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 framework based on the principles of nonlinear dynamics and synergetics. Such decoupling emulates total parameter optimization in a lower dimensional manifold, while a mutual synergistic relationship among the parameters is exploited to ensure characteristic accuracy via a non-iterative energy correction. 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 establish 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 the efficient utilization of near-term quantum hardware resources.

Synthesis and biological evaluation of new naphthalimide-thiourea derivatives as potent antimicrobial agents active against multidrug-resistant Staphylococcus aureus and Mycobacterium tuberculosis.

The emergence of antibiotic resistance to S. aureus and M. tuberculosis, particularly MRSA, VRSA, and drug-resistant tuberculosis, poses a serious threat to human health. Towards discovering new antibacterial agents, we designed and synthesized a series of new naphthalimide-thiourea derivatives and evaluated them against a panel of bacterial strains consisting of E. coli, S. aureus, K. pneumoniae, P. aeruginosa, A. baumannii and various mycobacterial pathogens. Compounds 4a, 4l, 4m, 4n, 4q, 9f, 9l, 13a, 13d, 13e, 17a, 17b, 17c, 17d, and 17e demonstrated potent antibacterial activity against S. aureus with MIC 0.03-8 µg mL-1. In addition, these compounds have also exhibited potent inhibition against MDR strains of S. aureus, including VRSA with MICs 0.06-4 µg mL-1. Compounds 4h, 4j, 4l, 4m, 4q, 4r, 9a, 9b, 9c, 9d, 9e, 9g, 9h, 9j, 13f and 17e also exhibited good antimycobacterial activity against M. tuberculosis with MIC 2-64 µg mL-1. The cytotoxicity assay using Vero cells revealed that all the compounds were non-toxic and exhibited a favorable selectivity index (SI >40). Time kill kinetics data indicated that compounds exhibited concentration-dependent killing. Furthermore, in silico studies were performed to decipher the possible mechanism of action. Comprehensively, these results highlight the potential of naphthalimide-thiourea derivatives as promising antibacterial agents.

Noise-independent route toward 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, dynamically structured ansätze that are expected to be realizable in Noisy Intermediate-Scale Quantum (NISQ) devices. However, such ansätze construction strategies hitherto developed involve considerable measurements, and thus, they deviate significantly in the NISQ platform from their ideal structures. Therefore, it is imperative that the usage of quantum resources 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 ab initio many-body perturbation theory that requires no pre-circuit measurement and, thus, 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 ansätze.

Machine learning assisted 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, making the practical exploitation of Noisy Intermediate-Scale Quantum (NISQ) hardware for molecular simulations increasingly viable. However, such ansatz construction protocols incur 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 theoretical measures to construct a highly expressive and shallow ansatz within the variational quantum eigensolver (VQE) framework with limited measurement costs. The regenerative machine learning model used in our work 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 resource-efficient approach is quintessential for determining spectroscopic and other molecular properties, thereby facilitating the study of emerging chemical phenomena in the near-term quantum computing framework.

Antimicrobial peptide mimetic minimalistic approach leads to very short peptide amphiphiles-gold nanostructures for potent antibacterial activity.

Strategically controlling concentrations of lipid-conjugated L-tryptophan (vsPA) guides the self-assembly of nanostructures, transitioning from nanorods to fibres and culminating in spherical shapes. The resulting Peptide-Au hybrids, exhibiting size-controlled 1D, 2D, and 3D nanostructures, show potential in antibacterial applications. Their high biocompatibility, favourable surface area-to-volume ratio, and plasmonic properties contribute to their effectiveness against clinically relevant bacteria. This controlled approach not only yields diverse nanostructures but also holds promise for applications in antibacterial therapeutics.

One-pot synthesis of thioethers from indoles and p-quinone methides using thiourea as a sulfur source.

Thiourea is an inexpensive and user friendly sulfur reagent that acts as a sulfur source. A simple and efficient protocol has been developed to access thioethers by reacting indoles with p-quinone methides using thiourea as the sulfur source. In our experiments, the reaction apparently proceeded through an S-(3-indolyl)isothiuronium iodide intermediate and subsequent generation of indolethiol that attacked the 1,6 position of p-quinone methides to give desired thioethers in good to excellent yields.

Development of zero-noise extrapolated projective 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 in 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 eliminate or mitigate 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. Moreover, we perform a detailed analysis of how various components involved in it affect the accuracy and efficiency of the reciprocated energy convergence trajectory. Additionally, we investigate the underlying mechanism that leads to 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.

