Quantum Chemistry in the Age of Quantum Computing

Nonadiabatic Molecular Dynamics with Fermionic Subspace-Expansion Algorithms on Quantum Computers

We introduce a novel computational framework for excited-state molecular quantum dynamics simulations driven by quantum-computing-based electronic-structure calculations. This framework leverages the fewest-switches surface-hopping method for simulating the nuclear dynamics and calculates the required excited-state transition properties with different flavors of the quantum subspace expansion and quantum equation-of-motion algorithms. We apply our method to simulate the collision reaction between a hydrogen atom and a hydrogen molecule. For this system, we critically compare the accuracy and efficiency of different quantum subspace expansion and equation-of-motion algorithms and show that only methods that can capture both weak and strong electron correlation effects can properly describe the nonadiabatic effects that tune the reactive event.

Pd(II)-Catalyzed Site-Selective Cross Coupling Reaction: Synthesis of Highly Fluorescent Aryl-Formyl-Chromenes and its Iminoantipyrine Analogues as Selective AChE Inhibitors

A versatile and efficient chemo selective synthesis of 4-aryl-3-formyl-2H-chromenes (AFC) was undertaken using Pd-catalyzed cross-coupling conditions. The key oxidative transmetalation was successfully applied to a significant range of substitutions on the chromene moiety and aryl ring in Ar(BOH)3, accommodating both electron-rich and electron-deficient groups. These π-extended scaffolds exhibited green-yellow fluorescence with a large Stokes shift and high quantum yield. Measurement of photophysical properties revealed that the compound with methoxy substitution in the chromene ring, 3t, caused a significant bathochromic shift. The AFCs obtained from this method can be transformed into biologically active 4-aryl-3-iminoantipyrine-2H-chromenes (AAC) through functionalization of the formyl chromenes. The AFCs and AACs with methoxy substitutions (3t and 4e) were docked against AChE inhibition, and compound 4e had the lowest binding energy of -11.20 kcal/mol. DFT calculations performed on representative compounds revealed that compound 4e is more reactive than 3t, which is in accordance with the docking studies.

Fighting Noise with Noise: A Stochastic Projective Quantum Eigensolver

In the current noisy intermediate scale quantum era of quantum computation, available hardware is severely limited by both qubit count and noise levels, precluding the application of many current hybrid quantum-classical algorithms to nontrivial quantum chemistry problems. In this paper we propose applying some of the fundamental ideas of conventional Quantum Monte Carlo algorithms─stochastic sampling of both the wave function and the Hamiltonian─to quantum algorithms in order to significantly decrease quantum resource costs. In the context of an imaginary-time propagation based projective quantum eigensolver, we present a novel approach to estimating physical observables which can lead to an order of magnitude reduction in the required sampling of the quantum state to converge the ground state energy of a system relative to current state-of-the-art eigensolvers. The method can be equally applied to excited-state calculations and, combined with stochastic approximations of the system Hamiltonian, provides a promising near-term approach to Hamiltonian simulation for general chemistry on quantum devices.

Toward Accurate Calculation of Excitation Energies on Quantum Computers with ΔADAPT-VQE: A Case Study of BODIPY Derivatives

Quantum chemistry simulations offer a cost-effective way to computationally design BODIPY photosensitizers. However, accurate predictions of excitation energies pose a challenge for time-dependent density functional theory and equation-of-motion coupled-cluster singles and doubles methods. By contrast, reliable predictions can be achieved by multireference quantum chemistry methods; unfortunately, their computational cost increases exponentially with the number of electrons. Alternatively, quantum computing holds potential for an exact simulation of the photophysical properties in a computationally more efficient way. Herein, we introduce the state-specific ΔUCCSD-VQE (unitary coupled-cluster singles and doubles-variational quantum eigensolver) and ΔADAPT-VQE methods in which the electronically excited state is calculated via a non-Aufbau configuration. We show for six BODIPY derivatives that the proposed methods predict accurate excitation energies that are in good agreement with those from experiments. Due to its performance and simplicity, we believe that ΔADAPT will become a useful approach for the simulation of BODIPY photosensitizers on near-term quantum devices.

Probing Quantum Efficiency: Exploring System Hardness in Electronic Ground State Energy Estimation

We consider the question of how correlated the system hardness is between classical algorithms of electronic structure theory in ground state estimation and quantum algorithms. To define the system hardness for classical algorithms, we employ empirical criterion based on the deviation of electronic energies produced by coupled cluster and configuration interaction methods from the exact ones along multiple bonds dissociation in a set of molecular systems. For quantum algorithms, we have selected the Variational Quantum Eigensolver (VQE) and Quantum Phase Estimation (QPE) methods. As characteristics of the system hardness for quantum methods, we analyzed circuit depths for the state preparation, the number of quantum measurements needed for the energy expectation value, and various cost characteristics for the Hamiltonian encodings via Trotter approximation and linear combination of unitaries (LCU). Our results show that the quantum resource requirements are mostly unaffected by classical hardness, with the only exception being the state preparation part, which contributes to both VQE and QPE algorithm costs. However, there are clear indications that constructing the initial state with a significant overlap with the true ground state is easier than obtaining the state with an energy expectation value within chemical precision. These results support optimism regarding the identification of a molecular system where a quantum algorithm excels over its classical counterpart, as quantum methods can maintain efficiency in classically challenging systems.

A primer for quantum computing and its applications to healthcare and biomedical research

OBJECTIVES

To introduce quantum computing technologies as a tool for biomedical research and highlight future applications within healthcare, focusing on its capabilities, benefits, and limitations.

TARGET AUDIENCE

Investigators seeking to explore quantum computing and create quantum-based applications for healthcare and biomedical research.

SCOPE

Quantum computing requires specialized hardware, known as quantum processing units, that use quantum bits (qubits) instead of classical bits to perform computations. This article will cover (1) proposed applications where quantum computing offers advantages to classical computing in biomedicine; (2) an introduction to how quantum computers operate, tailored for biomedical researchers; (3) recent progress that has expanded access to quantum computing; and (4) challenges, opportunities, and proposed solutions to integrate quantum computing in biomedical applications.

Physically Motivated Improvements of Variational Quantum Eigensolvers

The adaptive derivative-assembled pseudo-Trotter variational quantum eigensolver (ADAPT-VQE) has emerged as a pivotal promising approach for electronic structure challenges in quantum chemistry with noisy quantum devices. Nevertheless, to surmount existing technological constraints, this study endeavors to enhance ADAPT-VQE's efficacy. Leveraging insights from the electronic structure theory, we concentrate on optimizing state preparation without added computational burden and guiding ansatz expansion to yield more concise wave functions with expedited convergence toward exact solutions. These advancements culminate in shallower circuits and, as demonstrated, reduced measurement requirements. This research delineates these enhancements and assesses their performance across mono, di, and tridimensional arrangements of H4 models, as well as in the water molecule. Ultimately, this work attests to the viability of physically motivated strategies in fortifying ADAPT-VQE's efficiency, marking a significant stride in quantum chemistry simulations.

