arXiv subjects

Ayush Asthana

Publications and source records attributed to Ayush Asthana.

10 recordsLinked to original sources

arXiv2026

Quantum simulation of molecular excited-state manifolds and energies using the TEPID-ADAPT-VQE algorithm

The simulation of molecular excited states is a key challenge in quantum chemistry and a promising application for quantum computing. In this work, we investigate the efficacy of the truncated eigenvalue parametrized initial density adaptive variational algorithm (TEPID-ADAPT-VQE) for computing low-lying excited states and potential energy surfaces. TEPID-ADAPT variationally diagonalizes a truncated low-temperature Gibbs state, enabling the simultaneous preparation of multiple excited states within a single optimization. We apply the method to H$_2$, LiH, and linear H$_4$ across bond lengths spanning weakly and strongly correlated regimes. The adaptive derivative-assembled problem-tailored (ADAPT) ansatz construction yields compact circuits suitable for near-term hardware. We also implement a modified version of the MORE-ADAPT-VQE algorithm for comparison with TEPID-ADAPT. We find that both algorithms accurately reproduce excited-state spectra and potential energy curves within chemical accuracy for all the molecules and geometries studied. However, TEPID-ADAPT has the advantage of utilizing only a single, physically motivated hyperparameter (temperature) that controls the energy scale at which excited states are targeted, while MORE-ADAPT utilizes multiple hyperparameters whose optimal values depend sensitively on the target problem. These results demonstrate that combining adaptive ansatz construction with density-matrix-based formulations provides an efficient framework for excited-state quantum chemistry on near-term devices.

quant-ph↗

arXiv2026

Molecular Excited States using Quantum Subspace Methods: Accuracy, Resource Reduction, and Error-Mitigated Hardware Implementation of q-sc-EOM

Problems in quantum chemical simulations, especially achieving accurate excited-state potential energy surfaces, are among the primary applications to achieve quantum utility. On near-term quantum hardware, variants of the variational quantum eigensolver (VQE) algorithms are the primary choice for chemistry simulation. In this study, a combination of leading ground and excited state quantum algorithms for general excited states, namely, ADAPT-VQE/LUCJ and q-sc-EOM, are utilized to calculate accurate excited state potential energy surfaces in challenging bond-breaking scenarios and compared with the classical scalable EOM-CCSD method. This work investigates avenues toward quantum utility in excited-state quantum chemistry using the q-sc-EOM approach. We assess its accuracy while mitigating major scaling bottlenecks through the Davidson algorithm and basis rotation grouping, reducing the measurement scaling from O(N$^{12}$) to O(N$^{5}$), and implementing the method on quantum hardware with various error mitigation strategies to reduce gate and measurement errors in excited states. The hardware implementation of the q-sc-EOM algorithm, augmented by mitigation of M3 readout error and symmetry projection, produces reasonably accurate excited-state energies with gate noise identified as the predominant source of error. This paves the way for accurate and scalable, generally applicable quantum excited-state methods with potential for quantum utility while identifying critical problems that require advancements.

quant-ph↗

arXiv2026

On the generalized eigenvalue problem in subspace-based excited state methods for quantum computers

Solving challenging problems in quantum chemistry is one of the most promising applications of quantum computers. Within the quantum algorithms proposed for problems in excited state quantum chemistry, subspace-based quantum algorithms, including quantum subspace expansion (QSE), quantum equation of motion (qEOM) and quantum self-consistent equation-of-motion (q-sc-EOM), are promising for pre-fault-tolerant quantum devices. The working equation of QSE and qEOM requires solving a generalized eigenvalue equation with associated matrix elements measured on a quantum computer. Our careful analytical and numerical analysis of the standard and generalized eigenvalue problems, especially in the context of excited-state methods, shows that the errors in eigenvalues magnify drastically with an increase in the condition number of the overlap matrix when a generalized eigenvalue equation is solved in the presence of statistical sampling errors. This makes methods such as QSE unstable to errors that are unavoidable when using quantum computers. Further, at very high condition numbers of the overlap matrix, the QSE's working equation could not be solved without any additional steps in the presence of sampling errors, as it becomes ill-conditioned. It was possible to use the thresholding technique in this case to solve the equation, but the solutions achieved had missing excited states, which may be a problem for future chemical studies. We also show that excited-state methods that have an eigenvalue equation as the working equation, such as q-sc-EOM, do not have the problems associated with the condition number and could be generally more stable to errors, and therefore, more suitable candidates for excited-state quantum chemistry calculations using quantum computers.

