The Convergence Frontier: Integrating Machine Learning and High Performance Quantum Computing for Next-Generation Drug Discovery

Narjes Ansari; César Feniou; Nicolaï Gouraud; Daniele Loco; Siwar Badreddine; Baptiste Claudon; Félix Aviat; Marharyta Blazhynska

quant-phMar 18, 2026

The Convergence Frontier: Integrating Machine Learning and High Performance Quantum Computing for Next-Generation Drug Discovery

Authors: Narjes Ansari, César Feniou, Nicolaï Gouraud, Daniele Loco, Siwar Badreddine, Baptiste Claudon, Félix Aviat, Marharyta Blazhynska,

Organizations: Qubit Pharmaceuticals, Advanced Research Department, 75014 Paris, France · Qubit Pharmaceuticals Inc, Advanced Research Department, Chicago, IL, USA · Sorbonne Université, Laboratoire de Chimie Théorique, UMR 7616 CNRS, 75005 Paris, France

Abstract

Integrating quantum mechanics into drug discovery marks a decisive shift from empirical trial-and-error toward quantitative precision. However, the prohibitive cost of ab initio molecular dynamics has historically forced a compromise between chemical accuracy and computational scalability. This paper identifies the convergence of High-Performance Computing (HPC), Machine Learning (ML), and Quantum Computing (QC) as the definitive solution to this bottleneck. While ML foundation models, such as FeNNix-Bio1, enable quantum-accurate simulations, they remain tethered to the inherent limits of classical data generation. We detail how High-Performance Quantum Computing (HPQC), utilizing hybrid QPU-GPU architectures, will serve as the ultimate accelerator for quantum chemistry data. By leveraging Hilbert space mapping, these systems can achieve true chemical accuracy while bypassing the heuristics of classical approximations. We show how this tripartite convergence optimizes the drug discovery pipeline, spanning from initial system preparation to ML-driven, high-fidelity simulations. Finally, we position quantum-enhanced sampling as the beyond GPU frontier for modeling reactive cellular systems and pioneering next-generation materials.

Figures & tables

Figure 1: ML/HPC/QC convergence leveraging all type of computing plateforms: from classical Graphics Card Units (GPUs) and Central Processing Units (CPUs) to Quantum Processing Units (QPUs) for simulations in drug design and beyond, from synthetic data (A/B) to system preparation (C) and applications (D/E).

Figure 2: Detailed, step-by-step workflow followed to implement our protein’s hydration pocket hybrid NISQ/classical approach; each step is briefly described in a simple flow diagram, whose components are grouped and attached to one of the five main phases in which we schematically partition the procedure: Input, Problem Formulation, QUBO, Hybrid NISQ/Classical procedure and Output. Pictures and formulas are used to illustrate the most relevant steps. The notation used for the formulas can be found in the original paper presenting the method [ 41 ] .

Figure 3: Example of accuracy comparison between: our method performing a quantum optimisation on IBM Heron R3 Pittsburgh (violet) on a simplified protein instance encompassing 123 binary variables (qubits), to meat the current hardware limitations; our method performing the optimisation classically (red), to scale-up (900 and 3974 binary variables, respectively) to reach the required complexity in the Drug Discovery application; two of the existing alternative solutions (green), namely Hydraprot [ 47 ] and Placevent [ 48 ] ); the bar plot represents the percentage of crystal water molecules identified in the binding pocket of the 3be7 drug-protein complex structure (PDB). The results demonstrate how, increasing the QUBO complexity to reach the order of 1000 variables, our approach perform comparably to the neural-network Hydraprot.