Quantum circuit for high order perturbation theory corrections

Perturbation theory (PT) might be one of the most powerful and fruitful tools for both physicists and chemists, which has led to a wide variety of applications. Over the past decades, advances in quantum computing provide opportunities for alternatives to classical methods. Recently, a general quantum circuit estimating the low order PT corrections has been proposed. In this article, we revisit the quantum circuits for PT calculations, and develop the methods for higher order PT corrections of eigenenergy, especially the 3rd and 4th order corrections. We present the feasible quantum circuit to estimate each term in these PT corrections. There are two the fundamental operations in the proposed circuit. One approximates the perturbation terms, the other approximates the inverse of unperturbed energy difference. The proposed method can be generalized to higher order PT corrections.

Reducing the Runtime of Fault-Tolerant Quantum Simulations in Chemistry through Symmetry-Compressed Double Factorization

Quantum phase estimation based on qubitization is the state-of-the-art fault-tolerant quantum algorithm for computing ground-state energies in chemical applications. In this context, the 1-norm of the Hamiltonian plays a fundamental role in determining the total number of required iterations and also the overall computational cost. In this work, we introduce the symmetry-compressed double factorization (SCDF) approach, which combines a CDF of the Hamiltonian with the symmetry shift technique, significantly reducing the 1-norm value. The effectiveness of this approach is demonstrated numerically by considering various benchmark systems, including the FeMoco molecule, cytochrome P450, and hydrogen chains of different sizes. To compare the efficiency of SCDF to other methods in absolute terms, we estimate Toffoli gate requirements, which dominate the execution time on fault-tolerant quantum computers. For the systems considered here, SCDF leads to a sizable reduction of the Toffoli gate count in comparison to other variants of DF or even tensor hypercontraction, which is usually regarded as the most efficient approach for qubitization.

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.

QM-DLA: an efficient qubit mapping method based on dynamic look-ahead strategy

Quantum computing has already demonstrated great computational potential across multiple domains and has received more and more attention. However, due to the connectivity limitations of Noisy Intermediate-Scale Quantum (NISQ) devices, most of the quantum algorithms cannot be directly executed without the help of inserting SWAP gates. Nevertheless, more SWAP gates lead to a longer execution time and, inevitably, lower fidelity of the algorithm. To this end, this paper proposes an optimized qubit mapping algorithm based on a dynamic look-ahead strategy to minimize the number of SWAP gates inserted. Firstly, a heuristic algorithm is proposed based on maximizing physical qubit connectivity to generate the optimal initial qubit mapping, which reduces the need for logical qubit shifts during subsequent SWAP gate insertion. Secondly, in the form of directed acyclic graphs, we identify quantum gates that violate the constraints of physical coupling and insert SWAP gates to remap qubits, thereby overcoming the limitations of qubit interactions. Finally, the optimal SWAP gate insertion strategy is built by comparing the cost of different SWAP gate insertion strategies through a multi-window look-ahead strategy to reduce the number of SWAP gates inserted. The experimental results show that the strategy in this paper decreases the number of SWAP gate insertions and significantly reduces the depth of quantum circuits when performing qubit mapping compared with state-of-the-art methods.

Quantum-centric high performance computing for quantum chemistry

High performance computing (HPC) is renowned for its capacity to tackle complex problems. Meanwhile, quantum computing (QC) provides a potential way to accurately and efficiently solve quantum chemistry problems. The emerging field of quantum-centric high performance computing (QCHPC), which merges these two powerful technologies, is anticipated to enhance computational capabilities for solving challenging problems in quantum chemistry. The implementation of QCHPC for quantum chemistry requires interdisciplinary research and collaboration across multiple fields, including quantum chemistry, quantum physics, computer science and so on. This perspective provides an introduction to the quantum algorithms that are suitable for deployment in QCHPC, focusing on conceptual insights rather than technical details. Parallel strategies to implement these algorithms on quantum-centric supercomputers are discussed. We also summarize high performance quantum emulating simulators, which are considered a viable tool to explore QCHPC. We conclude with challenges and outlooks in this field.

PointGAT: A Quantum Chemical Property Prediction Model Integrating Graph Attention and 3D Geometry

Predicting quantum chemical properties is a fundamental challenge for computational chemistry. While the development of graph neural networks has advanced molecular representation learning and property prediction, their performance could be further enhanced by incorporating three-dimensional (3D) structural geometry into two-dimensional (2D) molecular graph representation. In this study, we introduce the PointGAT model for quantum molecular property prediction, which integrates 3D molecular coordinates with graph-attention modeling. Comparison with other current models in molecular prediction tasks showed that PointGAT could provide higher predictive accuracy in various benchmark data sets from MoleculeNet, including ESOL, FreeSolv, Lipop, HIV, and 6 out of 12 tasks of the QM9 data set. To further examine PointGAT prediction of quantum mechanical (QM) energies, we constructed a C10 data set comprising 11,841 charged and chiral carbocation intermediates with QM energies calculated at the DM21/6-31G*//B3LYP/6-31G* levels. Notably, PointGAT achieved an R2 value of 0.950 and an MAE of 1.616 kcal/mol, outperforming even the best-performing graph neural network model with a reduction of 0.216 kcal/mol in MAE and an improvement of 0.050 in R2. Additional ablation studies indicated that incorporating molecular geometry into the model resulted in markedly higher predictive accuracy, reducing the MAE value from 1.802 to 1.616 kcal/mol. Moreover, visualization of PointGAT atomic attention weights suggested its predictions were interpretable. Findings in this study support the application of PointGAT as a powerful and versatile tool for quantum chemical property prediction that can facilitate high-accuracy modeling for fundamental exploration of chemical space as well as drug design and molecular engineering.

