arXiv subjects

Sonaldeep Halder

Publications and source records attributed to Sonaldeep Halder.

11 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↗

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

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

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

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

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

Development of Zero-Noise Extrapolated Projection Based Quantum Algorithm for Accurate Evaluation of Molecular Energetics in Noisy Quantum Devices

The recently developed Projective Quantum Eigensolver (PQE) offers an elegant procedure to evaluate the ground state energies of molecular systems on quantum computers. However, the noise in available quantum hardware can result in significant errors in computed outcomes, limiting the realization of quantum advantage. Although PQE comes equipped with some degree of inherent noise resilience, any practical implementation with apposite accuracy would require additional routines to suppress the errors further. In this work, we propose a way to enhance the efficiency of PQE by developing an optimal framework for introducing Zero Noise Extrapolation (ZNE) in the nonlinear iterative procedure that outlines the PQE; leading to the formulation of ZNE-PQE. For this method, we perform a detailed analysis of how various components involved in it affect the accuracy and efficiency of the reciprocated energy convergence trajectory. Moreover, we investigate the reasons behind the improvements observed in ZNE-PQE over conventional PQE by performing a comparative analysis of their residue norm landscape. This approach is expected to facilitate practical applications of quantum computing in fields related to molecular sciences, where it is essential to determine molecular energies accurately.

quant-ph↗

arXiv2023

Machine Learning Aided Dimensionality Reduction towards a Resource Efficient Projective Quantum Eigensolver

The recently developed Projective Quantum Eigensolver (PQE) has been demonstrated as an elegant methodology to compute the ground state energy of molecular systems in Noisy Intermdiate Scale Quantum (NISQ) devices. The iterative optimization of the ansatz parameters involves repeated construction of residues on a quantum device. The quintessential pattern of the iteration dynamics, when projected as a time discrete map, suggests a hierarchical structure in the timescale of convergence, effectively partitioning the parameters into two distinct classes. In this work, we have exploited the collective interplay of these two sets of parameters via machine learning techniques to bring out the synergistic inter-relationship among them that triggers a drastic reduction in the number of quantum measurements necessary for the parameter updates while maintaining the characteristic accuracy of PQE. Furthermore the machine learning model may be tuned to capture the noisy data of NISQ devices and thus the predicted energy is shown to be resilient under a given noise model.

quant-ph↗

arXiv2023

On-the-fly Tailoring towards a Rational Ansatz Design for Digital Quantum Simulations

Recent advancements in quantum information and quantum technology has stimulated a good deal of interest in the development of quantum algorithms for energetics and properties of many-fermionic systems. While the variational quantum eigensolver is the most optimal algorithm in the Noisy Intermediate Scale Quantum era, it is imperative to develop low depth quantum circuits that are physically realizable in quantum devices. Within the unitary coupled cluster framework, we develop COMPASS, a disentangled ansatz construction protocol that can dynamically tailor an optimal ansatz using the one and two-body cluster operators and a selection of rank-two scatterers. The construction of the ansatz may potentially be performed in parallel quantum architecture through energy sorting and operator commutativity prescreening. With significant reduction in the circuit depth towards the simulation of molecular strong correlation, COMPASS is shown to be highly accurate and resilient to the noisy circumstances of the near-term quantum hardware.

quant-ph↗

arXiv2022

A Synergistic Approach towards Optimization of Coupled Cluster Amplitudes by Exploiting Dynamical Hierarchy

The coupled cluster iteration scheme for determining the cluster amplitudes involves a set of nonlinearly coupled difference equations. In the space spanned by the amplitudes, the set of equations are analysed as a multivariate time-discrete map where the concept of time appears in an implicit manner. With the observation that the cluster amplitudes have difference in their relaxation timescales with respect to the distributions of their magnitudes, the coupled cluster iteration dynamics are considered as a synergistic motion of coexisting slow and fast relaxing modes, manifesting a dynamical hierarchical structure. With the identification of the highly damped auxiliary amplitudes, their time variation can be neglected compared to the principal amplitudes which take much longer time to reach the fixed points. We analytically establish the adiabatic approximation where each of these auxiliary amplitudes are expressed as unique parametric functions of the collective principal amplitudes, allowing us to study the optimization with the latter taken as the independent degrees of freedom. Such decoupling of the amplitudes significantly reduces the computational scaling without sacrificing the accuracy in the ground state energy as demonstrated by a number of challenging molecular applications. A road-map to treat higher order post-adiabatic effects is also discussed.

physics.comp-ph↗