Panel of Figure 4 — Figure 4: Left: Exact classical (CPLEX) vs QPU optimisation results on a 123 variables/qubit hydration site prediction problem formulated as a QUBO. Top panel shows the incumbent solution (light-blue line) over time compared to the best solution identified using the QPU optimisation on IBM R3 Pittsburgh (dashed red line). Bottom panel shows the optimality gap over time, during the 3h optimisation run. [ 44 ] . Right: scaling and resources estimation performed on a protein complex, varying QUBO complexity; the number of 2-qubits gates is plot against the number of QUBO variables/qubits. [ 44 ]

Method
tUCCSDT [ 67 ]	1. Fermionic singles/doubles, $\mathcal{O}(N^{4})$ . 3. Energy, $\mathcal{O}(N^{4})$ Pauli strings. 5. Global, non-convex. 7. Small systems, moderate correlation.	2. Fixed. 4. Pre-determined. 6. Weak. 8. Chemically inspired, lacks flexibility.
ADAPT [ 70 ]	1. Any, up to $\mathcal{O}(N^{4})$ . 3. Energy, $\mathcal{O}(N^{4})$ Pauli strings. 5. Global, non-convex. 7. Small systems, moderate/high correlation.	2. Adaptive, operator-wise. 4. On-the-fly energy gradient. 6. Weak. 8. Barren-plateaus resilience.
GGA [ 71 ]	1. Any. 3. Energy, $\mathcal{O}(N^{4})$ Pauli strings. 5. Sequential, deterministic update. 7. Small systems, weak correlation	2. Adaptive, operator-wise. 4. On-the-fly energy line-search. 6. Moderate/strong. 8. High trainability, low expressivity.
Overlap-ADAPT [ 72 ]	1. Any. 3. Overlap, $\mathcal{O}(1)$ observable. 5. Global, convex. 7. Strong correlation levels.	2. Adaptive, operator-wise. 4. On-the-fly overlap gradient. 6. Strong. 8. Needs accurate target state.
MB-ADAPT [ 69 ]	1. Minimal complete pool, $\mathcal{O}(N)$ . 3. Energy, $\mathcal{O}(N^{4})$ Pauli strings. 5. Global, non-convex. 7. Large systems, all correlation levels.	2. Adaptive, batch of operators. 4. On-the-fly energy gradients. 6. Intermediate. 8. Reduced gradient costs w.r.t ADAPT.
NI-DUCC(MCPs) [ 68 , 69 ]	1. Minimal complete pool, $\mathcal{O}(N)$ . 3. Energy, $\mathcal{O}(N^{4})$ Pauli strings. 5. Global, non-convex. 7. Large systems, all correlation levels.	2. Fixed, layered. 4. Pre-determined. 6. Intermediate. 8. Very expressive ansatz.

Table 1: Comparison of representative Variational Quantum Eigensolver (VQE) methods for quantum chemistry. Criteria: (1) Operator Pool, (2) Ansatz Structure, (3) Cost Function, (4) Operator Selection Criterion, (5) Optimisation, (6) Near-term Hardware Compatibility, (7) Target Chemical Regime, (8) Comments.

Figure 6: Relative error in optimizing the angle at iteration $k$ of the GGA-VQE algorithm using only the QPU. Data from ref. [ 71 ] .

Figure 7: Dissociation curve of H 2 : binding energy versus internuclear distance for our transcorrelated (TC) method on nonuniform grids, compared to FCI at the CBS limit. Grids studied contain 2000, 3000, and 4000 total points (20, 30, and 40 radial points combined with 50 angular quadrature points per atom), corresponding to Hamiltonian matrices of dimensions $4$ , $9$ , and $16$ millions, respectively. Data from ref. [ 77 ] .

	Real-space basis	Molecular-Orbital basis
Quantization	First quantization	Second quantization
Qubit count	$\mathcal{O}(\eta\log N)$ ; logarithmic in basis	$\mathcal{O}(N)$ ; no explicit particle dependence
Hamiltonian terms	Typically $\mathcal{O}(N^{2})$ ; diagonal Coulomb term	Typically $\mathcal{O}(N^{4})$ ;
Quantum algorithms	QPE, QEVE (FTQC)	VQE (NISQ), QPE (FTQC)
Spatial resolution tricks	Adaptive grids, Transcorrelated Hamiltonian	Adaptive basis sets (SABS), orbital rotations

Table 2: Comparison between real-space first-quantized and molecular-orbital second-quantized frameworks

