arXiv subjects

Rahul Maitra

Publications and source records attributed to Rahul Maitra.

At least 19 recordsLinked to original sources

arXiv2026

Quantum Wavefunction Augmentation via Variational Autoencoders

Sample-based quantum diagonalization (SQD) has emerged as a promising route for quantum-centric supercomputing, relying on classical diagonalization of the molecular Hamiltonian within a hardware-sampled determinant subspace. However, its accuracy degrades in strongly correlated regimes where the relevant determinant space exceeds what finite-shot sampling can capture. In this work, we introduce Quantum Wavefunction Augmentation via Variational Autoencoders (Q-WAVE), a hybrid method that combines determinants sampled via SqDRIFT Krylov circuits and configuration interaction singles and doubles (CISD) determinants with generative machine learning. Using a custom $\beta$-annealed variational autoencoder (VAE) model, Q-WAVE iteratively expands this basis toward the variational ground state. The VAE learns the wavefunction's primary support structure from the combined hardware and CISD seed in a continuous latent space, generating new dominant determinants beyond any fixed excitation hierarchy. The resulting compact wavefunction exceeds what can be extracted from raw hardware samples alone. We demonstrate sub-millihartree accuracy compared to full configuration interaction for $\text{H}_2\text{O}$ and $\text{N}_2$ dissociation. Finally, we establish Q-WAVE's scalability on a 52-qubit ethylene system (achieving sub-millihartree accuracy versus CCSD(T)) and a highly correlated 60-qubit $\text{Cr}_2$ stress test that attains chemical accuracy upon a final perturbative correction.

quant-ph↗

arXiv2026

Machine-Learned Compact Subspace Generation for Quantum Selected Configuration Interaction within Density Matrix Embedding Framework

Sample-based Quantum Diagonalization (SQD), an extension of Quantum Selected Configuration Interaction (QSCI), has emerged as a promising hybrid quantum-classical paradigm for computing molecular ground state energies. By leveraging quantum sampling instead of variational optimization, QSCI avoids barren plateaus and enables direct reconstruction of correlated electronic wavefunctions. However, existing configuration recovery techniques primarily enforce symmetry constraints without guaranteeing optimal selection of the most physically relevant configurations, often leading to unnecessarily large subspaces and increased classical diagonalization costs. In this work, we introduce a machine-learned compact subspace generation protocol based on Restricted Boltzmann Machines (RBMs), termed QSCI-RBM, and integrate it within the Density Matrix Embedding Theory (DMET) framework. The RBM is trained on quantum-sampled configurations to learn the underlying probability distribution of dominant determinants, enabling the targeted generation of high-probability configurations. We apply this framework to the simulation of a protein-ligand complex involving the inhibitor Carmofur bound to the SARS-CoV-2 main protease ($M^{\text{pro}}$). Our results demonstrate that DMET-QSCI-RBM achieves energies within the chemical accuracy threshold by accessing only approximately 4% of the configuration subspace. In contrast, standard DMET-SQD simulations failed to reach chemical accuracy while accessing up to 20% of the subspace, even as the chemical potential itself nearly converged. These findings highlight that RBM-assisted configuration generation produces significantly more compact subspaces while preserving physical accuracy, thereby reducing classical computational overhead and enabling the scalable quantum embedding simulation of complex biological systems.

quant-ph↗

arXiv2026

Advancing Practical Quantum Embedding Simulations via Operator Commutativity Based State Preparation for Complex Chemical Systems

Determining the exponentially scaled ground state wavefunction and the associated molecular properties remains one of the central challenges in quantum chemistry. Hybrid quantum-classical algorithms implemented on quantum computers offer a promising route toward addressing this problem. However, despite several successful demonstrations on small molecular systems, accurate simulations of large and chemically realistic molecules remain difficult due to the limited capability of noisy intermediate scale quantum (NISQ) hardware. To bypass the limitations of NISQ devices, while simultaneously retaining the accuracy of the ground state energy estimations, we propose a dynamic ansatz construction strategy based on operator commutativity and energy driven screening within density matrix embedding theory (DMET) framework. The partitioning of the full system allows us to dynamically construct the ansatz over individual embedded subsystems, allowing each embedding problem be solved individually to a desired accuracy. The embedding Hamiltonian is updated in a self-consistent manner with dynamically formulated wavefunction, and their coupled optimization leads to accurate and efficient description of the overall system. To assess the performance of this approach, we apply it to several molecular systems and chemical processes with up to 144 qubits. These simulations require at most 20 qubits at a time and demonstrate improved accuracy and significantly reduced quantum gate requirements compared with conventional ansatze. We further investigate the impact of various fragmentation strategies and demonstrate the adaptability of our approach at each step of the DMET self-consistency cycle that leads to significantly improved accuracy for strongly correlated system.

