arXiv subjects

Stefano Mensa

Publications and source records attributed to Stefano Mensa.

17 recordsLinked to original sources

arXiv2026

SCALAR: A Neurosymbolic Framework for Automated Conjecture and Reasoning in Quantum Circuit Analysis

In this paper, we present SCALAR (Symbolic Conjecture and LLM-Assisted Reasoning), a neurosymbolic framework for automated conjecture generation in quantum circuit analysis built on top of the CUDA-Q open source framework. The system integrates quantum simulation, symbolic conjecture generation, and LLM-based interpretation. We evaluate SCALAR on 82 MaxCut instances from the MQLib benchmark dataset and extend the analysis to 2,000 randomly generated graphs across four topologies: regular, Erdos-Renyi, Barabasi-Albert, and Watts-Strogatz. The framework generates conjectured bounds relating optimal QAOA parameters to graph invariants, including known relationships such as periodicity constraints on the phase separation parameter $\gamma$. SCALAR also recovers previously reported parameter transfer phenomena across structurally similar instances. Additionally, the system identifies correlations between graph structural features and optimization landscape properties, which we characterize through invariant-based descriptors. Using CUDA-Q tensor network simulator, we scale experiments to instances of up to 77 qubits. We discuss the accuracy, generality, and limitations of the generated conjectures, including sensitivity to graph class and quantum circuit depth.

quant-ph↗

arXiv2025

Boosting Sparsity in Graph Decompositions with QAOA Sampling

We study the problem of decomposing a graph into a weighted sum of a small number of matchings, a task that arises in network resource allocation problems such as peer-to-peer energy exchange. Computing such decompositions is challenging for classical algorithms, even for small instances. To address this problem, we propose E-FCFW, a hybrid quantum-classical algorithm based on the Fully-Corrective Frank-Wolfe (FCFW) algorithm that incorporates a matching-sampling subroutine. We design a QAOA version of this subroutine and benchmark it against classical approaches (random sampling and simulated annealing) on demand graphs derived from complete, bipartite, and heavy-hex topologies. The quantum subroutine is executed using the Qiskit Aer state-vector and MPS simulators and on IBM Kingston hardware (7-111 qubits). On complete and bipartite graphs with 6-10 nodes, E-FCFW with QAOA yields consistently sparser decompositions than the classical baselines, and even beats the best-known solution for one instance. On heavy-hex graphs with 50, 70 and 100 nodes, E-FCFW with QAOA outperforms the other methods in terms of approximation error, demonstrating performance on utility-scale quantum hardware. For the largest graphs (100 nodes) E-FCFW with QAOA performs much better when using MPS circuit simulation, compared to using quantum hardware. This indicates that at this scale, the performance is severely impacted by hardware noise.

quant-ph↗

arXiv2025

Quantum chemistry with provable convergence via randomized sample-based Krylov quantum diagonalization

Quantum algorithms based on classical processing of individual samples have recently emerged as the most effective and robust methods to approximate ground-state wave functions of many-body quantum systems on pre-fault-tolerant and early-fault-tolerant quantum devices. In these algorithms, the quantum computer acts as a sampling engine that generates the subspace in which the Hamiltonian is classically diagonalized. The recently proposed Sample-based Krylov Quantum Diagonalization (SKQD), uses quantum Krylov states as circuits from which samples are collected. Convergence guarantees can be derived for SKQD under similar assumptions to those of quantum phase estimation, provided that the ground-state wave function is well approximated by a polynomial subset of the full Hilbert space. However, implementations of SKQD for complex many-body Hamiltonians, such as quantum chemistry ones, are limited by the depths of time-evolution circuits needed to generate Krylov vectors. In this work, we introduce a method that combines SKQD with a qDRIFT randomized compilation of the Hamiltonian propagator. The resulting algorithm, termed SqDRIFT, enables quantum chemistry experiments on quantum processors, while preserving the convergence guarantees similar to the phase estimation algorithm. We demonstrate its viability by applying SqDRIFT to calculate the electronic ground-state energy of several polycyclic aromatic hydrocarbons, up to system sizes beyond the reach of exact diagonalization.

quant-ph↗

arXiv2025

Encoding molecular structures in quantum machine learning

Quantum machine learning (QML) has great potential for the analysis of chemical datasets. However, conventional quantum data-encoding schemes, such as fingerprint encoding, are generally unfeasible for the accurate representation of chemical moieties in such datasets. In this contribution, we introduce the quantum molecular structure encoding (QMSE) scheme, which encodes the molecular bond orders and interatomic couplings expressed as a hybrid Coulomb-adjacency matrix, directly as one- and two-qubit rotations within parameterised circuits. We show that this strategy provides an efficient and interpretable method in improving state separability between encoded molecules compared to other fingerprint encoding methods, which is especially crucial for the success in preparing feature maps in QML workflows. To benchmark our method, we train a parameterised ansatz on molecular datasets to perform classification of state phases and regression on boiling points, demonstrating the competitive trainability and generalisation capabilities of QMSE. We further prove a fidelity-preserving chain-contraction theorem that reuses common substructures to cut qubit counts, with an application to long-chain fatty acids. We expect this scalable and interpretable encoding framework to greatly pave the way for practical QML applications of molecular datasets.