Size-consistency and orbital-invariance issues revealed by VQE-UCCSD calculations with the FMO scheme

The fragment molecular orbital (FMO) scheme is one of the popular fragmentation-based methods and has the potential advantage of making the circuit shallow for quantum chemical calculations on quantum computers. In this study, we used a GPU-accelerated quantum simulator (cuQuantum) to perform the electron correlation part of the FMO calculation as unitary coupled-cluster singles and doubles (UCCSD) with the variational quantum eigensolver (VQE) for hydrogen-bonded (FH)3 $$ {}_3 $$ and (FH)2 $$ {}_2 $$ -H2 $$ {}_2 $$ O systems with the STO-3G basis set. VQE-UCCSD calculations were performed using both canonical and localized MO sets, and the results were examined from the point of view of size-consistency and orbital-invariance affected by the Trotter error. It was found that the use of localized MO leads to better results, especially for (FH)2 $$ {}_2 $$ -H2 $$ {}_2 $$ O. The GPU acceleration was substantial for the simulations with larger numbers of qubits, and was about a factor of 6.7-7.7 for 18 qubit systems.

Hückel molecular orbital theory on a quantum computer: A scalable system-agnostic variational implementation with compact encoding

Hückel molecular orbital (HMO) theory provides a semi-empirical treatment of the electronic structure in conjugated π-electronic systems. A scalable system-agnostic execution of HMO theory on a quantum computer is reported here based on a variational quantum deflation (VQD) algorithm for excited state quantum simulation. A compact encoding scheme is proposed here that provides an exponential advantage over the direct mapping and allows for quantum simulation of the HMO model for systems with up to 2n conjugated centers with n qubits. The transformation of the Hückel Hamiltonian to qubit space is achieved by two different strategies: an iterative refinement transformation and the Frobenius-inner-product-based transformation. These methods are tested on a series of linear, cyclic, and hetero-nuclear conjugated π-electronic systems. The molecular orbital energy levels and wavefunctions from the quantum simulation are in excellent agreement with the exact classical results. However, the higher excited states of large systems are found to suffer from error accumulation in the VQD simulation. This is mitigated by formulating a variant of VQD that exploits the symmetry of the Hamiltonian. This strategy has been successfully demonstrated for the quantum simulation of C60 fullerene containing 680 Pauli strings encoded on six qubits. The methods developed in this work are easily adaptable to similar problems of different complexity in other fields of research.

Natural Orbitals and Sparsity of Quantum Mutual Information

Natural orbitals, defined in electronic structure and quantum chemistry as the molecular orbitals diagonalizing the one-particle reduced density matrix of the ground state, have been conjectured for decades to be the perfect reference orbitals to describe electron correlation. In the present work we applied the Wave function-Adapted Hamiltonian Through Orbital Rotation (WAHTOR) method to study correlated empirical ansätze for quantum computing. In all representative molecules considered, we show that the converged orbitals are coinciding with natural orbitals. Interestingly, the resulting quantum mutual information matrix built on such orbitals is also maximally sparse, providing a clear picture that such orbital choice is indeed able to provide the optimal basis to describe electron correlation. The correlation is therefore encoded in a smaller number of qubit pairs contributing to the quantum mutual information matrix.

Which Options Exist for NISQ-Friendly Linear Response Formulations?

Linear response (LR) theory is a powerful tool in classic quantum chemistry crucial to understanding photoinduced processes in chemistry and biology. However, performing simulations for large systems and in the case of strong electron correlation remains challenging. Quantum computers are poised to facilitate the simulation of such systems, and recently, a quantum linear response formulation (qLR) was introduced [Kumar et al., J. Chem. Theory Comput. 2023, 19, 9136-9150]. To apply qLR to near-term quantum computers beyond a minimal basis set, we here introduce a resource-efficient qLR theory, using a truncated active-space version of the multiconfigurational self-consistent field LR ansatz. Therein, we investigate eight different near-term qLR formalisms that utilize novel operator transformations that allow the qLR equations to be performed on near-term hardware. Simulating excited state potential energy curves and absorption spectra for various test cases, we identify two promising candidates, dubbed "proj LRSD" and "all-proj LRSD".

Subspace Methods for the Simulation of Molecular Response Properties on a Quantum Computer

We explore Davidson methods for obtaining excitation energies and other linear response properties within the recently developed quantum self-consistent linear response (q-sc-LR) method. Davidson-type methods allow for obtaining only a few selected excitation energies without explicitly constructing the electronic Hessian since they only require the ability to perform Hessian-vector multiplications. We apply the Davidson method to calculate the excitation energies of hydrogen chains (up to H10) and analyze aspects of statistical noise for computing excitation energies on quantum simulators. Additionally, we apply Davidson methods for computing linear response properties such as static polarizabilities for H2, LiH, H2O, OH-, and NH3, and show that unitary coupled cluster outperforms classical projected coupled cluster for molecular systems with strong correlation. Finally, we formulate the Davidson method for damped (complex) linear response, with application to the nitrogen K-edge X-ray absorption of ammonia, and the C6 coefficients of H2, LiH, H2O, OH-, and NH3.

Advancing biomolecular simulation through exascale HPC, AI and quantum computing

Biomolecular simulation can act as both a digital microscope and a crystal ball; offering the potential for a deeper understanding of experimental observations whilst also presenting a forward-looking avenue for the in silico design and evaluation of hitherto unsynthesized compounds. Indeed, as the intricacy of our scientific inquiries has grown, so too has the computational prowess we seek to deploy in our pursuit of answers. As we enter the Exascale era, this mini-review surveys the computational landscape from both the point of view of the development of new and ever more powerful systems, and the simulations that are run on them. Moreover, as we stand on the cusp of a transformative phase in computational biology, this article offers a contemplative glance into the future, speculating on the profound implications of artificial intelligence and quantum computing for large-scale biomolecular simulations.

Optoelectronic Response to the Fluor Ion Bond on 4-(4,4,5,5-Tetramethyl-1,3,2-dioxoborolan-2-yl)benzaldehyde

Boronate esters are a class of compounds containing a boron atom bonded to two oxygen atoms in an ester group, often being used as precursors in the synthesis of other materials. The characterization of the structure and properties of esters is usually carried out by UV-visible, infrared, and nuclear magnetic resonance (NMR) spectroscopic techniques. With the aim to better understand our experimental data, in this article, the density functional theory (DFT) is used to analyze the UV-visible and infrared spectra, as well as the isotropic shielding and chemical shifts of the hydrogen atoms 1H, carbon 13C and boron 11B in the compound 4-(4,4,5,5-tetramethyl-1,3,2-dioxoborolan-2-yl)benzaldehyde. Furthermore, this study considers the change in its electronic and spectroscopic properties of this particular ester, when its boron atom is coordinated with a fluoride anion. The calculations were carried out using the LSDA and B3LYP functionals in Gaussian-16, and PBE in CASTEP. The results show that the B3LYP functional gives the best approximation to the experimental data. The formation of a coordinated covalent B-F bond highlights the remarkable sensitivity of the NMR chemical shifts of carbon, oxygen, and boron atoms and their surroundings. Furthermore, this bond also highlights the changes in the electron transitions bands n → π* and π → π* during the absorption and emission of a photon in the UV-vis, and in the stretching bands of the C=C bonds, and bending of BO2 in the infrared spectrum. This study not only contributes to the understanding of the properties of boronate esters but also provides important information on the interactions and responses optoelectronic of the compound when is bonded to a fluorine atom.