quant-ph↗

arXiv2025

Physics-Informed Generative Machine Learning for Accelerated Quantum-centric Supercomputing

Quantum centric supercomputing (QCSC) framework, such as sample-based quantum diagonalization (SQD) holds immense promise toward achieving practical quantum utility to solve challenging problems. QCSC leverages quantum computers to perform the classically intractable task of sampling the dominant fermionic configurations from the Hilbert space that have substantial support to a target state, followed by Hamiltonian diagonalization on a classical processor. However, noisy quantum hardware produces erroneous samples upon measurements, making robust and efficient configuration-recovery strategies essential for a scalable QCSC pipeline. Toward this, in this work, we introduce PIGen-SQD, an efficiently designed QCSC workflow that utilizes the capability of generative machine learning (ML) along with physics-informed configuration screening via implicit low-rank tensor decompositions for accurate fermionic state reconstruction. The physics-informed pruning is based on a class of efficient perturbative measures that, in conjunction with hardware samples, provide a substantial overlap with the target state. This distribution induces an anchoring effect on the generative ML models to stochastically explore only the dominant sector of the Hilbert space for effective identification of additional important configurations in a self-consistent manner. Our numerical experiments performed on IBM Heron R2 quantum processors demonstrate this synergistic workflow produces compact, high-fidelity subspaces that substantially reduce diagonalization cost while maintaining chemical accuracy under strong electronic correlations. By embedding classical many body intuitions directly into the generative ML model, PIGen-SQD advances the robustness and scalability of QCSC algorithms, offering a promising pathway toward chemically reliable quantum simulations on utility-scale quantum hardware.

quant-ph↗

arXiv2025

Resource Estimation for VQE on Small Molecules: Impact of Fermion Mappings and Hamiltonian Reductions

Accurate determination of ground-state energies for molecules remains a challenge in quantum chemistry and a cornerstone for progress in fields such as drug discovery and materials design. The Variational Quantum Eigensolver (VQE) represents a leading hybrid quantum-classical paradigm for addressing this challenge; however, its widespread realization is limited by noise and the restricted scalability of current quantum hardware. Achieving efficient simulations on Noisy Intermediate-Scale Quantum (NISQ) devices and forthcoming Fault-Tolerant Application-Scalable Quantum (FASQ) systems demands a detailed understanding of how computational resources scale with molecular complexity and fermion-to-qubit encodings. In this study, resource requirements for VQE implementations employing the Unitary Coupled Cluster Singles and Doubles (UCCSD) ansatz are systematically analyzed. The molecular Hamiltonian is formulated in second quantization and mapped to qubit operators through the Jordan-Wigner (JW), Bravyi-Kitaev (BK), and Parity (Pa) transformations. Hamiltonian reduction strategies, including $\mathbb{Z}_2$ tapering and frozen-core approximations, are examined to assess their effect on quantum resource scaling. The analysis reveals that appropriate transformations, when combined with symmetry-based reductions, can substantially reduce qubit counts by up to $\approx 50\%$ and quantum gate counts by up to $\approx 27.5\times$ and Hamiltonian Pauli string counts by up to $\approx 2.75\times$, relative to the corresponding unreduced Hamiltonian representations within the same active-space configuration for the representative set of molecular systems under study. These findings provide practical circuit-level insights for executing chemically relevant simulations on NISQ hardware, while establishing physical-resource baselines that may inform future logical-level analyses targeting FASQ systems.

quant-ph↗

arXiv2025

Quantum Simulation of Ligand-like Molecules through Sample-based Quantum Diagonalization in Density Matrix Embedding Framework