quant-ph↗

arXiv2025

Approximate quantum circuit compilation for proton-transfer kinetics on quantum processors

Proton transfer reactions are fundamental to many chemical and biological systems, where quantum effects such as tunneling, delocalization, and zero-point motion play key kinetic control roles. However, classical methods capable of accurately capturing these phenomena scale prohibitively with system size. Here, we develop and demonstrate quantum computing algorithms based on the Nuclear-Electronic Orbital framework, treating the transferring proton quantum mechanically. We assess the potential of current quantum devices for simulating proton transfer kinetics with high accuracy. We first construct a deep initial ans\"atze within a truncated orbital space by employing the frozen natural orbital approximation. Then, to balance circuit depth against state fidelity, we implement an adaptive form of approximate quantum compiling. Using resulting circuits at varying compression levels transpiled for the ibm_fez device, we compute barrier heights and delocalised proton densities along the proton transfer pathway using a realistic hardware noise model. We find that, although current quantum hardware introduces significant noise relative to the demanding energy tolerances involved, our approach allows substantial circuit simplification while maintaining energy barrier estimates within 13% of the reference value. Despite present hardware limitations, these results offer a practical means of approximating key circuit segments in near-term devices and early fault-tolerant quantum computing systems.

quant-ph↗

arXiv2025

Quantum resources in resource management systems

Quantum computing resources are increasingly being incorporated into high-performance computing (HPC) environments as co-processors for hybrid workloads. To support this paradigm, quantum devices must be treated as schedulable first-class resources within existing HPC infrastructure. This enables consistent workload management, unified resource visibility, and support for hybrid quantum-classical job execution models. This paper presents a reference architecture and implementation for the integration of quantum computing resources, both on-premises and cloud-hosted into HPC centers via standard workload managers. We introduce a Slurm plugin designed to abstract and control quantum backends, enabling seamless resource scheduling, minimizing queue duplication, and supporting job co-scheduling with classical compute nodes. The architecture supports heterogeneous quantum resources and can be extended to any workload (and container) management systems.

quant-ph↗

arXiv2025

Qiskit Machine Learning: an open-source library for quantum machine learning tasks at scale on quantum hardware and classical simulators

We present Qiskit Machine Learning (ML), a high-level Python library that combines elements of quantum computing with traditional machine learning. The API abstracts Qiskit's primitives to facilitate interactions with classical simulators and quantum hardware. Qiskit ML started as a proof-of-concept code in 2019 and has since been developed to be a modular, intuitive tool for non-specialist users while allowing extensibility and fine-tuning controls for quantum computational scientists and developers. The library is available as a public, open-source tool and is distributed under the Apache version 2.0 license.

quant-ph↗

arXiv2025

Variational preparation of normal matrix product states on quantum computers

Preparing matrix product states (MPSs) on quantum computers is an essential routine in the simulation of many-body physics. However, widely-used schemes based on staircase circuits are often too deep to execute on current hardware. Here we demonstrate that MPSs with short-range correlations can be prepared with shallow circuits by leveraging heuristics from approximate quantum compiling (AQC). We achieve this with ADAPT-AQC, an adaptive-ansatz preparation algorithm, and introduce a generalised initialisation procedure for the existing AQC-Tensor algorithm. We first compare these methods for the task of preparing a molecular electronic structure ground state. We then use them to prepare an antiferromagnetic (AFM) ground state of the 50-site Heisenberg XXZ spin chain near the AFM-XY phase boundary. Through the execution of circuits with up to 59 CZ depth and 1251 CZ gates, we perform a global quench and observe the relaxation of magnetic ordering in a parameter regime previously inaccessible due to deep ground state preparation circuits. Our results demonstrate how the integration of quantum and classical resources can push the boundary of what can be studied on quantum computers.

quant-ph↗

arXiv2024

Evolving a multi-population evolutionary-QAOA on distributed QPUs

Our work integrates an Evolutionary Algorithm (EA) with the Quantum Approximate Optimization Algorithm (QAOA) to optimize ansatz parameters in place of traditional gradient-based methods. We benchmark this Evolutionary-QAOA (E-QAOA) approach on the Max-Cut problem for $d$-3 regular graphs of 4 to 26 nodes, demonstrating equal or higher accuracy and reduced variance compared to COBYLA-based QAOA, especially when using Conditional Value at Risk (CVaR) for fitness evaluations. Additionally, we propose a novel distributed multi-population EA strategy, executing parallel, independent populations on two quantum processing units (QPUs) with classical communication of 'elite' solutions. Experiments on quantum simulators and IBM hardware validate the approach. We also discuss potential extensions of our method and outline promising future directions in scalable, distributed quantum optimization on hybrid quantum-classical infrastructures.