Calculating Potential Energy Surfaces with Quantum Computers by Measuring Only the Density Along Adiabatic Transitions

We show that chemically accurate potential energy surfaces (PESs) can be generated from quantum computers by measuring only the density along an adiabatic transition between different molecular geometries. In lieu of using phase estimation, the energy is evaluated by performing line-integration using the inverted real-space time-dependent density functional theory Kohn-Sham (KS) potential obtained from the geometry-varying densities of the full wave function. The accuracy of this method depends on the validity of the adiabatic evolution itself and the potential inversion process (which is theoretically exact but can be numerically unstable), whereas the total evolution time is the defining factor for the precision of phase estimation. We examine the method with a one-dimensional system of two electrons for both the ground and first triplet states in first quantization, as well as the ground state of three- and four-electron systems in second quantization. It is shown that few accurate measurements can be utilized to obtain chemical accuracy across the full potential energy curve, with a shorter propagation time than may be required using phase estimation for a similar accuracy. We also show that an accurate potential energy curve can be calculated by making many imprecise density measurements (using a few shots) along the time evolution and smoothing the resulting density evolution. Finally, it is important to note that the method is able to classically provide a check of its own accuracy by comparing the density resulting from a time-independent KS calculation using the inverted potential with the measured density. This can be used to determine whether longer adiabatic evolution times are required to satisfy the adiabatic theorem.

A degressive quantum convolutional neural network for quantum state classification and code recognition

With the rapid development of quantum computing, a variety of quantum convolutional neural networks (QCNNs) are proposed. However, only 1 / 2 n 2 features of an n-qubits input are transferred to the next layer in a quantum pooling layer, which results in the accuracy reduction. To solve this problem, a QCNN with a degressive circuit is proposed. In order to enhance the ability of extracting global features, we remove the parameters sharing strategy in the quantum convolutional layer and design a quantum convolutional kernel with global eyesight. In addition, to prevent a sharp feature reduction, a degressive parameterized quantum circuit is adopted to construct the pooling layer. Then the Z-basis measurement is only performed on the first qubit to control the operations on other qubits. Compared with the state-of-the-art QCNN, i.e., hybrid quantum-classical convolutional neural network, the accuracy of our model increased by 0.9%, 1%, and 3%, respectively, in three tasks: quantum state classification, binary code recognition, and quaternary code recognition.

Self-Consistent Field Approach for the Variational Quantum Eigensolver: Orbital Optimization Goes Adaptive

We present a self-consistent field (SCF) approach within the adaptive derivative-assembled problem-tailored ansatz variational quantum eigensolver (ADAPT-VQE) framework for efficient quantum simulations of chemical systems on near-term quantum computers. To this end, our ADAPT-VQE-SCF approach combines the idea of generating an ansatz with a small number of parameters, resulting in shallow-depth quantum circuits with a direct minimization of an energy expression that is correct to second order with respect to changes in the molecular orbital basis. Our numerical analysis, including calculations for the transition-metal complex ferrocene [Fe (C5H5)2], indicates that convergence in the self-consistent orbital optimization loop can be reached without a considerable increase in the number of two-qubit gates in the quantum circuit by comparison to a VQE optimization in the initial molecular orbital basis. Moreover, the orbital optimization can be carried out simultaneously within each iteration of the ADAPT-VQE cycle. ADAPT-VQE-SCF thus allows us to implement a routine analogous to the complete active space SCF, a cornerstone of state-of-the-art computational chemistry, in a hardware-efficient manner on near-term quantum computers. Hence, ADAPT-VQE-SCF paves the way toward a paradigm shift for quantitative quantum-chemistry simulations on quantum computers by requiring fewer qubits and opening up for the use of large and flexible atomic orbital basis sets in contrast to earlier methods that are predominantly based on the idea of full active spaces with minimal basis sets.

Interactions between DNA and the acridine intercalator: A computational study

Cancer is a global public health problem characterized by deviations in the mechanisms that control cell proliferation, resulting in mutations and variations in the structure of DNA. The mechanisms of action of chemotherapeutic drugs are related to their interactions and binding with DNA; consequently, the development of antineoplastic agents that target DNA has extensively focused on use of acridine, a heterocyclic molecule that binds to deoxyribonucleic acid via intercalation, a process that modifies DNA and makes replication impossible. In this context, this study aimed to computationally investigate how acridine intercalators interact with DNA by evaluating the mechanism of interactions, binding, and interaction energies using quantum mechanics calculations. Molecular electrostatic potential (MEP) analysis revealed that acridine has well- distributed negative charges in the center of the molecule, indicative of a dominant electron-rich region. Acridine exhibits well-defined π orbitals (HOMO and LUMO) on the aromatic rings, suggesting that charge transfer occurs within the molecule and may be responsible for the pharmacological activity of the compound. Structural analysis revealed that acridine interacts with DNA mainly through hydrogen bonds between HAcridine… ODNA with bond lengths ranging from 2.370 Å to 3.472 Å. The Binding energy (ΔEBind) showed that acridine interacts with DNA effectively for all complexes and the electronic energy results (E+ZPE) for complexes revealed that the complexes are more stable when the DNA-centered acridine molecule. The Laplacian-analysis topological QTAIM parameter (∇2ρ(r)) and total energy (H(r)) categorized the interactions as being non-covalent in nature. The RGD peak distribution in the NCI analysis reveals the presence of van der Waals interactions, predominantly between the intercalator and DNA. Accordingly, we confirm that acridine/DNA interactions are relevant for understanding how the intercalator acts within nucleic acids.