quant-ph↗

arXiv2026

Exact and Tunable Quantum Krylov Subspaces via Unitary Decomposition

Quantum Krylov subspace methods can extract ground and excited states by diagonalizing the Hamiltonian in a compact variational space. In practice, these spaces are almost always generated by real or imaginary time evolution, forcing a timestep trade-off between dynamical accuracy and basis collapse and often producing ill-conditioned overlap matrices that stall convergence. Here we introduce Quantum Krylov using Unitary Decomposition (QKUD), a time-evolution-free construction that maps Hamiltonian powers to implementable unitaries via the Hermitian transform $\sin(εH)/ε$. QKUD reduces to the exact Hamiltonian-power Krylov recursion as $ε\rightarrow0$, while finite $ε$ provides a controllable deformation that tunes subspace geometry and improves conditioning. Across molecular active-space benchmarks and a frustrated 2D J1-J2 Heisenberg model, QKUD reproduces exact-Krylov convergence in well-conditioned regimes and systematically restores variational improvement when both exact Krylov and time-evolution Krylov stagnate. These results identify overlap conditioning, instead of time-evolution fidelity, is the key resource for robust quantum Krylov simulation and provide a resilient way forward for accurate quantum simulation of challenging quantum many-body problems.

quant-ph↗

arXiv2026

Chemically decisive benchmarks on the path to quantum utility

Progress towards quantum utility in chemistry requires not only algorithmic advances, but also the identification of chemically meaningful problems whose electronic structure fundamentally challenges classical methods. Here, we introduce a curated hierarchy of chemically decisive benchmark systems designed to probe distinct regimes of electronic correlation relevant to molecular, bioinorganic, and heavy-element chemistry. Moving beyond minimal toy models, our benchmark set spans multireference bond breaking (N$_2$), high-spin transition-metal chemistry (FeS), biologically relevant iron-sulfur clusters ([2Fe-2S]), and actinide-actinide bonding (U$_2$), which exhibits extreme sensitivity to active-space choice, relativistic treatment, and correlation hierarchy even within advanced multireference frameworks. As a concrete realization, we benchmark a recently developed automated and adaptive quantum algorithm based on generator-coordinate-inspired subspace expansion,ADAPT-GCIM, using a black-box workflow that integrates entropy-based active-space selection via the ActiveSpaceFinder tool. Across this chemically diverse problem set, ADAPT-GCIM achieves high accuracy in challenging correlation regimes. Equally importantly, these benchmarks expose general failure modes and design constraints-independent of any specific algorithm-highlighting the necessity of problem-aware and correlation-specific strategies for treating strongly correlated chemistry on quantum computers. To support systematic benchmarking and reproducible comparisons, the Hamiltonians for all systems studied are made openly available.

physics.chem-ph↗

arXiv2025

Cyclic Variational Quantum Eigensolver: Escaping Barren Plateaus through Staircase Descent

We introduce the Cyclic Variational Quantum Eigensolver (CVQE), a hardware-efficient framework for accurate ground-state quantum simulation on noisy intermediate-scale quantum (NISQ) devices. CVQE departs from conventional VQE by incorporating a measurement-driven feedback cycle: Slater determinants with significant sampling probability are iteratively added to the reference superposition, while a fixed entangler (e.g., single-layer UCCSD) is reused throughout. This adaptive reference growth systematically enlarges the variational space in most promising directions, avoiding manual ansatz or operator-pool design, costly searches, and preserving compile-once circuits. The strategy parallels multi-reference methods in quantum chemistry, while remaining fully automated on quantum hardware. Remarkably, CVQE exhibits a distinctive staircase-like descent pattern, where successive energy drops sharply signal efficient escape from barren plateaus. Benchmarks show that CVQE consistently maintains chemical precision across correlation regimes, outperforms fixed UCCSD by several orders of magnitude, and achieves favorable accuracy-cost trade-offs compared to the Selected Configuration Interaction. These results position CVQE as a scalable, interpretable, and resource-efficient paradigm for near-term quantum simulation.

quant-ph↗

arXiv2023

Quantum self-consistent equation-of-motion method for computing molecular excitation energies, ionization potentials, and electron affinities on a quantum computer