The accurate treatment of electron correlation in extended molecular systems remains computationally challenging using classical electronic structure methods. Hybrid quantum-classical algorithms offer a potential route to overcome these limitations; however, their practical deployment on existing quantum computers requires strategies that both reduce problem size and mitigate hardware noise. In this work, we investigate ground-state energy calculations of ligand-like molecules using Sample-based Quantum Diagonalization (SQD) within the Density Matrix Embedding Theory (DMET) framework, focusing on low-symmetry systems with diverse bonding motifs that exhibit subsystem-dependent variations in fragment-environment entanglement. These entanglement-based variations directly influence bath orbital construction, impurity sizes, and the structure of the embedded Hamiltonians, posing nontrivial challenges for both embedding and quantum sampling. By combining DMET fragmentation with SQD-based construction of reduced configuration spaces through quantum sampling and iterative configuration recovery, we perform quantum simulations on IBM's Eagle R3 (IBM Sherbrooke) and IBM's Heron R3 (IBM Boston) superconducting quantum hardware thereby, showing that the entanglement structure across embedding subsystems plays a central role in determining the efficiency and accuracy of the simulations. Despite these complexities, we show that the DMET-SQD framework yields ground-state energies in strong agreement with DMET-FCI benchmarks, achieving chemical accuracy (1 kcal/mol) across all systems studied. These results demonstrate that SQD-based quantum simulations can be robustly extended to low-symmetry, chemically realistic, industry relevant molecules, and highlight the importance of entanglement-aware embedding strategies for scalable quantum electronic structure calculations.

quant-ph↗

arXiv2025

Fragment, Entangle, and Consolidate: Strong Correlation through Bi-fold Quantum Circuits

An accurate description of strong correlation is quintessential for the exploration of emerging chemical phenomena. While near-term variational quantum algorithms provide a theoretically scalable framework for quantum chemical problems, the accurate simulation of multireference effects remains elusive, hindering progress toward the rational design of novel chemical space. In this regard, we introduce a general and customizable scheme to handle strong electronic correlation, based on problem decomposition, entanglement buildup, and subsequent consolidation. Based on a problem-inspired molecular decomposition, the deployment of Hardware Efficient Ansatz to prepare entangled subsystems ensures efficient construction of a multireference state while concurrently adhering to the hardware topology. The dynamic correlation is subsequently introduced through a unitary coupled cluster framework, with static or dynamic ansatz parametrized by a set of inter-fragment generalized operators, and with the product state spanning various subsystems taken as the reference. The hybrid architecture ensures a judicious deployment of separate ansatze structures for capturing various degrees of correlation in a balanced manner, while concurrently retaining the scalability and flexibility provided by them individually. Over a number of numerical applications on a strongly correlated system, the proposed scheme is shown to be highly accurate, flexible, and robust in unlocking the potential to harness quantum advantage for quantum chemistry.

quant-ph↗

arXiv2025

Operator Commutativity Screening and Progressive Operator Block Reordering toward Many-body Inspired Quantum State Preparation

In the field of quantum chemistry, the variational quantum eigensolver (VQE) has emerged as a highly promising approach to determine molecular energies and properties within the noisy intermediate-scale quantum (NISQ) era. The central challenges of this approach lie in the design of an expressive ansatz capable of representing the exact ground state wavefunction while concurrently being efficient to avoid numerical instabilities during the classical optimization. Owing to the constraints of current quantum hardware, the ansatz must remain sufficiently compact while retaining the flexibility to capture essential correlation effects. To address these challenges, we propose a systematic dynamic ansatz construction strategy in which the dominant operator blocks are initially identified through commutativity screening, combined with an energy sorting criteria. Subsequently, the ansatz is progressively expanded in a stepwise manner via iterative operator block reordering. To minimize the overhead, the higher order correlation terms are incorporated via reduced lower-body tensor factorization in each operator block, while the adaptive construction strategy ensures that the optimization is guided along the optimal trajectory to mitigate potential numerical instabilities due to the presence of local traps. Benchmark applications to various molecular systems demonstrate that this strategy of progressive operator-block addition achieves accurate energetics with significantly fewer parameters while efficiently bypassing local traps. Moreover, in strongly correlated regions, such as bond dissociation, the method successfully reproduces the ground state, where other contemporary approaches often fail.

