arXiv subjects

César Feniou

Publications and source records attributed to César Feniou.

10 recordsLinked to original sources

arXiv2026

Real-Space Chemistry on Quantum Computers: A Fault-Tolerant Algorithm with Adaptive Grids and Transcorrelated Extension

First-quantized, real-space formulations of quantum chemistry on quantum computers are appealing: qubit count scales logarithmically with spatial resolution, and Coulomb operators achieve quadratic instead of quartic computational scaling of two-electron interactions. However, existing schemes employ uniform discretizations, so the resolution required to capture electron-nuclear cusps in high-density regions oversamples low-density regions, wasting computational resources. We address this by deploying non-uniform, molecule-adaptive grids that concentrate points where electronic density is high. Using Voronoi partitions of these grids, the molecular Hamiltonian is expressed in a Hermitian form and in a transcorrelated, isospectral form that eliminates Coulomb singularities and yields cusp-free eigenfunctions. Both formulations slot naturally into quantum eigenvalue solvers: Hermitian Quantum Phase Estimation (QPE) and the recent generalised Quantum Eigenvalue Estimation (QEVE) protocol for its non-Hermitian, transcorrelated counterpart. Numerical validation on benchmark systems confirms that this non-heuristic ab initio framework offers a promising path for accurate ground-state chemistry on quantum hardware.

quant-ph↗

arXiv2026

Strictly localized orbitals from spatial partitioning with the discontinuous Galerkin method

We present a rigorous electronic-structure theory of strictly localized orbitals associated with a spatial partition of the one-electron Hilbert space that remains well defined in the complete basis-set limit. Each strictly localized orbital is supported on a spatial domain and may be discontinuous at domain interfaces. Using the interior-penalty discontinuous Galerkin method, these strictly localized orbitals can be employed in variational electronic-structure calculations despite their discontinuities at domain interfaces. As a proof of concept, we present numerical illustrations on one-dimensional diatomic model systems. They show that variational calculations can be carried out in a basis of strictly localized orbitals while maintaining good agreement with conventional calculations. Moreover, these strictly localized orbitals naturally lead to chemically intuitive representations of many-electron wave functions in the spirit of valence-bond theory.

physics.chem-ph↗

arXiv2026

An Optimized Construction of Lie Algebra Generator Pools for Variational Quantum Eigensolvers in Chemistry

Lie algebras are essential mathematical structures used in physics to describe sets of quantum operators. Identifying a minimal set of generators to construct these algebras is a central challenge. The traditional search for such generators relies on greedy construction steps applied to an exponentially growing number of candidate operators, making it computationally intractable. Here we show a general, polynomial-scaling strategy, based on fundamental Lie-algebraic properties, to overcome this bottleneck. We apply this framework to quantum chemistry, specifically to adaptive variational algorithms that simulate molecular ground states. By integrating our mathematically verified generator pools into a batched algorithmic framework, we reduce the required quantum resources and improve convergence for strongly correlated systems. Furthermore, this approach eliminates computational bottlenecks that previously restricted fixed-ansatz non-iterative coupled-cluster methods to small molecules, enabling simulations of complex systems well beyond previous limits. This foundational framework also presents broad applications across quantum computing, including quantum error correction, machine learning, and hardware control.

quant-ph↗

arXiv2026

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

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.

quant-ph↗

arXiv2026

High Performance Quantum Emulation for Chemistry Applications with Hyperion

The strategic demand for quantum hardware currently outpaces the availability of near-term devices, necessitating high-performance software emulators to validate novel protocols. We introduce Hyperion, a massively parallel, GPU-accelerated quantum emulator architected to bypass the classical memory walls inherent in strongly correlated quantum chemistry simulations. Hyperion leverages custom-optimized Sparse Matrix-Sparse Vector (SpMspV) kernels to natively accelerate exact matrix-vector multiplications, enabling strictly accurate State-Vector (SV) ADAPT-VQE simulations for up to 32 qubits on multi-node platforms. To scale beyond this hardware limit, we address the trade-off in pure Matrix Product State (MPS) emulators, where standard compression yields severe truncation errors and strict compression triggers intractable tensor rank explosions. We propose a novel partitioned emulation, namely the SV-MPS strategy: by routing non-interacting terms into an exact sparse SV core and delegating interacting terms to the MPS engine, this approach achieves emulation of 36 to 40 qubits with controlled approximations. This partitioning significantly reduces GPU resource requirements while maintaining robust accuracy across ADAPT-VQE iterations. Ultimately, Hyperion offers a high-fidelity platform dedicated to the development of new quantum algorithms for chemistry, enabling the modeling of realistic chemical systems at accuracies approaching the exact Full Configuration Interaction (FCI) / Complete Basis Set (CBS) limit.