Probabilistic Interpolation of Quantum Rotation Angles

Quantum computing requires a universal set of gate operations; regarding gates as rotations, any rotation angle must be possible. However a real device may only be capable of B bits of resolution, i.e., it might support only 2^{B} possible variants of a given physical gate. Naive discretization of an algorithm's gates to the nearest available options causes coherent errors, while decomposing an impermissible gate into several allowed operations increases circuit depth. Conversely, demanding higher B can greatly complexify hardware. Here, we explore an alternative: probabilistic angle interpolation (PAI). This effectively implements any desired, continuously parametrized rotation by randomly choosing one of three discretized gate settings and postprocessing individual circuit outputs. The approach is particularly relevant for near-term applications where one would in any case average over many runs of circuit executions to estimate expected values. While PAI increases that sampling cost, we prove that (a) the approach is optimal in the sense that PAI achieves the least possible overhead and (b) the overhead is remarkably modest even with thousands of parametrized gates and only seven bits of resolution available. This is a profound relaxation of engineering requirements for first generation quantum computers where even 5-6 bits of resolution may suffice and, as we demonstrate, the approach is many orders of magnitude more efficient than prior techniques. Moreover we conclude that, even for more mature late noisy intermediate-scale quantum era hardware, no more than nine bits will be necessary.

The variational quantum eigensolver self-consistent field method within a polarizable embedded framework

We formulate and implement the Variational Quantum Eigensolver Self Consistent Field (VQE-SCF) algorithm in combination with polarizable embedding (PE), thereby extending PE to the regime of quantum computing. We test the resulting algorithm, PE-VQE-SCF, on quantum simulators and demonstrate that the computational stress on the quantum device is only slightly increased in terms of gate counts compared to regular VQE-SCF. On the other hand, no increase in shot noise was observed. We illustrate how PE-VQE-SCF may lead to the modeling of real chemical systems using a simulation of the reaction barrier of the Diels-Alder reaction between furan and ethene as an example.

Simulating chemical reaction dynamics on quantum computer

The electronic energies of molecules have been successfully evaluated on quantum computers. However, more attention is paid to the dynamics simulation of molecules in practical applications. Based on the variational quantum eigensolver (VQE) algorithm, Fedorov et al. proposed a correlated sampling (CS) method and demonstrated the vibrational dynamics of H2 molecules [J. Chem. Phys. 154, 164103 (2021)]. In this study, we have developed a quantum approach by extending the CS method based on the VQE algorithm (labeled eCS-VQE) for simulating chemical reaction dynamics. First, the CS method is extended to the three-dimensional cases for calculation of first-order energy gradients, and then, it is further generalized to calculate the second-order gradients of energies. By calculating atomic forces and vibrational frequencies for H2, LiH, H+ + H2, and Cl- + CH3Cl systems, we have seen that the approach has achieved the CCSD level of accuracy. Thus, we have simulated dynamics processes for two typical chemical reactions, hydrogen exchange and chlorine substitution, and obtained high-precision reaction dynamics trajectories consistent with the classical methods. Our eCS-VQE approach, as measurement expectations and ground-state wave functions can be reused, is less demanding in quantum computing resources and is, therefore, a feasible means for the dynamics simulation of chemical reactions on the current noisy intermediate-scale quantum-era quantum devices.

Harvesting Chemical Understanding with Machine Learning and Quantum Computers

It is tenable to argue that nobody can predict the future with certainty, yet one can learn from the past and make informed projections for the years ahead. In this Perspective, we overview the status of how theory and computation can be exploited to obtain chemical understanding from wave function theory and density functional theory, and then outlook the likely impact of machine learning (ML) and quantum computers (QC) to appreciate traditional chemical concepts in decades to come. It is maintained that the development and maturation of ML and QC methods in theoretical and computational chemistry represent two paradigm shifts about how the Schrödinger equation can be solved. New chemical understanding can be harnessed in these two new paradigms by making respective use of ML features and QC qubits. Before that happens, however, we still have hurdles to face and obstacles to overcome in both ML and QC arenas. Possible pathways to tackle these challenges are proposed. We anticipate that hierarchical modeling, in contrast to multiscale modeling, will emerge and thrive, becoming the workhorse of in silico simulations in the next few decades.

Folded Spectrum VQE: A Quantum Computing Method for the Calculation of Molecular Excited States

The recent developments of quantum computing present novel potential pathways for quantum chemistry as the scaling of the computational power of quantum computers could be harnessed to naturally encode and solve electronic structure problems. Theoretically exact quantum algorithms for chemistry have been proposed (e.g., quantum phase estimation), but the limited capabilities of current noisy intermediate-scale quantum devices motivated the development of less demanding hybrid algorithms. In this context, the variational quantum eigensolver (VQE) algorithm was successfully introduced as an effective method to compute the ground-state energies of small molecules. This study investigates the folded spectrum (FS) method as an extension of the VQE algorithm for the computation of molecular excited states. It provides the possibility of directly computing excited states around a selected target energy using the same quantum circuit as for the ground-state calculation. Inspired by the variance-based methods from the quantum Monte Carlo literature, the FS method minimizes the energy variance, thus, in principle, requiring a computationally expensive squared Hamiltonian to be applied. We alleviate this potentially poor scaling by employing a Pauli grouping procedure to identify sets of commuting Pauli strings that can be evaluated simultaneously. This allows for a significant reduction in the computational cost. We applied the FS-VQE method to small molecules (H2, LiH), obtaining all electronic excited states with chemical accuracy on ideal quantum simulators. Furthermore, we explore the application of quantum error mitigation techniques, demonstrating improved energy accuracy on noisy simulators compared with simulations without mitigation.

Implementation of the Projective Quantum Eigensolver on a Quantum Computer

We study the performance of our previously proposed projective quantum eigensolver (PQE) on IBM's quantum hardware in conjunction with error mitigation techniques. For a single qubit model of H2, we find that we are able to obtain energies within 4 millihartree (2.5 kcal/mol) of the exact energy along the entire potential energy curve, with the accuracy limited by both the stochastic error and the inconsistent performance of the IBM devices. We find that an optimization algorithm using direct inversion of the iterative subspace can converge swiftly, even to excited states, but stochastic noise can prompt large parameter updates. For the 4-site transverse-field Ising model at its critical point, PQE with an appropriate application of qubit tapering can recover 99% of the correlation energy, even after discarding several parameters. The large number of CNOT gates needed for the additional parameters introduces a concomitant error that, on the IBM devices, results in a loss of accuracy despite the increased expressivity of the trial state. Error extrapolation techniques and tapering or postselection are recommended to mitigate errors in PQE hardware experiments.

An elementary review on basic principles and developments of qubits for quantum computing

An elementary review on principles of qubits and their prospects for quantum computing is provided. Due to its rapid development, quantum computing has attracted considerable attention as a core technology for the next generation and has demonstrated its potential in simulations of exotic materials, molecular structures, and theoretical computer science. To achieve fully error-corrected quantum computers, building a logical qubit from multiple physical qubits is crucial. The number of physical qubits needed depends on their error rates, making error reduction in physical qubits vital. Numerous efforts to reduce errors are ongoing in both existing and emerging quantum systems. Here, the principle and development of qubits, as well as the current status of the field, are reviewed to provide information to researchers from various fields and give insights into this promising technology.