Near-term quantum computers are expected to facilitate material and chemical research through accurate molecular simulations. Several developments have already shown that accurate ground-state energies for small molecules can be evaluated on present-day quantum devices. Although electronically excited states play a vital role in chemical processes and applications, the search for a reliable and practical approach for routine excited-state calculations on near-term quantum devices is ongoing. Inspired by excited-state methods developed for the unitary coupled-cluster theory in quantum chemistry, we present an equation-of-motion-based method to compute excitation energies following the variational quantum eigensolver algorithm for ground-state calculations on a quantum computer. We perform numerical simulations on H$_2$, H$_4$, H$_2$O, and LiH molecules to test our quantum self-consistent equation-of-motion (q-sc-EOM) method and compare it to other current state-of-the-art methods. q-sc-EOM makes use of self-consistent operators to satisfy the vacuum annihilation condition, a critical property for accurate calculations. It provides real and size-intensive energy differences corresponding to vertical excitation energies, ionization potentials and electron affinities. We also find that q-sc-EOM is more suitable for implementation on NISQ devices as it is expected to be more resilient to noise compared with the currently available methods.

quant-ph↗

arXiv2023

Quantum simulation of molecular response properties

Accurate modeling of the response of molecular systems to an external electromagnetic field is challenging on classical computers, especially in the regime of strong electronic correlation. In this paper, we develop a quantum linear response (qLR) theory to calculate molecular response properties on near-term quantum computers. Inspired by the recently developed variants of the quantum counterpart of equation of motion (qEOM) theory, the qLR formalism employs "killer condition" satisfying excitation operator manifolds that offers a number of theoretical advantages along with reduced quantum resource requirements. We also used the qEOM framework in this work to calculate state-specific response properties. Further, through noise-less quantum simulations, we show that response properties calculated using the qLR approach are more accurate than the ones obtained from the classical coupled-cluster based linear response models due to the improved quality of the ground-state wavefunction obtained using the ADAPT-VQE algorithm.

quant-ph↗

arXiv2022

Minimizing state preparation times in pulse-level variational molecular simulations

Quantum simulation on NISQ devices is severely limited by short coherence times. A variational pulse-shaping algorithm known as ctrl-VQE was recently proposed to address this issue by eliminating the need for parameterized quantum circuits, which lead to long state preparation times. Here, we find the shortest possible pulses for ctrl-VQE to prepare target molecular wavefunctions for a given device Hamiltonian describing coupled transmon qubits. We find that the time-optimal pulses that do this have a bang-bang form consistent with Pontryagin's maximum principle. We further investigate how the minimal state preparation time is impacted by truncating the transmons to two versus more levels. We find that leakage outside the computational subspace (something that is usually considered problematic) speeds up the state preparation, further reducing device coherence-time demands. This speedup is due to an enlarged solution space of target wavefunctions and to the appearance of additional channels connecting initial and target states.

quant-ph↗

arXiv2022

Accurate quantum simulation of molecular ground and excited states with a transcorrelated Hamiltonian

NISQ era devices suffer from a number of challenges like limited qubit connectivity, short coherence times and sizable gate error rates. Thus, quantum algorithms are desired that require shallow circuit depths and low qubit counts to take advantage of these devices. We attempt to realize this with the help of classical quantum chemical theories of canonical transformation and explicit correlation. In this work, compact ab initio Hamiltonians are generated classically through an approximate similarity transformation of the Hamiltonian with a) an explicitly correlated two-body unitary operator with generalized pair excitations that remove the Coulombic electron-electron singularities from the Hamiltonian and b) a unitary one-body operator to efficiently capture the orbital relaxation effects required for accurate description of the excited states. The resulting transcorelated Hamiltonians are able to describe both ground and excited states of molecular systems in a balanced manner. Using the fermionic-ADAPT-VQE method based on the unitary coupled cluster with singles and doubles (UCCSD) ansatz and only a minimal basis set (ANO-RCC-MB), we demonstrate that the transcorrelated Hamiltonians can produce ground state energies comparable to the much larger cc-pVTZ basis. This leads to a potential reduction in the number of required CNOT gates by more than three orders of magnitude for the chemical species studied in this work. Furthermore, using the qEOM formalism in conjunction with the transcorrelated Hamiltonian, we reduce the errors in excitation energies by an order of magnitude. The transcorrelated Hamiltonians developed here are Hermitian and contain only one- and two-body interaction terms and thus can be easily combined with any quantum algorithm for accurate electronic structure simulations.

physics.chem-ph↗