Figure 8: Hardware demonstration on the Quantinuum H2 trapped-ion processor of a degree-one polynomial-amplitude state preparation. The plotted values correspond to the square roots of the postselected measurement frequencies of each computational-basis outcome, showing good agreement with the target polynomial profile. Data from ref. [ 81 ]

Figure 9: Overview of the Hyperion quantum emulator

H100 GPUs	Total Memory	Hyperion-1	Hyperion-2 (MPS)	Hyperion-2 (Partitioned)
		Maximum Logical Qubits
1	$80\text{\,}\mathrm{G}$	24	30	28
4	$320\text{\,}\mathrm{G}$	-	32	30
8	$640\text{\,}\mathrm{G}$	28	-	31
16	$1280\text{\,}\mathrm{G}$	-	36*	32
64	$5120\text{\,}\mathrm{G}$	-	-	36

Table 3: Simulation capacity limit in logical qubits on NVIDIA H100 (80 GB) GPUs. The Table compares the initial Hyperion-1 state-vector approach to the new Partitioned SV-MPS architecture of Hyperion-2 (from Ref [ 13 ] . Both implementations can reach CNOT counts beyond 13000.

Software	Max Qubits	Accuracy	SV	MPS	GPUs
Hyperion-1 (SV) 1	32	Exact	✓	$\times$	✓
Hyperion-2 (Partitioned SV/MPS) 1	36 (40 1 )	Locally Exact+Locally bounded	✓	✓	✓
Hyperion-2 MPS 1	36	Globally bounded	$\times$	✓	✓
quantumlib qsim SV (Google) 2	12	Exact	✓	$\times$	$\times$
cuStateVec SV (NVIDIA) 3	32	Exact	✓	$\times$	✓
cuTensorNet MPS (NVIDIA) 4	36	Globally bounded	$\times$	✓	✓

Table 4: List of Quantum Emulator Packages with Demonstrated Applications to Quantum Chemistry (standard ADAPT-VQE), and Corresponding Features. SV=State-Vector, MPS= Matrix Product States

Figure 10: Convergence of the GGA-VQE algorithm’s energy as a function of iteration count. The blue curve provides the classical ansatz reference. In contrast, the green and orange curves represent the GGA-VQE ansatz energy as evaluated via a hybrid approach and a 25-qubit QPU, respectively. The hybrid results were obtained by extracting the QPU-generated wavefunction and re-simulating it on the Hyperion-1 HPC emulator to calculate the variational energy. Data from ref. [ 71 ] .

Component	Description
Model Nature	A foundation machine learning model designed for accurate, reactive atomistic simulations of biological systems.
Architectural Variants	Consists of FeNNix-Bio1(S) (light-weight, high-throughput) and FeNNix-Bio1(M) (heavier, higher accuracy).
Training Data	Trained on the Ignis dataset ( 2.23M conformations) derived exclusively from synthetic DFT quantum chemistry data
Energy Decomposition	Total energy is decomposed into atomic contributions using a Mixture-of-Experts (MoE) multilayer perceptron.
Charge Modeling	Employs multi-Qeq embedding to globally distribute total charge, enabling non-local differentiation of charge states.
Receptive Field	Uses two-layer equivariant message-passing with a total receptive field of 11Å , comparable to traditional force fields.

Table 5: Summary of FeNNix-Bio1 Foundation Model Methodology

Application Domain	Specific Description	Notable Performance / Result
Liquid Water Properties	Calculation of radial distribution functions, density, and enthalpy of vaporization.	Reaches the quality of accurate polarizable models while outperforming other foundation models at lower cost.
Ions in Solution	Study of the behavior of $Na^{+}$ and $Cl^{-}$ ions in a water box.	Achieves agreement with polarizable force fields.
Hydration Free Energies (HFEs)	Prediction of HFEs for over 600 molecules in the Freesolv dataset.	Provides sub-kcal/mol accuracy and converges at least 60 times faster than other foundation models.
Protein Folding	Study of the reversible folding of the Chignolin protein (CLN025).	Recovers folded, misfolded, and unfolded states; first time achieved with a foundation ML model.
Protein-Ligand Complexes	MD simulation of complexes such as the Benzamidine-Trypsin complex.	Maintains a well-preserved binding mode over several nanoseconds of trajectory.
Absolute Binding Free Energy	Calculation of standard binding free energy for Phenol and Benzene to Lysozyme.	Obtains values close to experimental results, such as $-4.4$ kcal/mol for benzene-lysozyme.