Physics-Constrained Hardware-Efficient Ansatz on Quantum Computers That Is Universal, Systematically Improvable, and Size-Consistent

Variational wave function ansätze are at the heart of solving quantum many-body problems in physics and chemistry. Previous designs of hardware-efficient ansatz (HEA) on quantum computers are largely based on heuristics and lack rigorous theoretical foundations. In this work, we introduce a physics-constrained approach for designing HEA with rigorous theoretical guarantees by imposing a few fundamental constraints. Specifically, we require that the target HEA to be universal, systematically improvable, and size-consistent, which is an important concept in quantum many-body theories for scalability but has been overlooked in previous designs of HEA. We extend the notion of size-consistency to HEA and present a concrete realization of HEA that satisfies all these fundamental constraints while only requiring linear qubit connectivity. The developed physics-constrained HEA is superior to other heuristically designed HEA in terms of both accuracy and scalability, as demonstrated numerically for the Heisenberg model and some typical molecules. In particular, we find that restoring size-consistency can significantly reduce the number of layers needed to reach a certain accuracy. In contrast, the failure of other HEA to satisfy these constraints severely limits their scalability to larger systems with more than 10 qubits. Our work highlights the importance of incorporating physical constraints into the design of HEA for efficiently solving many-body problems on quantum computers.

Quantum many-body simulations on digital quantum computers: State-of-the-art and future challenges

Simulating quantum many-body systems is a key application for emerging quantum processors. While analog quantum simulation has already demonstrated quantum advantage, its digital counterpart has recently become the focus of intense research interest due to the availability of devices that aim to realize general-purpose quantum computers. In this perspective, we give a selective overview of the currently pursued approaches, review the advances in digital quantum simulation by comparing non-variational with variational approaches and identify hardware and algorithmic challenges. Based on this review, the question arises: What are the most promising problems that can be tackled with digital quantum simulation? We argue that problems of a qualitative nature are much more suitable for near-term devices then approaches aiming purely for a quantitative accuracy improvement.

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.

Quantum hardware calculations of the activation and dissociation of nitrogen on iron clusters and surfaces

Catalytic processes are the cornerstone of chemical industry, and catalytic conversion of nitrogen to ammonia remains one of the largest industrial processes implemented. Rational design of catalysts and catalytic reactions largely depends on approximate computational chemistry methods, such as density functional theory, which, however, suffer from limited accuracy, especially for strongly-correlated materials. Rigorous ab initio methods which account for static and dynamic electron correlation, while arbitrarily accurate for small systems, are generally too expensive to be applied to modelling of catalytic cycles, due to prohibitive time and space computational complexity with respect to the size of the active space. Recent advances in quantum computing give hope for enabling access to accurate ab initio methods at scale. Herein, we present a prototype hybrid quantum-classical workflow for modeling chemical reactions on surfaces, applied to proof-of-concept models of activation and dissociation of nitrogen on small Fe clusters and a single-layer (221) iron surface. First, we determined the structures of species present in the catalytic cycle at DFT level and studied their electronic structure using CASSCF. We show that it is possible to decouple the half-filled Fe-3d band from the Fe-N and N-N bond orbitals, thereby reducing the active space significantly. Subsequently, we translated the CASSCF wavefunctions into corresponding qubit quantum states, using the Adaptive Variational Quantum Eigensolver, and estimated their energies using a state vector simulator, H1-1E quantum emulator and (for selected systems) H1-1 quantum computer. We demonstrated that if a sufficiently small active orbital space is chosen, ground state energies obtained with classical methods and with the quantum computer are in reasonable agreement. We argue that once quantum computing methods are scaled up so that larger active spaces are accessible, they can offer a tremendous practical advantage to the computational catalysis community.

Simulating Polaritonic Ground States on Noisy Quantum Devices

The recent advent of quantum algorithms for noisy quantum devices offers a new route toward simulating strong light-matter interactions of molecules in optical cavities for polaritonic chemistry. In this work, we introduce a general framework for simulating electron-photon-coupled systems on small, noisy quantum devices. This method is based on the variational quantum eigensolver (VQE) with the polaritonic unitary coupled cluster (PUCC) ansatz. To achieve chemical accuracy, we exploit various symmetries in qubit reduction methods, such as electron-photon parity, and use recently developed error mitigation schemes, such as the reference zero-noise extrapolation method. We explore the robustness of the VQE-PUCC approach across a diverse set of regimes for the bond length, cavity frequency, and coupling strength of the H2 molecule in an optical cavity. To quantify the performance, we measure two properties: ground-state energy, fundamentally relevant to chemical reactivity, and photon number, an experimentally accessible general indicator of electron-photon correlation.

The electron density: a fidelity witness for quantum computation

There is currently no combination of quantum hardware and algorithms that can provide an advantage over conventional calculations of molecules or materials. However, if or when such a point is reached, new strategies will be needed to verify predictions made using quantum devices. We propose that the electron density, obtained through experimental or computational means, can serve as a robust benchmark for validating the accuracy of quantum computation of chemistry. An initial exploration into topological features of electron densities, facilitated by quantum computation, is presented here as a proof of concept. Additionally, we examine the effects of constraining and symmetrizing measured one-particle reduced density matrices on noise-driven errors in the electron density distribution. We emphasize the potential benefits and future need for high-quality electron densities derived from diffraction experiments for validating classically intractable quantum computations of materials.

Quantum Computing in the Next-Generation Computational Biology Landscape: From Protein Folding to Molecular Dynamics

Modern biological science is trying to solve the fundamental complex problems of molecular biology, which include protein folding, drug discovery, simulation of macromolecular structure, genome assembly, and many more. Currently, quantum computing (QC), a rapidly emerging technology exploiting quantum mechanical phenomena, has developed to address current significant physical, chemical, biological issues, and complex questions. The present review discusses quantum computing technology and its status in solving molecular biology problems, especially in the next-generation computational biology scenario. First, the article explained the basic concept of quantum computing, the functioning of quantum systems where information is stored as qubits, and data storage capacity using quantum gates. Second, the review discussed quantum computing components, such as quantum hardware, quantum processors, and quantum annealing. At the same time, article also discussed quantum algorithms, such as the grover search algorithm and discrete and factorization algorithms. Furthermore, the article discussed the different applications of quantum computing to understand the next-generation biological problems, such as simulation and modeling of biological macromolecules, computational biology problems, data analysis in bioinformatics, protein folding, molecular biology problems, modeling of gene regulatory networks, drug discovery and development, mechano-biology, and RNA folding. Finally, the article represented different probable prospects of quantum computing in molecular biology.