quant-ph↗

arXiv2026

Logarithmic-depth quantum state preparation of polynomials

Quantum state preparation is a central primitive in many quantum algorithms, yet it is generally resource intensive, with efficient constructions known only for structured families of states. This work introduces a method for preparing quantum states whose amplitudes are given by a degree$-d$ polynomial, using circuits with logarithmic depth in the number $n$ of qubits and only $\mathcal O(n)$ ancilla qubits, improving previous approaches that required linear-depth circuits. The construction first relies on a block-encoding of an affine diagonal operator based on its Pauli-basis decomposition, which involves only $n$ terms. A modified linear-combination-of-unitaries (LCU) technique is introduced to implement this decomposition in logarithmic depth, together with a novel circuit for the EXACT-one oracle that flags basis states in which exactly one qubit is in the state $|1\rangle$. It then uses a generalized quantum eigenvalue transformation (GQET) to promote this affine operator to an arbitrary degree polynomial. Theoretical analysis and numerical simulations are reported along with a proof-of-principle implementation on a trapped-ion quantum processor using $14$ qubits and more than $500$ primitive quantum gates. Because polynomial approximations are ubiquitous in scientific computing, this construction provides a scalable and resource-efficient approach to quantum state preparation, further improving the potential of quantum algorithms in fields such as chemistry, physics, engineering, and finance.

quant-ph↗

arXiv2025

Greedy Gradient-free Adaptive Variational Quantum Algorithms on a Noisy Intermediate Scale Quantum Computer

Hybrid quantum-classical adaptive Variational Quantum Eigensolvers (VQE) hold the potential to outperform classical computing for simulating many-body quantum systems. However, practical implementations on current quantum processing units (QPUs) are challenging due to the noisy evaluation of a polynomially scaling number of observables, undertaken for operator selection and high-dimensional cost function optimization. We introduce an adaptive algorithm using analytic, gradient-free optimization, called Greedy Gradient-free Adaptive VQE (GGA-VQE). In addition to demonstrating the algorithm's improved resilience to statistical sampling noise in the computation of simple molecular ground states, we execute GGA-VQE on a 25-qubit error-mitigated QPU by computing the ground state of a 25-body Ising model. Although hardware noise on the QPU produces inaccurate energies, our implementation outputs a parameterized quantum circuit yielding a favorable ground-state approximation. We demonstrate this by retrieving the parameterized operators calculated on the QPU and evaluating the resulting ansatz wave-function via noiseless emulation (i.e., hybrid observable measurement).

quant-ph↗

arXiv2024

Shortcut to Chemically Accurate Quantum Computing via Density-based Basis-set Correction

Using GPU-accelerated state-vector emulation, we propose to embed a quantum computing ansatz into density-functional theory via density-based basis-set corrections (DBBSC) to obtain quantitative quantum-chemistry results on molecules that would otherwise require brute-force quantum calculations using hundreds of logical qubits. Indeed, accessing a quantitative description of chemical systems while minimizing quantum resources is an essential challenge given the limited qubit capabilities of current quantum processors. We provide a shortcut towards chemically accurate quantum computations by approaching the complete-basis-set limit through coupling the DBBSC approach, applied to any given variational ansatz, to an on-the-fly crafting of basis sets specifically adapted to a given system and user-defined qubit budget. The resulting approach self-consistently accelerates the basis-set convergence, improving electronic densities, ground-state energies, and first-order properties (e.g. dipole moments), but can also serve as a classical, a posteriori, energy correction to quantum hardware calculations with expected applications in drug design and materials science.

physics.chem-ph↗

arXiv2024

Polylogarithmic-depth controlled-NOT gates without ancilla qubits

Controlled operations are fundamental building blocks of quantum algorithms. Decomposing $n$-control-NOT gates ($C^n(X)$) into arbitrary single-qubit and CNOT gates, is a crucial but non-trivial task. This study introduces $C^n(X)$ circuits outperforming previous methods in the asymptotic and non-asymptotic regimes. Three distinct decompositions are presented: an exact one using one borrowed ancilla with a circuit depth $Θ\left(\log(n)^{3}\right)$, an approximating one without ancilla qubits with a circuit depth $\mathcal O \left(\log(n)^{3}\log(1/ε)\right)$ and an exact one with an adjustable-depth circuit which decreases with the number $m\leq n$ of ancilla qubits available as $O(log(2n/m)^3+log(m/2))$. The resulting exponential speedup is likely to have a substantial impact on fault-tolerant quantum computing by improving the complexities of countless quantum algorithms with applications ranging from quantum chemistry to physics, finance and quantum machine learning.

quant-ph↗

arXiv2023

Overlap-ADAPT-VQE: Practical Quantum Chemistry on Quantum Computers via Overlap-Guided Compact Ansätze

ADAPT-VQE is a robust algorithm for hybrid quantum-classical simulations of quantum chemical systems on near-term quantum computers. While its iterative process systematically reaches the ground state energy, ADAPT-VQE is sensitive to local energy minima, leading to over-parameterized ansätze. We introduce the Overlap-ADAPT-VQE to grow wave-functions by maximizing their overlap with any intermediate target wave-function that already captures some electronic correlation. By avoiding building the ansatz in the energy landscape strewn with local minima, the Overlap-ADAPT-VQE produces ultra-compact ansätze suitable for high-accuracy initializations of a new ADAPT procedure. Spectacular advantages over ADAPT-VQE are observed for strongly correlated systems including massive savings in circuit depth. Since this compression strategy can also be initialized with accurate Selected-Configuration Interaction (SCI) classical target wave-functions, it paves the way for chemically accurate simulations of larger systems, and strengthens the promise of decisively surpassing classical quantum chemistry through the power of quantum computing.

quant-ph↗