Table 6: Applications of the FeNNix-Biol Foundation Model

Figure 11: Performance in millions of steps per day of various Machine Learning Potentials, compared to the AMOEBA force field, with varying system size for 1fs simulations (i.e. no multi-timestep). Data from ref [ 10 ]

Figure 12: Ignis Database: Jacob’s Ladder Strategy for the Quantum Chemistry Computations

Dataset Component	Description & Scope	Quantum Level of Theory
Core Base Set	$\sim$ 2.1 million molecular conformations including SPICE2 and 100K ANI-2X configurations selected via active learning.	DFT: $\omega$ B97M-D3BJ with ccECP and aug-cc-pVTZ basis sets.
Solvated Ions	28,000 conformations of biologically relevant ions (e.g., Na, Cl, Zn) in varying water cluster sizes (2–10 molecules).	DFT: $\omega$ B97M-D3BJ-ccECP. Finetuned with AMOEBA-03 force predictions for monovalent ions.
Intermolecular Data	64,080 molecule-water dimers sampled from the Freesolv database to capture subtle solvation energies.	DFT: Interaction energies computed as the difference between dimer and monomer sum.
Physical Limits	Synthetic data for isolated atoms and highly distorted water molecules to ensure correct dissociation behavior.	DFT: Adjusted to match the formation energy of the chosen functional.
High-Accuracy Subset	$\sim$ 40,000 configurations (20,251 with full forces) extracted for “beyond DFT” refinement.	QMC: Diffusion Monte Carlo (DMC) operating in the infinite-basis set limit.
Strong Correlation	2,000 configurations specifically targeting significant electronic correlation effects.	Multideterminant QMC: DMC with Selected-CI wavefunctions (1.4M determinants).

Table 7: Summary of the 2025 status for the Ignis Database

Figure 13: Shortcut to chemically accurate quantum computing via density-based basis-set correction: ground-state energy errors with respect to the extrapolated CBS limit for the LiH molecule. Dot markers correspond to energies without basis-set corrections. Cross markers correspond to the corrected energies. On the x-axis, the labels with a

+

sign symbolize basis-set corrected values. The blue box corresponds to a range of 1.6 mHa around the extrapolated CBS limit. Full convergence is obtained with only 28 qubits providing a 10-fold reduction in qubits requirements. Data from ref. [ 55 ] .

Feature	Standard ADAPT-VQE	ADAPT-VQE + DBBSC
Primary Goal	Minimize energy within a fixed, finite basis set.	Approach the Complete-Basis-Set (CBS) limit using small basis sets.
Basis Set Requirements	Requires large basis sets (e.g., cc-pVTZ) for high-accuracy predictions.	Achieves high accuracy using minimal basis sets (e.g., STO-3G, 6-31G).
Qubit Resources	Qubit count scales linearly with the large basis size, often requiring hundreds of qubits.	Drastically reduced; enables accurate simulations with as few as 10–30 qubits.
Correction Strategy	None; results are limited by basis-set truncation errors.	Hybrid: Combines quantum solver with classical density-functional and HF corrections.
Implementation	Purely variational quantum algorithm.	Can be applied a posteriori (Strategy 1) or self-consistently (Strategy 2).
Convergence Rate	Slow convergence with respect to basis-set size.	Accelerated convergence to the CBS limit through self-consistent improvement.