Benford's Law and distributions for better drug design

INTRODUCTION

Modern drug discovery incorporates various tools and data, heralding the beginning of the data-driven drug design (DD) era. The distributions of chemical and physical data used for Artificial Intelligence (AI)/Machine Learning (ML) and to drive DD have thus become highly important to be understood and used effectively.

AREAS COVERED

The authors perform a comprehensive exploration of the statistical distributions driving the data-intensive era of drug discovery, including Benford's Law in AI/ML-based DD.

EXPERT OPINION

As the relevance of data-driven discovery escalates, we anticipate meticulous scrutiny of datasets utilizing principles like Benford's Law to enhance data integrity and guide efficient resource allocation and experimental planning. In this data-driven era of the pharmaceutical and medical industries, addressing critical aspects such as bias mitigation, algorithm effectiveness, data stewardship, effects, and fraud prevention are essential. Harnessing Benford's Law and other distributions and statistical tests in DD provides a potent strategy to detect data anomalies, fill data gaps, and enhance dataset quality. Benford's Law is a fast method for data integrity and quality of datasets, the backbone of AI/ML and other modeling approaches, proving very useful in the design process.

Applications of noisy quantum computing and quantum error mitigation to "adamantaneland": a benchmarking study for quantum chemistry

The field of quantum computing has the potential to transform quantum chemistry. The variational quantum eigensolver (VQE) algorithm has allowed quantum computing to be applied to chemical problems in the noisy intermediate-scale quantum (NISQ) era. Applications of VQE have generally focused on predicting absolute energies instead of chemical properties that are relative energy differences and that are most interesting to chemists studying a chemical problem. We address this shortcoming by constructing a molecular benchmark data set in this work containing isomers of C10H16 and carbocationic rearrangements of C10H15+, calculated at a high-level of theory. Using the data set, we compared noiseless VQE simulations to conventionally performed density functional and wavefunction theory-based methods to understand the quality of results. We also investigated the effectiveness of a quantum state tomography-based error mitigation technique in applications of VQE under noise (simulated and real). Our findings reveal that the use of quantum error mitigation is crucial in the NISQ era and advantageous to yield almost noiseless quality results.

Fragment molecular orbital-based variational quantum eigensolver for quantum chemistry in the age of quantum computing

Quantum computers offer significant potential for complex system analysis, yet their application in large systems is hindered by limitations such as qubit availability and quantum hardware noise. While the variational quantum eigensolver (VQE) was proposed to address these issues, its scalability remains limited. Many efforts, including new ansätze and Hamiltonian modifications, have been made to overcome these challenges. In this work, we introduced the novel Fragment Molecular Orbital/Variational Quantum Eigensolver (FMO/VQE) algorithm. This method combines the fragment molecular orbital (FMO) approach with VQE and efficiently utilizes qubits for quantum chemistry simulations. Employing the UCCSD ansatz, the FMO/VQE achieved an absolute error of just 0.053 mHa with 8 qubits in a [Formula: see text] system using the STO-3G basis set, and an error of 1.376 mHa with 16 qubits in a [Formula: see text] system with the 6-31G basis set. These results indicated a significant advancement in scalability over conventional VQE, maintaining accuracy with fewer qubits. Therefore, our FMO/VQE method exemplifies how integrating fragment-based quantum chemistry with quantum algorithms can enhance scalability, facilitating more complex molecular simulations and aligning with quantum computing advancements.

Variational Quantum Eigensolver Boosted by Adiabatic Connection

In this work, we integrate the variational quantum eigensolver (VQE) with the adiabatic connection (AC) method for efficient simulations of chemical problems on near-term quantum computers. Orbital-optimized VQE methods are employed to capture the strong correlation within an active space, and classical AC corrections recover the dynamical correlation effects comprising electrons outside of the active space. On two challenging strongly correlated problems, namely, the dissociation of N2 and the electronic structure of the tetramethyleneethane biradical, we show that the combined VQE-AC approach enhances the performance of VQE dramatically. Moreover, since the AC corrections do not bring any additional requirements on quantum resources or measurements, they can actually boost the VQE algorithms. Our work paves the way toward quantum simulations of real-life problems on near-term quantum computers.

Toward Chemical Accuracy with Shallow Quantum Circuits: A Clifford-Based Hamiltonian Engineering Approach

Achieving chemical accuracy with shallow quantum circuits is a significant challenge in quantum computational chemistry, particularly for near-term quantum devices. In this work, we present a Clifford-based Hamiltonian engineering algorithm, namely CHEM, that addresses the trade-off between circuit depth and accuracy. Based on a variational quantum eigensolver and hardware-efficient ansatz, our method designs the Clifford-based Hamiltonian transformation that (1) ensures a set of initial circuit parameters corresponding to the Hartree-Fock energy can be generated, (2) effectively maximizes the initial energy gradient with respect to circuit parameters, (3) imposes negligible overhead for classical processing and does not require additional quantum resources, and (4) is compatible with any circuit topology. We demonstrate the efficacy of our approach using a quantum hardware emulator, achieving chemical accuracy for systems as large as 12 qubits with fewer than 30 two-qubit gates. Our Clifford-based Hamiltonian engineering approach offers a promising avenue for practical quantum computational chemistry on near-term quantum devices.

Development of a machine learning finite-range nonlocal density functional

Kohn-Sham density functional theory has been the most popular method in electronic structure calculations. To fulfill the increasing accuracy requirements, new approximate functionals are needed to address key issues in existing approximations. It is well known that nonlocal components are crucial. Current nonlocal functionals mostly require orbital dependence such as in Hartree-Fock exchange and many-body perturbation correlation energy, which, however, leads to higher computational costs. Deviating from this pathway, we describe functional nonlocality in a new approach. By partitioning the total density to atom-centered local densities, a many-body expansion is proposed. This many-body expansion can be truncated at one-body contributions, if a base functional is used and an energy correction is approximated. The contribution from each atom-centered local density is a single finite-range nonlocal functional that is universal for all atoms. We then use machine learning to develop this universal atom-centered functional. Parameters in this functional are determined by fitting to data that are produced by high-level theories. Extensive tests on several different test sets, which include reaction energies, reaction barrier heights, and non-covalent interaction energies, show that the new functional, with only the density as the basic variable, can produce results comparable to the best-performing double-hybrid functionals, (for example, for the thermochemistry test set selected from the GMTKN55 database, BLYP based machine learning functional gives a weighted total mean absolute deviations of 3.33 kcal/mol, while DSD-BLYP-D3(BJ) gives 3.28 kcal/mol) with a lower computational cost. This opens a new pathway to nonlocal functional development and applications.