quant-ph↗

arXiv2024

Boosted Imaginary Time Evolution of Matrix Product States

In this work, we consider the imaginary time evolution of matrix product states. We present a novel quantum-inspired classical method that, when combined with time evolving block decimation (TEBD), is able to potentially speed-up the convergence to a ground state compared to TEBD alone. Our method, referred to as boosted imaginary time evolution, relies on the use of reflections to boost to lower energy states. Interleaving TEBD steps with boosts reduces the total number of TEBD steps and potentially the computational cost required to imaginary time evolve a matrix product state to a ground state. We give the mathematical details of the method followed by an algorithmic implementation and finally some results for a simple test case.

quant-ph↗

arXiv2024

Efficient Parameter Optimisation for Quantum Kernel Alignment: A Sub-sampling Approach in Variational Training

Quantum machine learning with quantum kernels for classification problems is a growing area of research. Recently, quantum kernel alignment techniques that parameterise the kernel have been developed, allowing the kernel to be trained and therefore aligned with a specific dataset. While quantum kernel alignment is a promising technique, it has been hampered by considerable training costs because the full kernel matrix must be constructed at every training iteration. Addressing this challenge, we introduce a novel method that seeks to balance efficiency and performance. We present a sub-sampling training approach that uses a subset of the kernel matrix at each training step, thereby reducing the overall computational cost of the training. In this work, we apply the sub-sampling method to synthetic datasets and a real-world breast cancer dataset and demonstrate considerable reductions in the number of circuits required to train the quantum kernel while maintaining classification accuracy.

quant-ph↗

arXiv2023

Challenges and Opportunities in Quantum Optimization

Recent advances in quantum computers are demonstrating the ability to solve problems at a scale beyond brute force classical simulation. As such, a widespread interest in quantum algorithms has developed in many areas, with optimization being one of the most pronounced domains. Across computer science and physics, there are a number of different approaches for major classes of optimization problems, such as combinatorial optimization, convex optimization, non-convex optimization, and stochastic extensions. This work draws on multiple approaches to study quantum optimization. Provably exact versus heuristic settings are first explained using computational complexity theory - highlighting where quantum advantage is possible in each context. Then, the core building blocks for quantum optimization algorithms are outlined to subsequently define prominent problem classes and identify key open questions that, if answered, will advance the field. The effects of scaling relevant problems on noisy quantum devices are also outlined in detail, alongside meaningful benchmarking problems. We underscore the importance of benchmarking by proposing clear metrics to conduct appropriate comparisons with classical optimization techniques. Lastly, we highlight two domains - finance and sustainability - as rich sources of optimization problems that could be used to benchmark, and eventually validate, the potential real-world impact of quantum optimization.

quant-ph↗

arXiv2023

Toward Accurate Post-Born-Oppenheimer Molecular Simulations on Quantum Computers: An Adaptive Variational Eigensolver with Nuclear-Electronic Frozen Natural Orbitals

Nuclear quantum effects such as zero-point energy and hydrogen tunnelling play a central role in many biological and chemical processes. The nuclear-electronic orbital (NEO) approach captures these effects by treating selected nuclei quantum mechanically on the same footing as electrons. On classical computers, the resources required for an exact solution of NEO-based models grow exponentially with system size. By contrast, quantum computers offer a means of solving this problem with polynomial scaling. However, due to the limitations of current quantum devices, NEO simulations are confined to the smallest systems described by minimal basis sets whereas realistic simulations beyond the Born--Oppenheimer approximation require more sophisticated basis sets. For this purpose, we herein extend a hardware-efficient ADAPT-VQE method to the NEO framework in the frozen natural orbital (FNO) basis. We demonstrate on H$_2$ and D$_2$ molecules that the NEO-FNO-ADAPT-VQE method reduces the CNOT count by a several orders of magnitude relative to the NEO unitary coupled cluster method with singles and doubles (NEO-UCCSD) while maintaining the desired accuracy. This extreme reduction in the CNOT gate count is sufficient to permit practical computations employing the NEO method -- an important step toward accurate simulations involving non-classical nuclei and non--Born--Oppenheimer effects on near-term quantum devices. We further show that the method can capture isotope effects and we demonstrate that inclusion of correlation energy systematically improves the prediction of $Δ$ZPE.