Discovery of benzoxazole-thiazolidinone hybrids as promising antibacterial agents against Staphylococcus aureus and Enterococcus species.

Antibiotic resistance is rapidly exacerbating the unceasing rise in nosocomial infections caused by drug-resistant bacterial pathogens such as methicillin-resistant Staphylococcus aureus (MRSA), carbapenem-resistant Enterobacteriaceae (CRE) and vancomycin-resistant Enterococcus (VRE). Therefore, there is a dire need for new therapeutic agents that can mitigate the unbridled emergence of drug-resistant pathogens. In the present study, several benzoxazole-thiazolidinone hybrids (BT hybrids) were synthesized and evaluated for their antibacterial activity against the ESKAP pathogen panel. The preliminary screening revealed the selective and potent inhibitory activity of hydroxy BT hybrids against S. aureus with MIC ≤ 4 µg mL-1. Hydroxy compounds (BT25, BT26, BT18, BT12, and BT11) exhibited a good selectivity index (SI > 20), which were determined to be non-toxic to Vero cells. An engaging fact is that two compounds BT25 and BT26 showed potent activity against various clinically-relevant and highly drug resistant S. aureus (MRSA & VRSA) and Enterococcus (VRE) isolates. These hybrids showed concentration-dependent bactericidal activity that is comparable to vancomycin. These experimental results were corroborated with docking, molecular dynamics, and free energy studies to discern the antibacterial mechanisms of hydroxy BT hybrids with three bacterial enzymes DNA gyrase B, MurB, and penicillin binding protein 4 (PBP4). The reassuring outcome of the current investigation confirmed that the aforementioned BT hybrids could be used as very promisingly potent antibacterial agents for the treatment of Staphylococcus aureus and Enterococcus infections.

Development of a compact Ansatz via operator commutativity screening: Digital quantum simulation of molecular systems.

Recent advancements in quantum information and quantum technology have stimulated a good deal of interest in the development of quantum algorithms toward the determination of the 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 compact Ansätze with low-depth quantum circuits that are physically realizable in quantum devices. Within the unitary coupled cluster framework, we develop 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 over multiple quantum processors through energy sorting and operator commutativity prescreening. With a significant reduction in the circuit depth toward the simulation of molecular strong correlation, our dynamic Ansatz construction protocol is shown to be highly accurate and resilient to the noisy circumstances of the near-term quantum hardware.

Fixing the catastrophic breakdown of single reference coupled cluster theory for strongly correlated systems: Two paradigms toward the implicit inclusion of high-rank correlation with low-spin channels.

The dual exponential coupled cluster theory proposed by Tribedi et al.[J. Chem. Theory Comput. 16, 10, 6317-6328 (2020)] performs significantly better for a wide range of weakly correlated systems than the coupled cluster theory with singles and doubles excitations due to the implicit inclusion of high-rank excitations. The high-rank excitations are included through the action of a set of vacuum annihilating scattering operators that act non-trivially on certain correlated wavefunctions and are determined via a set of local denominators involving the energy difference between certain excited states. This often leads the theory to be prone to instabilities. In this paper, we show that restricting the correlated wavefunction, on which the scattering operators act, to be spanned by only the singlet-paired determinants can avoid catastrophic breakdown. For the first time, we present two nonequivalent approaches to arrive at the working equations, viz., the projective approach with sufficiency conditions and the amplitude form with many-body expansion. Although the effect of the triple excitation is quite small around molecular equilibrium geometry, this scheme leads to a better qualitative description of the energetics in the regions of strong correlation. With many pilot numerical applications, we have demonstrated the performance of the dual-exponential scheme with both the proposed solution strategies while restricting the excitation subspaces coupled to the corresponding lowest spin channels.

Machine learning aided dimensionality reduction toward a resource efficient projective quantum eigensolver: Formal development and pilot applications.