Table 8: Comparison of Standard ADAPT-VQE vs ADAPT-VQE + DBBSC

System	Method / Basis	N qubits	Energy (Ha)	$\Delta$ vs CBS (mHa)
H 2 O	6-31G (ADAPT-VQE)	24	-76.11989	258
	V5Z-11 with SC(ADAPT+PBE)+ $\Delta$ HF**	30	-76.33570	42.42
	cc-pVTZ (FCI)	114	-76.33250	46
	FCI (CBS)	400 †	-76.37812
LiH	6-31G (ADAPT-VQE)	20	-7.99800	27
	V5Z-10 with SC(ADAPT+PBE)+ $\Delta$ HF*	28	-8.02540	0.58

Table 9: Comparison of ground-state energy errors (in mHa) and qubit requirements for noiseless ADAPT-VQE. For H 2 O, LiH, H 2 and N 2 molecules, we compare standard ADAPT-VQE using the largest basis set that can be fitted in maximum 30 qubit with the use of our best adaptive basis sets and DBBSC. Last column presents the error with the chemical accuracy threshold (

\sim 1.6

mHa) as the target reference. For complete results, see Ref. [ 55 ]

Molecule	$N_{qubits}$	$N_{CNOT}$ (QEB)	$N_{CNOT}$ (qubit)
$H_{2}O$
6-31G	24	12657	5862
V5Z-11	30	12647	5858
LiH
6-31G	20	511	242
V5Z-10	28	1083	506

Table 10: CNOT-gate counts for qubit and qubit-excitation-based (QEB) operator pools for ADAPT-VQE/DBBSC from ref [ 55 ]

Figure 14: Free energy surface (FES) profiles for a protein-ligand binding event . The upper panel illustrates the rugged transition state barrier and the high energy required to move between the unbound and bound states. In standard Molecular Dynamics (MD), these high barriers lead to kinetic trapping in local minima. The lower panel demonstrates the application of enhanced sampling techniques, which effectively flatten the free energy landscape. This reduction in barrier height allows the simulation to overcome energetic bottlenecks and explore both states within a feasible computational timescale.

Cpd.	$\Delta G_{EXP}$	$\Delta G_{LAO}$	$\Delta G_{FL}$	$\Delta G_{OO}$	Total Time (ns)			LAO Speedup
		(Ours)			LAO a	FL b	OO c	vs. FL	vs. OO
L1	$-9.8\pm 0.1$	$-10.56\pm 0.46$	$-10.4\pm 0.6$	$-10.5\pm 0.3$	192	840	4000	4.4x	20.8x
L2	$-9.6\pm 0.1$	$-8.26\pm 0.22$	$-9.5\pm 0.4$	$-7.8\pm 0.2$	192	840	5600	4.4x	29.2x
L3	$-9.0\pm 0.1$	$-9.19\pm 0.30$	$-9.2\pm 0.5$	$-8.8\pm 0.4$	192	840	4000	4.4x	20.8x
L4	$-8.9\pm 0.1$	$-10.13\pm 0.15$	$-9.4\pm 0.8$	$-9.5\pm 0.5$	192	840	4800	4.4x	25.0x
L5	$-8.8\pm 0.1$	$-8.27\pm 0.52$	$-8.6\pm 0.3$	$-8.4\pm 0.5$	192	840	4000	4.4x	20.8x

Table 11: Binding free energy (

\Delta G

, kcal/mol) and computational cost (ns) comparison across LAO, FL, and OO methods for BRD4 ligands.

Method	Calculations	Total Sim. (ns)	Net Savings
LAO (Ours)	11 Ligands $\times$ 3 Repeats	6,336	–
Fixed- $\lambda$ (FL)	11 Ligands $\times$ 3 Repeats	27,720	21,384 ns saved
oneOPES (OO)	11 Ligands (Single Runs)	57,600	51,264 ns saved

Table 12: Total computational cost comparison for the 11-ligand BRD4 set. Total time for LAO and FL includes 3 independent repeats per ligand to account for statistical convergence. OO represents the sum of the individual production runs required for the 11-ligand set.