quant-ph↗

arXiv2025

Efficient quantum state preparation through seniority driven operator selection

Quantum algorithms require accurate representations of electronic states on a quantum device, yet the approximation of electronic wave functions for strongly correlated systems remains a profound theoretical challenge, with existing methods struggling to balance the competing demands of chemical accuracy and gate efficiency. Moreover, a critical limitation of the most of the state-of-the-art methods developed to date lies in their substantial reliance on extensive pre-circuit measurements, which introduce significant overheads and contribute to inefficiencies in practical implementation. To address these interconnected challenges and establish a harmonious synergy between them, we propose an algorithmic framework that focuses on efficiently capturing the molecular strong correlation through an ordered set of computationally less demanding rank-one and seniority-zero excitations, yielding a parameterized ansatz with shallow gate depth. Furthermore, to achieve minimal pre-circuit measurement overhead, we implement a selective pruning of excitations through a hybrid approach that combines intuition-based selection with shallow-depth, rank-one excitations driven uni-parameter circuit optimization strategy. With the incorporation of qubit-based excitations via particle-preserving exchange circuits, we demonstrate a further reduction in quantum complexities, enhancing the overall resource efficiency of the approach. With a range of challenging applications on strongly correlated systems, we demonstrate that our dynamic ansatz not only significantly enhances computational efficiency but also delivers exceptional accuracy, robustness, and resilience to the noisy environments inherent in near-term quantum hardware.

quant-ph↗

arXiv2025

Energy Landscape Plummeting in Variational Quantum Eigensolver: Subspace Optimization, Non-iterative Corrections and Generator-informed Initialization for Improved Quantum Efficiency

Variational Quantum Eigensolver (VQE) faces significant challenges due to hardware noise and the presence of barren plateaus and local traps in the optimization landscape. To mitigate the detrimental effects of these issues, we introduce a general formalism that optimizes hardware resource utilization and accuracy by projecting VQE optimizations on to a reduced-dimensional subspace, followed by a set of posteriori corrections. Our method partitions the ansatz into a lower dimensional principal subspace and a higher-dimensional auxiliary subspace based on a conjecture of temporal hierarchy present among the parameters during optimization. The adiabatic approximation exploits this hierarchy, restricting optimization to the lower dimensional principal subspace only. This is followed by an efficient higher dimensional auxiliary space reconstruction without the need to perform variational optimization. These reconstructed auxiliary parameters are subsequently included in the cost-function via a set of auxiliary subspace corrections (ASC) leading to a "plummeting effect" in the energy landscape toward a more optimal minima without utilizing any additional quantum hardware resources. Numerical simulations show that, when integrated with any chemistry-inspired ansatz, our method can provide one to two orders of magnitude better estimation of the minima. Additionally, based on the adiabatic approximation, we introduce a novel initialization strategy driven by unitary rotation generators for accelerated convergence of gradient-informed dynamic quantum algorithms. Our method shows heuristic evidences of alleviating the effects of local traps, facilitating convergence toward a more optimal minimum.

quant-ph↗

arXiv2025

Machine Learning Approach towards Quantum Error Mitigation for Accurate Molecular Energetics

Despite significant efforts, the realization of the hybrid quantum-classical algorithms has predominantly been confined to proof-of-principles, mainly due to the hardware noise. With fault-tolerant implementation being a long-term goal, going beyond small molecules with existing error mitigation (EM) techniques with current noisy intermediate scale quantum (NISQ) devices has been a challenge. That being said, statistical learning methods are promising approaches to learning the noise and its subsequent mitigation. We devise a graph neural network and regression-based machine learning (ML) architecture for practical realization of EM techniques for molecular Hamiltonian without the requirement of the exponential overhead. Given the short coherence time of the quantum hardware, the ML model is trained with either ideal or mitigated expectation values over a judiciously chosen ensemble of shallow sub-circuits adhering to the native hardware architecture. The hardware connectivity network is mapped to a directed graph which encodes the information of the native gate noise profile to generate the features for the neural network. The training data is generated on-the-fly during ansatz construction thus removing the computational overhead. We demonstrate orders of magnitude improvements in predicted energy over a few strongly correlated molecules.

quant-ph↗

arXiv2025

Construction of Chemistry Inspired Dynamic Ansatz Utilizing Generative Machine Learning