physics.chem-ph↗

arXiv2023

Nonadiabatic nuclear-electron dynamics: a quantum computing approach

The combined quantum electron-nuclear dynamics is often associated with the Born-Huang expansion of the molecular wave function and the appearance of nonadiabatic effects as a perturbation. On the other hand, native multicomponent representations of electrons and nuclei also exist, which do not rely on any a priori approximation. However, their implementation is hampered by prohibitive scaling costs and therefore quantum computers offer a unique opportunity for extending their use to larger systems. Here, we propose a quantum algorithm for the simulation of the time-evolution of molecular systems in the second quantization framework, which is applied to the simulation of the proton transfer dynamics in malonaldehyde. After partitioning the dynamics into slow and fast components, we show how the entanglement between the electronic and nuclear degrees of freedom can persist over long times if electrons are not adiabatically following the nuclear displacement. The proposed quantum algorithm may become a valid candidate for the study of electron-nuclear quantum phenomena when sufficiently powerful quantum computers become available.

quant-ph↗

arXiv2023

A Practitioner's Guide to Quantum Algorithms for Optimisation Problems

Quantum computing is gaining popularity across a wide range of scientific disciplines due to its potential to solve long-standing computational problems that are considered intractable with classical computers. One promising area where quantum computing has potential is in the speed-up of NP-hard optimisation problems that are common in industrial areas such as logistics and finance. Newcomers to the field of quantum computing who are interested in using this technology to solve optimisation problems do not have an easily accessible source of information on the current capabilities of quantum computers and algorithms. This paper aims to provide a comprehensive overview of the theory of quantum optimisation techniques and their practical application, focusing on their near-term potential for noisy intermediate scale quantum devices. Two main paradigms for quantum hardware are then discussed: quantum annealing and gate-based quantum computing. While quantum annealers are effective for some optimisation problems, they have limitations and cannot be used for universal quantum computation. In contrast, gate-based quantum computers offer the potential for universal quantum computation, but they face challenges with hardware limitations and accurate gate implementation. The paper provides a detailed mathematical discussion with references to key works in the field, as well as a more practical discussion with relevant examples. The most popular techniques for quantum optimisation on gate-based quantum computers, the quantum approximate optimisation (QAO) algorithm and the quantum alternating operator ansatz (QAOA) framework, are discussed in detail. The paper concludes with a discussion of the challenges facing quantum optimisation techniques and the need for further research and development to identify new, effective methods for achieving quantum advantage.

quant-ph↗

arXiv2023

A Quantum Computing Implementation of Nuclear-Electronic Orbital (NEO) Theory: Towards an Exact pre-Born-Oppenheimer Formulation of Molecular Quantum Systems

Nuclear quantum phenomena beyond the Born-Oppenheimer approximation are known to play an important role in a growing number of chemical and biological processes. While there exists no unique consensus on a rigorous and efficient implementation of coupled electron-nuclear quantum dynamics, it is recognised that these problems scale exponentially with system size on classical processors and therefore may benefit from quantum computing implementations. Here, we introduce a methodology for the efficient quantum treatment of the electron-nuclear problem on near-term quantum computers, based upon the Nuclear-Electronic Orbital (NEO) approach. We generalize the electronic two-qubit tapering scheme to include nuclei by exploiting symmetries inherent in the NEO framework; thereby reducing the hamiltonian dimension, number of qubits, gates, and measurements needed for calculations. We also develop parameter transfer and initialisation techniques, which improve convergence behavior relative to conventional initialisation. These techniques are applied to H$_2$ and malonaldehyde for which results agree with Nuclear-Electronic Orbital Full Configuration Interaction and Nuclear-Electronic Orbital Complete Active Space Configuration Interaction benchmarks for ground state energy to within $10^{-6}$ Ha and entanglement entropy to within $10^{-4}$. These implementations therefore significantly reduce resource requirements for full quantum simulations of molecules on near-term quantum devices while maintaining high accuracy.

quant-ph↗

arXiv2022

Quantum Machine Learning Framework for Virtual Screening in Drug Discovery: a Prospective Quantum Advantage

Machine Learning (ML) for Ligand Based Virtual Screening (LB-VS) is an important in-silico tool for discovering new drugs in a faster and cost-effective manner, especially for emerging diseases such as COVID-19. In this paper, we propose a general-purpose framework combining a classical Support Vector Classifier (SVC) algorithm with quantum kernel estimation for LB-VS on real-world databases, and we argue in favor of its prospective quantum advantage. Indeed, we heuristically prove that our quantum integrated workflow can, at least in some relevant instances, provide a tangible advantage compared to state-of-art classical algorithms operating on the same datasets, showing strong dependence on target and features selection method. Finally, we test our algorithm on IBM Quantum processors using ADRB2 and COVID-19 datasets, showing that hardware simulations provide results in line with the predicted performances and can surpass classical equivalents.

quant-ph↗