In recent times, a variety of hybrid quantum-classical algorithms have been developed that aim to calculate the ground state energies of molecular systems on Noisy Intermediate-Scale Quantum (NISQ) devices. Albeit the utilization of shallow depth circuits in these algorithms, the optimization of ansatz parameters necessitates a substantial number of quantum measurements, leading to prolonged runtimes on the scantly available quantum hardware. Through our work, we lay the general foundation for an interdisciplinary approach that can be used to drastically reduce the dependency of these algorithms on quantum infrastructure. We showcase these pertinent concepts within the framework of the recently developed Projective Quantum Eigensolver (PQE) that involves iterative optimization of the nonlinearly coupled parameters through repeated residue measurements on quantum hardware. We demonstrate that one may perceive such a nonlinear optimization problem as a collective dynamic interplay of fast and slow relaxing modes. As such, the synergy among the parameters is exploited using an on-the-fly supervised machine learning protocol that dynamically casts the PQE optimization into a smaller subspace by reducing the effective degrees of freedom. We demonstrate analytically and numerically that our proposed methodology ensures a drastic reduction in the number of quantum measurements necessary for the parameter updates without compromising the characteristic accuracy. 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.

Synthesis of tryptanthrin appended dispiropyrrolidine oxindoles and their antibacterial evaluation.

The synthesis of sixteen tryptanthrin appended dispiropyrrolidine oxindoles, employing [3 + 2] cycloaddition of tryptanthrin-derived azomethine ylides with isatilidenes, and their detailed antibacterial evaluation is described. The in vitro antibacterial activities of the compounds were evaluated against ESKAPE pathogens and clinically relevant drug-resistant MRSA/VRSA strains, from which the bromo-substituted dispiropyrrolidine oxindole 5b (MIC = 0.125 µg mL-1) was found to be a potent molecule against S. aureus ATCC 29213 with a good selectivity index.

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 analyzed 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.

Dual exponential coupled cluster theory: Unitary adaptation, implementation in the variational quantum eigensolver framework and pilot applications.

In this paper, we have developed a unitary variant of a double exponential coupled cluster theory, which is capable of handling molecular strong correlation with arbitrary electronic complexity. With the Hartree-Fock determinant taken as the reference, we introduce a sequential product of parameterized unitary Ansätze. While the first unitary, containing the excitation operators, acts directly on the reference determinant, the second unitary, containing a set of rank-two, vacuum-annihilating scattering operators, has nontrivial action only on certain entangled states. We demonstrate the theoretical bottleneck of such an implementation in a classical computer, whereas the same is implemented in the hybrid quantum-classical variational quantum eigensolver framework with a reasonably shallow quantum circuit without any additional approximation. We have further introduced a number of variants of the proposed Ansatz with different degrees of sophistication by judiciously approximating the scattering operators. With a number of applications on strongly correlated molecules, we have shown that all our schemes can perform uniformly well throughout the molecular potential energy surface without significant additional implementation cost over the conventional unitary coupled cluster approach with single and double excitations.

A double exponential coupled cluster theory in the fragment molecular orbital framework.

Fragmentation-based methods enable electronic structure calculations for large chemical systems through partitioning them into smaller fragments. Here, we have developed and benchmarked a dual exponential operator-based coupled cluster theory to account for high-rank electronic correlation of large chemical systems within the fragment molecular orbital (FMO) framework. Upon partitioning the molecular system into several fragments, the zeroth order reference determinants for each fragment and fragment pair are constructed in a self-consistent manner with two-body FMO expansion. The dynamical correlation is induced through a dual exponential ansatz with a set of fragment-specific rank-one and rank-two operators that act on the individual reference determinants. While the single and double excitations for each fragment are included through the conventional rank-one and rank-two cluster operators, the triple excitation space is spanned via the contraction between the cluster operators and a set of rank-two scattering operators over a few optimized fragment-specific occupied and virtual orbitals. Thus, the high-rank dynamical correlation effects within the FMO framework are computed with rank-one and rank-two parametrization of the wave operator, leading to significant reduction in the number of variables and associated computational scaling over the conventional methods. Through a series of pilot numerical applications on various covalent and non-covalently bonded systems, we have shown the quantitative accuracy of the proposed methodology compared to canonical, as well as FMO-based coupled-cluster single double triple. The accuracy of the proposed method is shown to be systematically improvable upon increasing the number of contractible occupied and virtual molecular orbitals employed to simulate triple excitations.

A hybrid coupled cluster-machine learning algorithm: Development of various regression models and benchmark applications.