Generative machine learning models like the Restricted Boltzmann Machine (RBM) provide a practical approach for ansatz construction within the quantum computing framework. This work introduces a method that efficiently leverages RBM and many-body perturbative measures to build a compact chemistry-inspired ansatz for determining accurate molecular energetics. By training on low-rank determinants derived from an approximate wavefunction, RBM predicts the key high-rank determinants that dominate the ground-state wavefunction. A shallow depth ansatz is constructed to explicitly incorporate these dominant determinants after dynamically decomposing them into low-rank components and applying many-body perturbative measures for further screening. The method requires no additional measurements beyond the initial training phase. Moreover, it incorporates Bayesian hyperparameter optimization for the RBM, ensuring efficient performance with minimal training data during its limited usage. This approach facilitates the efficient computation of molecular properties, paving the way for exploring new chemical phenomena with near-term quantum computers.

physics.chem-ph↗

arXiv2024

Projective Quantum Eigensolver with Generalized Operators

Determination of molecular energetics and properties is one of the core challenges in the near-term quantum computing. To this end, hybrid quantum-classical algorithms are preferred for Noisy Intermediate Scale Quantum (NISQ) architectures. The Projective Quantum Eigensolver (PQE) is one such algorithms that optimizes the parameters of the chemistry-inspired unitary coupled cluster (UCC) ansatz using a conventional coupled cluster-like residual minimization. Such a strategy involves the projection of the Schrodinger equation on to linearly independent basis towards the parameter optimization, restricting the ansatz is solely defined in terms of the excitation operators. This warrants the inclusion of high-rank operators for strongly correlated systems, leading to increased utilization of quantum resources. In this manuscript, we develop a methodology for determining the generalized operators in terms of a closed form residual equations in the PQE framework that can be efficiently implemented in a quantum computer with manageable quantum resources. Such a strategy requires the removal of the underlying redundancy in high-rank excited determinants, generated due to the presence of the generalized operators in the ansatz, by projecting them on to an internally contracted lower dimensional manifold. With the application on several molecular systems, we have demonstrated our ansatz achieves similar accuracy to the (disentangled) UCC with singles, doubles and triples (SDT) ansatz, while utilizing an order of magnitude fewer quantum gates. Furthermore, when simulated under stochastic Gaussian noise or depolarizing hardware noise, our method shows significantly improved noise resilience compared to the other members of PQE family and the state-of-the-art variational quantum eigensolver.

quant-ph↗

arXiv2024

Towards a Resource-Optimized Dynamic Quantum Algorithm via Non-iterative Auxiliary Subspace Corrections

Recent quantum algorithms pertaining to electronic structure theory primarily focus on threshold-based dynamic construction of ansatz by selectively including important many-body operators. These methods can be made systematically more accurate by tuning the threshold to include more number of operators into the ansatz. However, such improvements come at the cost of rapid proliferation of the circuit depth, especially for highly correlated molecular systems. In this work, we address this issue by the development of a novel theoretical framework that relies on the segregation of an ansatz into a dynamically selected core principal component, which is, by construction adiabatically decoupled from the remaining operators. This enables us to perform computations involving the principal component using extremely shallow-depth circuits whereas, the effect of the remaining auxiliary component is folded into the energy function via a cost-efficient non-iterative correction, ensuring the requisite accuracy. We propose a formalism that analytically predicts the auxiliary parameters from the principal ones, followed by a suite of non-iterative auxiliary subspace correction techniques with different levels of sophistication. The auxiliary subspace corrections incur no additional quantum resources, yet complement an inadequately expressive core of the ansatz to recover significant amount of electronic correlations. We have numerically validated the resource efficiency and accuracy of our formalism with a number of strongly correlated molecular systems.

quant-ph↗

arXiv2024

Projective Quantum Eigensolver via Adiabatically Decoupled Subsystem Evolution: a Resource Efficient Approach to Molecular Energetics in Noisy Quantum Computers