System	Challenge Type	Method	Sampling/Edge	RMSE	$R^{2}$	Speedup/Edge
PWWP1	Charge-Changing	Dual-LAO	24 ns a	0.46	0.62	30x
	(Ionic Change)	FEP+ [ 194 ]	960 ns b [ 193 ]	1.14	0.79	–
BRD4	Buried Water	Dual-LAO	24 ns a	0.64	0.76	15x
	(Displacement)	FEP+ [ 193 ]	480 ns c	2.05	$\approx$ 0	–
P38	Fragment-like	Dual-LAO	24 ns a	0.82	0.77	15x
	(Large Shift)	FEP+ [ 193 ]	480 ns c	0.90	0.56	–

Table 13: Performance and Efficiency Benchmark: Dual-LAO vs. FEP+ Method. Summary of accuracy (RMSE in kcal/mol) and computational cost. Dual-LAO consistently achieves higher accuracy with significantly lower total sampling times compared to standard FEP+ protocol.

System	No. Edges	FEP+ Total (ns)	Dual-LAO Total (ns)	Net Savings (ns)
PWWP1	30 $\times$ 3 Rep.	46,080	2160	93,920
BRD4	11 $\times$ 3 Rep.	15,840	990	14,850
P38	7 $\times$ 3 Rep.	10,080	630	9,450
CHK1	8 $\times$ 3 Rep.	15,360	720	14,640
Total	56 $\times$ 3 Rep.	86,360	4,500	82,860

Table 14: System-Specific Computational Savings with Dual-LAO. Comparison of cumulative sampling time (ns) required across all 56 transformations. By reducing the sampling per edge to a unified 24 ns, Dual-LAO achieves a total reduction of 82,860 ns (approx. 82,7

\mu

s).

Measured $E_{\pi}(f)$ :	0	0.5	1
H2-1	12	444	29
Helios	8	464	16
Expected	0	500	0

Table 15: Measurements of

E_{\pi}(f)

with

10^{3}

shots via the linear combination of unitaries method. The state preparation was successful

485

times on H2-1 and

488

times on Helios. Data from ref. [ 12 ] .

Figure 15: Measurement statistics of

10^{4}

measurements of

V\ket{0}

and

\mathcal{W}V\ket{0}

on Quantinuum’s H2-1, H2-2 and Helios devices. We expect

V\ket{0}

to be a

1

eigenvector of

\mathcal{W}

, thus should remain unchanged after the application of the walk operator. The eigenstate is

V\ket{0}=\mathcal{W}V\ket{0}=\frac{1}{\sqrt{8}}\left(\ket{10}+\ket{12}+\ket{18}+\ket{20}+\ket{42}+\ket{44}+\ket{50}+\ket{52}\right).

Data from ref. [ 12 ] .

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Open paper AskPDF arXiv

Quantitative Structure-Activity Relationship (

\mathtt{QSAR}

) modeling is a foundational computational methodology in early-stage drug discovery, heavily relied upon for predicting compound toxicity, bioavailability, and therapeutic potential. However, classical methods often struggle to effectively map the highly complex, non-linear, and high-dimensional interactions inherent in molecular data, leading to reduced predictive accuracy and costly late-stage clinical failures. In this paper, we present a Quantum Multiple Kernel Learning (

\mathtt{QMKL}

) framework, dubbed Next-Gen

\mathtt{Q^2SAR}

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\mathtt{QSVMs}

) to overcome these classical limitations. By encoding molecular descriptors into exponentially large quantum Hilbert spaces, our approach substantially enhances the expressiveness of non-linear modeling. Benchmarking our quantum-enhanced framework on a dataset targeting the

\mathtt{DYRK1A}

kinase (a critical target for Alzheimer's disease), the

\mathtt{QMKL}

\mathtt{SVM}

achieves an impressive Area Under the Curve (

\mathtt{AUC}

) score of

0.8750

, significantly outperforming classical state-of-the-art Gradient Boosting models (

\mathtt{AUC} = 0.8037

). Furthermore, we establish a theoretical and empirical pathway toward resolving classical data bottlenecks through projected quantum kernels (

\mathtt{PQK}

) and measurement accelerators. As quantum computing architecture matures, this framework paves the way for autonomous cognitive architectures and self-improving drug discovery pipelines, promising to unlock deeper insights across vast chemical spaces and to accelerate the development of life-saving therapeutics.

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