The iterative solution of the coupled cluster equations exhibits a synergistic relationship among the various cluster amplitudes. The iteration scheme is analyzed as a multivariate discrete time propagation of nonlinearly coupled equations, which is dictated by only a few principal cluster amplitudes. These principal amplitudes usually correspond to only a few valence excitations, whereas all other cluster amplitudes are enslaved and behave as auxiliary variables [Agarawal et al., J. Chem. Phys. 154, 044110 (2021)]. We develop a coupled cluster-machine learning hybrid scheme where various supervised machine learning strategies are introduced to establish the interdependence between the principal and auxiliary amplitudes on-the-fly. While the coupled cluster equations are solved only to determine the principal amplitudes, the auxiliary amplitudes, on the other hand, are determined via regression as unique functionals of the principal amplitudes. This leads to significant reduction in the number of independent degrees of freedom during the iterative optimization, which saves significant computation time. A few different regression techniques have been developed, which have their own advantages and disadvantages. The scheme has been applied to several molecules in their equilibrium and stretched geometries, and our scheme, with all the regression models, shows a significant reduction in computation time over the canonical coupled cluster calculations without unduly sacrificing the accuracy.

An approximate coupled cluster theory via nonlinear dynamics and synergetics: The adiabatic decoupling conditions.

The coupled cluster iteration scheme is analyzed as a multivariate discrete time map using nonlinear dynamics and synergetics. The nonlinearly coupled set of equations to determine the cluster amplitudes are driven by a fraction of the entire set of cluster amplitudes. These driver amplitudes enslave all other amplitudes through a synergistic inter-relationship, where the latter class of amplitudes behave as the auxiliary variables. The driver and the auxiliary variables exhibit vastly different time scales of relaxation during the iteration process to reach the fixed points. The fast varying auxiliary amplitudes are small in magnitude, while the driver amplitudes are large, and they have a much longer time scale of relaxation. Exploiting their difference in relaxation time scale, we employ an adiabatic decoupling approximation, where each of the fast relaxing auxiliary modes is expressed as a unique function of the principal amplitudes. This results in a tremendous reduction in the independent degrees of freedom. On the other hand, only the driver amplitudes are determined accurately via exact coupled cluster equations. We will demonstrate that the iteration scheme has an order of magnitude reduction in computational scaling than the conventional scheme. With a few pilot numerical examples, we would demonstrate that this scheme can achieve very high accuracy with significant savings in computational time.

Accelerating coupled cluster calculations with nonlinear dynamics and supervised machine learning.

In this paper, the iteration scheme associated with single reference coupled cluster theory has been analyzed using nonlinear dynamics. The phase space analysis indicates the presence of a few significant cluster amplitudes, mostly involving valence excitations, that dictate the dynamics, while all other amplitudes are enslaved. Starting with a few initial iterations to establish the inter-relationship among the cluster amplitudes, a supervised machine learning scheme with a polynomial kernel ridge regression model has been employed to express each of the enslaved amplitudes uniquely in terms of the former set of amplitudes. The subsequent coupled cluster iterations are restricted solely to determine those significant excitations, and the enslaved amplitudes are determined through the already established functional mapping. We will show that our hybrid scheme leads to a significant reduction in the computational time without sacrificing the accuracy.

Stability analysis of a double similarity transformed coupled cluster theory.

In this paper, we have analyzed the time series associated with the iterative scheme of a double similarity transformed coupled cluster theory. The coupled iterative scheme to solve the ground state Schrödinger equation is cast as a multivariate time-discrete map, and the solutions show the universal Feigenbaum dynamics. Using recurrence analysis, it is shown that the dynamics of the iterative process is dictated by a small subgroup of cluster operators, mostly those involving chemically active orbitals, whereas all other cluster operators with smaller amplitudes are enslaved. Using synergetics, we will indicate how the master-slave dynamics can suitably be exploited to develop a novel coupled-cluster algorithm in a much reduced dimension.

Formulation of a Dressed Coupled-Cluster Method with Implicit Triple Excitations and Benchmark Application to Hydrogen-Bonded Systems.

In this paper, we present a coupled-cluster theory based on a double-exponential wave operator ansatz, which is capable of mimicking the effects of connected triple excitations in an iterative manner. The triply excited manifold is spanned via the action of a set of scattering operators on doubly excited determinants, whereas their action annihilates the Hartree-Fock reference determinant. The effect of triple excitations is included at a computational scaling slightly higher than that of conventional coupled-cluster singles and doubles. Furthermore, we demonstrate two approximate schemes, which arise naturally, and argue that both these schemes come equipped with certain renormalization terms capable of handling nonbonding interactions due to robust inclusion of the screened Coulomb interaction. We justify our claims from both a theoretical perspective and a number of numerical applications to prototypical water clusters, in a number of basis functions. Our methods show overall comparable performance to the canonical coupled-cluster theory with singles, doubles, and perturbative triples (CCSD(T)) and allied methods, however, at a lower computational scaling.