Quantum computing for chemistry and physics applications from a Monte Carlo perspective

This Perspective focuses on the several overlaps between quantum algorithms and Monte Carlo methods in the domains of physics and chemistry. We will analyze the challenges and possibilities of integrating established quantum Monte Carlo solutions into quantum algorithms. These include refined energy estimators, parameter optimization, real and imaginary-time dynamics, and variational circuits. Conversely, we will review new ideas for utilizing quantum hardware to accelerate the sampling in statistical classical models, with applications in physics, chemistry, optimization, and machine learning. This review aims to be accessible to both communities and intends to foster further algorithmic developments at the intersection of quantum computing and Monte Carlo methods. Most of the works discussed in this Perspective have emerged within the last two years, indicating a rapidly growing interest in this promising area of research.

Computer-Aided Drug Design and Drug Discovery: A Prospective Analysis

In the dynamic landscape of drug discovery, Computer-Aided Drug Design (CADD) emerges as a transformative force, bridging the realms of biology and technology. This paper overviews CADDs historical evolution, categorization into structure-based and ligand-based approaches, and its crucial role in rationalizing and expediting drug discovery. As CADD advances, incorporating diverse biological data and ensuring data privacy become paramount. Challenges persist, demanding the optimization of algorithms and robust ethical frameworks. Integrating Machine Learning and Artificial Intelligence amplifies CADDs predictive capabilities, yet ethical considerations and scalability challenges linger. Collaborative efforts and global initiatives, exemplified by platforms like Open-Source Malaria, underscore the democratization of drug discovery. The convergence of CADD with personalized medicine offers tailored therapeutic solutions, though ethical dilemmas and accessibility concerns must be navigated. Emerging technologies like quantum computing, immersive technologies, and green chemistry promise to redefine the future of CADD. The trajectory of CADD, marked by rapid advancements, anticipates challenges in ensuring accuracy, addressing biases in AI, and incorporating sustainability metrics. This paper concludes by highlighting the need for proactive measures in navigating the ethical, technological, and educational frontiers of CADD to shape a healthier, brighter future in drug discovery.

Deep Neural Network Assisted Quantum Chemistry Calculations on Quantum Computers

The variational quantum eigensolver (VQE) is a widely employed method to solve electronic structure problems in the current noisy intermediate-scale quantum (NISQ) devices. However, due to inherent noise in the NISQ devices, VQE results on NISQ devices often deviate significantly from the results obtained on noiseless statevector simulators or traditional classical computers. The iterative nature of VQE further amplifies the errors in each loop. Recent works have explored ways to integrate deep neural networks (DNN) with VQE to mitigate iterative errors, albeit primarily limited to the noiseless statevector simulators. In this work, we trained DNN models across various quantum circuits and examined the potential of two DNN-VQE approaches, DNN1 and DNNF, for predicting the ground state energies of small molecules in the presence of device noise. We carefully examined the accuracy of the DNN1, DNNF, and VQE methods on both noisy simulators and real quantum devices by considering different ansatzes of varying qubit counts and circuit depths. Our results illustrate the advantages and limitations of both VQE and DNN-VQE approaches. Notably, both DNN1 and DNNF methods consistently outperform the standard VQE method in providing more accurate ground state energies in noisy environments. However, despite being more accurate than VQE, the energies predicted using these methods on real quantum hardware remain meaningful only at reasonable circuit depths (depth = 15, gates = 21). At higher depths (depth = 83, gates = 112), they deviate significantly from the exact results. Additionally, we find that DNNF does not offer any notable advantage over VQE in terms of speed. Consequently, our study recommends DNN1 as the preferred method for obtaining quick and accurate ground state energies of molecules on current quantum hardware, particularly for quantum circuits with lower depth and fewer qubits.

Synergistic pretraining of parametrized quantum circuits via tensor networks

Parametrized quantum circuits (PQCs) represent a promising framework for using present-day quantum hardware to solve diverse problems in materials science, quantum chemistry, and machine learning. We introduce a "synergistic" approach that addresses two prominent issues with these models: the prevalence of barren plateaus in PQC optimization landscapes, and the difficulty to outperform state-of-the-art classical algorithms. This framework first uses classical resources to compute a tensor network encoding a high-quality solution, and then converts this classical output into a PQC which can be further improved using quantum resources. We provide numerical evidence that this framework effectively mitigates barren plateaus in systems of up to 100 qubits using only moderate classical resources, with overall performance improving as more classical or quantum resources are employed. We believe our results highlight that classical simulation methods are not an obstacle to overcome in demonstrating practically useful quantum advantage, but rather can help quantum methods find their way.

Quantum Neural Network Inspired Hardware Adaptable Ansatz for Efficient Quantum Simulation of Chemical Systems

The variational quantum eigensolver is a promising way to solve the Schrödinger equation on a noisy intermediate-scale quantum (NISQ) computer, while its success relies on a well-designed wave function ansatz. Inspired by the quantum neural network, we propose a new hardware heuristic ansatz where its expressibility can be improved by increasing either the depth or the width of the circuit. Such a character makes this ansatz adaptable to different hardware environments. More importantly, it provides a general framework to improve the efficiency of the quantum resource utilization. For example, on a superconducting quantum computer where circuit depth is usually the bottleneck and the qubits thus cannot be fully used, circuit depth can be significantly reduced by introducing ancilla qubits. Ancilla qubits also make the circuit less sensitive to noises in practical application. These results open a new avenue to develop practical applications of quantum computation in the NISQ era.

Block-Invariant Symmetry Shift: Preprocessing Technique for Second-Quantized Hamiltonians to Improve Their Decompositions to Linear Combination of Unitaries

Computational cost of energy estimation for molecular electronic Hamiltonians via quantum phase estimation (QPE) grows with the difference between the largest and smallest eigenvalues of the Hamiltonian. In this work, we propose a preprocessing procedure that reduces the norm of the Hamiltonian without changing its eigenspectrum for the target states of a particular symmetry. The new procedure, block-invariant symmetry shift (BLISS), builds an operator T̂ such that the cost of implementing H ^ - T ^ is reduced compared to that of Ĥ, yet H ^ - T ^ acts on the subspaces of interest the same way as Ĥ does. BLISS performance is demonstrated for a linear combination of unitaries (LCU)-based QPE approaches on a set of small molecules. Using the number of electrons as the symmetry specifying the target set of states, BLISS provided a factor of 2 reduction of 1-norm for several LCU decompositions compared to their unshifted versions.