Quantum computers hold immense potential in the field of chemistry, ushering new frontiers to solve complex many body problems that are beyond the reach of classical computers. However, noise in the current quantum hardware limits their applicability to large chemical systems. This work encompasses the development of a projective formalism that aims to compute ground-state energies of molecular systems accurately using Noisy Intermediate Scale Quantum (NISQ) hardware in a resource efficient manner. Our approach is reliant upon the formulation of a bipartitely decoupled parameterized ansatz within the disentangled unitary coupled cluster (dUCC) framework based on the principles of synergetics. Such decoupling emulates the total parameter optimization in a lower dimensional manifold, while a mutual synergistic relationship among the parameters is exploited to ensure characteristic accuracy. Without any pre-circuit measurements, our method leads to a highly compact fixed-depth ansatz with shallower circuits and fewer expectation value evaluations. Through analytical and numerical demonstrations, we demonstrate the method's superior performance under noise while concurrently ensuring requisite accuracy in future fault-tolerant systems. This approach enables rapid exploration of emerging chemical spaces by efficient utilization of near-term quantum hardware resources.

quant-ph↗

arXiv2023

Noise-independent Route towards the Genesis of a COMPACT Ansatz for Molecular Energetics: a Dynamic Approach

Recent advances in quantum information and quantum science have inspired the development of various compact dynamic structured ans\"{a}tze that are expected to be realizable in the Noisy Intermediate-Scale Quantum (NISQ) devices. However, such ans\"{a}tze construction strategies hitherto developed involve considerable measurements, and thus they deviate significantly in NISQ platform from their ideal structures. Therefore, it is imperative that the usage of quantum resources must be minimized while retaining the expressivity and dynamical structure of the ansatz that can adapt itself depending on the degree of correlation. We propose a novel ansatz construction strategy based on the \textit{ab-initio} many-body perturbation theory that requires \textit{no} pre-circuit measurement and thus it remains structurally unaffected by any hardware noise. The accuracy and quantum complexity associated with the ansatz are solely dictated by a pre-defined perturbative order as desired and hence are tunable. Furthermore, the underlying perturbative structure of the ansatz construction pipeline enables us to decompose any high-rank excitation that appears in higher perturbative orders into the product of various low-rank operators, and it thus keeps the execution gate-depth to its minimum. With a number of challenging applications on strongly correlated systems, we demonstrate that our ansatz performs significantly better, both in terms of accuracy, parameter count and circuit depth, in comparison to the allied unitary coupled cluster based ans\"{a}tze.

quant-ph↗

arXiv2023

Machine Learning Assisted Cognitive Construction of a Shallow Depth Dynamic Ansatz for Noisy Quantum Hardware

The development of various dynamic ansatz-constructing techniques has ushered in a new era, rendering the practical exploitation of Noisy Intermediate-Scale Quantum (NISQ) hardware for molecular simulations increasingly viable. However, they exhibit substantial measurement costs during their execution. This work involves the development of a novel protocol that capitalizes on regenerative machine learning methodologies and many-body perturbation theoretic measures to construct a highly expressive and shallow ansatz within the variational quantum eigensolver (VQE) framework. The machine learning methodology is trained with the basis vectors of a low-rank expansion of the N-electron Hilbert space to identify the dominant high-rank excited determinants without requiring a large number of quantum measurements. These selected excited determinants are iteratively incorporated within the ansatz through their low-rank decomposition. The reduction in the number of quantum measurements and ansatz depth manifests in the robustness of our method towards hardware noise, as demonstrated through numerical applications. Furthermore, the proposed method is highly compatible with state-of-the-art neural error mitigation techniques. This approach significantly enhances the feasibility of quantum simulations in molecular systems, paving the way for impactful advancements in quantum computational chemistry.

quant-ph↗

arXiv2023

Accurate determination of excitation energy: An equation-of-motion approach over a bi-exponential Coupled Cluster theory

The calculation of molecular excited states is critically important to decipher a plethora of molecular properties. In this manuscript, we develop an equation of motion formalism on top of a bi-exponentially parametrized ground state wavefunction towards the determination of excited states. While the ground state bi-exponential parametrization ensures an accurate description of the wavefunction through the inclusion of high-rank correlation effects, the excited state is parametrized by a novel linear response operator with an effective excitation rank beyond two. To treat the ground and the excited states in the same footings, in addition to the conventional one and two-body response operators, we introduced certain two-body "generalized" response operators with an effective excitation rank of one. We introduce a projective formulation towards the determination of the perturbed amplitudes for the set of "generalized" operators. Our formulation entails a significantly small number of unknown parameters and is shown to be highly accurate compared to allied methods for several difficult chemical systems.

physics.chem-ph↗