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

• URL: http://arxiv.org/abs/2512.01605v1
• Date: Mon, 01 Dec 2025 12:24:00 GMT
• Title: Resource Estimation for VQE on Small Molecules: Impact of Fermion Mappings and Hamiltonian Reductions
• Authors: Anurag K. S. V., Ashish Kumar Patra, Vikas Dattatraya Ghevade, Sai Shankar P., Ruchika Bhat, Raghavendra V., Rahul Maitra, Jaiganesh G,
• Abstract summary: Variational Quantumsolver (VQE) represents a leading hybrid quantum-classical paradigm for addressing this challenge.<n>Resource requirements for VQE implementations employing the Unitary Coupled Cluster Singles and Doubles (UCCSD) ansatz are systematically analyzed.<n>Hamiltonian reduction strategies, including $mathbbZ$ tapering and frozen-core approximations, are examined to assess their effect on quantum resource scaling.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 encoding schemes. 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 $\approx 45\times$ for the representative set of molecular systems under study. This provides practical insights for executing chemically relevant simulations on NISQ and FASQ hardware.

Related papers

• Hybrid Quantum Algorithms for Computational Chemistry: Application to the Pyridine-Li ion Complex [0.0]
  Three quantum algorithms are investigated for capturing electron correlation in large-scale molecular systems.<n>Results show how new generations of hybrid quantum-classical frameworks overcome the scalability and noise sensitivity that constrain conventional VQE approaches.<n>Both SQD and HI-VQE exhibit robustness against hardware noise, a critical improvement over earlier approaches.
  arXiv  Detail & Related papers  (2026-01-15T02:23:09Z)
• Performance Guarantees for Quantum Neural Estimation of Entropies [31.955071410400947]
  Quantum neural estimators (QNEs) combine classical neural networks with parametrized quantum circuits.<n>We study formal guarantees for QNEs of measured relative entropies in the form of non-asymptotic error risk bounds.<n>Our theory aims to facilitate principled implementation of QNEs for measured relative entropies.
  arXiv  Detail & Related papers  (2025-11-24T16:36:06Z)
• Molecular resonance identification in complex absorbing potentials via integrated quantum computing and high-throughput computing [36.94429692322632]
  We develop an algorithm that exploits the complex absorbing potential formalism to distill the problem of molecular resonance identification into a network of hybrid quantum-classical variational quantum eigensolver tasks.<n>We show qDRIVE successfully identifies resonance energies and wavefunctions in simulated quantum processors with current and planned specifications.
  arXiv  Detail & Related papers  (2025-11-20T02:28:05Z)
• Qumode-Based Variational Quantum Eigensolver for Molecular Excited States [43.148034499498586]
  We introduce the Qumode Subspace Variational Quantum Eigensolver (QSS-VQE), a hybrid quantum-classical algorithm for computing molecular excited states.<n>We demonstrate the performance of QSS-VQE through simulations of molecular excited states, including dihydrogen and a conical intersection in cytosine.
  arXiv  Detail & Related papers  (2025-09-05T00:53:51Z)
• VQC-MLPNet: An Unconventional Hybrid Quantum-Classical Architecture for Scalable and Robust Quantum Machine Learning [50.95799256262098]
  Variational quantum circuits (VQCs) hold promise for quantum machine learning but face challenges in expressivity, trainability, and noise resilience.<n>We propose VQC-MLPNet, a hybrid architecture where a VQC generates the first-layer weights of a classical multilayer perceptron during training, while inference is performed entirely classically.
  arXiv  Detail & Related papers  (2025-06-12T01:38:15Z)
• Variational Quantum Imaginary Time Evolution for Matrix Product State Ansatz with Tests on Transcorrelated Hamiltonians [11.985673663540688]
  The matrix product state (MPS) ansatz offers a promising approach for finding the ground state of molecular Hamiltonians. We enhance the optimization performance of the QCMPS ansatz by employing the variational quantum imaginary time evolution (VarQITE) approach.
  arXiv  Detail & Related papers  (2024-07-15T08:28:52Z)
• Non-unitary Coupled Cluster Enabled by Mid-circuit Measurements on Quantum Computers [37.69303106863453]
  We propose a state preparation method based on coupled cluster (CC) theory, which is a pillar of quantum chemistry on classical computers. Our approach leads to a reduction of the classical computation overhead, and the number of CNOT and T gates by 28% and 57% on average.
  arXiv  Detail & Related papers  (2024-06-17T14:10:10Z)
• Mitigating Errors on Superconducting Quantum Processors through Fuzzy Clustering [38.02852247910155]
  A new Quantum Error Mitigation (QEM) technique uses Fuzzy C-Means clustering to specifically identify measurement error patterns. We report a proof-of-principle validation of the technique on a 2-qubit register, obtained as a subset of a real NISQ 5-qubit superconducting quantum processor. We demonstrate that the FCM-based QEM technique allows for reasonable improvement of the expectation values of single- and two-qubit gates based quantum circuits.
  arXiv  Detail & Related papers  (2024-02-02T14:02:45Z)
• Potential energy surfaces inference of both ground and excited state using hybrid quantum-classical neural network [0.0]
  A hybrid quantum-classical neural network has been proposed for surrogate modeling of the variational quantum eigensolver. We extend the model by using the subspace-search variational quantum eigensolver procedure so that the PESs of the both ground and excited state can be inferred with chemical accuracy.
  arXiv  Detail & Related papers  (2022-12-06T14:28:44Z)
• Variational Quantum-Neural Hybrid Error Mitigation [6.555128824546528]
  Quantum error mitigation (QEM) is crucial for obtaining reliable results on quantum computers. We show how variational quantum-neural hybrid eigensolver (VQNHE) algorithm is inherently noise resilient with a unique QEM capacity.
  arXiv  Detail & Related papers  (2021-12-20T08:07:58Z)
• Towards the real-time evolution of gauge-invariant $\mathbb{Z}_2$ and $U(1)$ quantum link models on NISQ Hardware with error-mitigation [0.0]
  We benchmark the real-time dynamics of $mathbbZ$ and $U(1)$ gauge in plaquette models using noisy intermediate scale quantum (NISQ) hardware. We design quantum circuits for models of increasing complexity and measure physical observables such as the return probability to the initial state, and locally conserved charges.
  arXiv  Detail & Related papers  (2021-09-30T12:22:21Z)
• Scaling Up Electronic Structure Calculations on Quantum Computers: The Frozen Natural Orbital Based Method of Increments [0.0]
  The MI-FNO framework provides a systematic reduction of the occupied and virtual orbital spaces for quantum chemistry simulations. The correlation energies of the increments resulting from the MI-FNO reduction can then be solved by various algorithms. We show that the MI-FNO approach provides a significant reduction in the qubit requirements relative to the full system simulations.
  arXiv  Detail & Related papers  (2020-02-18T22:07:42Z)
• Computation of molecular excited states on IBM quantum computers using a discriminative variational quantum eigensolver [0.965964228590342]
  We propose a variational quantum machine learning based method to determine molecular excited states. Our method uses a combination of two parametrized quantum circuits, working in tandem, combined with a Variational Quantum Eigensolver (VQE) to iteratively find the eigenstates of a molecular Hamiltonian.
  arXiv  Detail & Related papers  (2020-01-14T17:56:04Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.