRC combines fixed coherent Floquet dynamics with controlled reset and classical readout for structural and dynamical molecular prediction. It improves over ESNs on the studied tasks, while dephasing and hardware noise delimit current performance and motivate joint drive, reset, and readout design.

  • Architecture: DTC-QRC provides a common framework that injects successive molecular events, transforms them with fixed Floquet dynamics, and predicts properties from endpoint observables.The architecture extends earlier DTC-QRC image classification with successive event injection and independently controlled reset.
  • Main results: At matched input lengths and readout widths, DTC-QRC improves long-prefix BACE and BBBP classification and studied ethene gap forecasts over an ESN.Weak reset benefits long graph prefixes, whereas ethene forecasts favor stronger emphasis on recent motion.
  • Design implications: A common low-error drive window near the DTC transition reference supports operating across targets and reset strengths without selecting a separate drive for each target.Dephasing lowers performance in both applications, consistent with a role for coherent propagation.
  • Hardware and outlook: Quafu experiments indicate that second-order correlations retain more task information on the DTC side under device noise.The outlook is to extend compact quantum representations to larger molecules, binding environments, and longer conformational trajectories.
  • Scope and reproducibility: The accompanying archive has no persistent public deposit identifier yet, limiting the immediate traceability of the analysis materials.The archive is described as containing data-derived arrays, split definitions, metrics, code, and figure-building scripts.

APPENDIX A: SUPERCONDUCTING DEVICES AND CONTROL EXPERIMENTS

The appendix evaluates molecular classification controls on superconducting quantum hardware and compares processor, circuit-depth, observable-family, and ESN-width effects. Hardware retains task information, while increased depth particularly affects pair-correlation observables.

  • Experimental setup: Hardware experiments use Baihua and Shenglian processors with specified six-qubit paths, native CZ gates, compilation enabled, disabled readout correction, and 1024 shots per circuit.The appendix reports published processor characteristics alongside the physical paths and shot counts used in the experiment.
  • Hardware classification: 0.679 ± 0.054 test AUC is achieved by matched ideal Z + ZZ features at L = 3, while all three Shenglian batches exceed 0.5.Shenglian batch means are 0.587 ± 0.061, 0.640 ± 0.100, and 0.528 ± 0.079; Baihua values are lower in each corresponding batch.
  • Circuit-depth controls: Shenglian depth folding changes AUC from 0.707 ± 0.078 to 0.633 ± 0.087, whereas Baihua changes from 0.496 ± 0.063 to 0.565 ± 0.102.The ideal matched AUC remains 0.654 ± 0.076 because the fold implements B†B while preserving the noiseless unitary.
  • Observable controls: −0.202 is the ZZ-only AUC change from base to fold3, larger than the Z-only change of −0.037 and combined change of −0.074.All ten nested ZZ analyses decrease, identifying pairwise correlations as the most depth-sensitive observable family.

APPENDIX B: ESN WIDTH DEPENDENCE

The appendix tests ESN width and drive dependence across molecular tasks, decoder families, and readout schemes. Larger ESNs are not consistently better, while favorable high-drive regions persist across configurations.

  • ESN width dependence: ESN comparisons use widths 78, 500, 1000, and 2000 at event lengths T = 12 and 30 on BACE and BBBP.The quantum reference uses Q = 12, g = 0.84, W = 0.50, L = 3, p = 0.10, and 78 final-state Z + ZZ coordinates.
  • ESN width dependence: At T = 30, the 500-node ESN gives BBBP AUC 0.765, close to QRC at 0.763, while 2000 nodes lower the ESN mean to 0.752.Both BACE and BBBP reach their highest scanned mean ESN AUC at 500 nodes rather than at the largest widths.
  • Drive dependence: The drive study spans 80 nonzero-p configurations from four targets, six reset values, two decoders, and two readouts over g = 0, 0.02, …, 0.98.Final readout provides 120 observables and TM3 provides 360 from three post-input sampling times.
  • Drive dependence: The favorable high-g window is g ≃0.86–0.90 across decoder and readout configurations, narrowing to g ≃0.86–0.88 when p = 0 is excluded.The shared region persists when only dissipative settings are considered.
  • Drive dependence: Dissipative ridge/TM3 favors g = 0.44, whereas dissipative RBF-SVR/TM3 favors g = 0.42 by mean rank and g = 0.90 by mean excess.Mean rank orders configurations by position, while percentage excess also reflects the magnitude of error differences.
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