Simulating Periodic Systems on a Quantum Computer Using Molecular Orbitals

Machine Learning Accelerates Precise Excited-State Potential Energy Surface Calculations on a Quantum Computer

Electronically excited-state problems represent a crucial research field in quantum chemistry, closely related to numerous practical applications in photophysics and photochemistry. The emerging of quantum computing provides a promising computational paradigm to solve the Schrödinger equation for predicting potential energy surfaces (PESs). Here, we present a deep neural network model to predict parameters of the quantum circuits within the framework of variational quantum deflation and subspace search variational quantum eigensolver, which are two popular excited-state algorithms to implement on a quantum computer. The new machine learning-assisted algorithm is employed to study the excited-state PESs of small molecules, achieving highly accurate predictions. We then apply this algorithm to study the excited-state properties of the ArF system, which is essential to a gas laser. Through this study, we believe that with future advancements in hardware capabilities, quantum computing could be harnessed to solve excited-state problems for a broad range of systems.

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.

Efficient and Robust Parameter Optimization of the Unitary Coupled-Cluster Ansatz

The variational quantum eigensolver (VQE) framework has been instrumental in advancing near-term quantum algorithms. However, parameter optimization remains a significant bottleneck for VQE, requiring a large number of measurements for successful algorithm execution. In this paper, we propose sequential optimization with approximate parabola (SOAP) as an efficient and robust optimizer specifically designed for parameter optimization of the unitary coupled-cluster ansatz on quantum computers. SOAP leverages sequential optimization and approximates the energy landscape as quadratic functions, minimizing the number of energy evaluations required to optimize each parameter. To capture parameter correlations, SOAP incorporates the average direction from previous iterations into the optimization direction set. Numerical benchmark studies on molecular systems demonstrate that SOAP achieves significantly faster convergence and greater robustness to noise compared with traditional optimization methods. Furthermore, numerical simulations of up to 20 qubits reveal that SOAP scales well with the number of parameters in the ansatz. The exceptional performance of SOAP is further validated through experiments on a superconducting quantum computer using a 2-qubit model system.

Circuit-Depth Reduction of Unitary-Coupled-Cluster Ansatz by Energy Sorting

Quantum computation represents a revolutionary approach to solving problems in quantum chemistry. However, due to the limited quantum resources in the current noisy intermediate-scale quantum (NISQ) devices, quantum algorithms for large chemical systems remain a major task. In this work, we demonstrate that the circuit depth of the unitary coupled cluster (UCC) and UCC-based ansatzes in the algorithm of the variational quantum eigensolver can be significantly reduced by an energy-sorting strategy. Specifically, subsets of excitation operators are first prescreened from the operator pool according to its contribution to the total energy. The quantum circuit ansatz is then iteratively constructed until convergence of the final energy to a typical accuracy. For demonstration, this method has been successfully applied to molecular and periodic systems. Particularly, a reduction of 50%-98% in the number of operators is observed while retaining the accuracy of the original UCCSD operator pools. This method can be straightforwardly extended to general parametric variational ansatzes.

Quantum Circuit Matrix Product State Ansatz for Large-Scale Simulations of Molecules

As demonstrated in the density matrix renormalization group (DMRG) method, approximating many-body wave function of electrons using a matrix product state (MPS) is a promising way to solve electronic structure problems. The expressibility of an MPS is determined by the size of the matrices or, in other words, the bond dimension, which unfortunately may be required to be very large in quantum chemistry simulations. In this study, we propose to calculate the ground state energies of molecular systems by variationally optimizing quantum circuit MPS (QCMPS) with a relatively small number of qubits. It is demonstrated that with carefully chosen circuit structure and orbital localization scheme, QCMPS can reach a similar accuracy as that achieved in DMRG with an exponentially large bond dimension. QCMPS simulation of a linear hydrogen molecular chain with 50 orbitals can reach the chemical accuracy using only 6 qubits at a moderate circuit depth. These results suggest that QCMPS is a promising wave function ansatz in the variational quantum eigensolver algorithm for molecular systems.

The landscape of computational approaches for artificial photosynthesis

Artificial photosynthesis is an attractive strategy for converting solar energy into fuels, largely because the Earth receives enough solar energy in one hour to meet humanity's energy needs for an entire year. However, developing devices for artificial photosynthesis remains difficult and requires computational approaches to guide and assist the interpretation of experiments. In this Perspective, we discuss current and future computational approaches, as well as the challenges of designing and characterizing molecular assemblies that absorb solar light, transfer electrons between interfaces, and catalyze water-splitting and fuel-forming reactions.

Towards practical and massively parallel quantum computing emulation for quantum chemistry

Quantum computing is moving beyond its early stage and seeking for commercial applications in chemical and biomedical sciences. In the current noisy intermediate-scale quantum computing era, the quantum resource is too scarce to support these explorations. Therefore, it is valuable to emulate quantum computing on classical computers for developing quantum algorithms and validating quantum hardware. However, existing simulators mostly suffer from the memory bottleneck so developing the approaches for large-scale quantum chemistry calculations remains challenging. Here we demonstrate a high-performance and massively parallel variational quantum eigensolver (VQE) simulator based on matrix product states, combined with embedding theory for solving large-scale quantum computing emulation for quantum chemistry on HPC platforms. We apply this method to study the torsional barrier of ethane and the quantification of the protein-ligand interactions. Our largest simulation reaches 1000 qubits, and a performance of 216.9 PFLOP/s is achieved on a new Sunway supercomputer, which sets the state-of-the-art for quantum computing emulation for quantum chemistry.

Exploring Accurate Potential Energy Surfaces via Integrating Variational Quantum Eigensolver with Machine Learning

The potential energy surface (PES) is crucial for interpreting a variety of chemical reaction processes. However, predicting accurate PESs with high-level electronic structure methods is a challenging task due to the high computational cost. As an appealing application of quantum computing, we show in this work that variational quantum algorithms can be integrated with machine learning (ML) techniques as a promising scheme for exploring accurate PESs. Different from using a ML model to represent the potential energy, we encode the molecular geometry information into a deep neural network (DNN) to represent parameters of the variational quantum eigensolver (VQE), leaving the PES to the wave function ansatz. Once the DNN model is trained, the variational optimization procedure that hinders the application of the VQE to complex systems is avoided, and thus the evaluation of PESs is significantly accelerated. Numerical results demonstrate that a simple DNN model is able to reproduce accurate PESs for small molecules.

Quantum embedding theories to simulate condensed systems on quantum computers

Quantum computers hold promise to improve the efficiency of quantum simulations of materials and to enable the investigation of systems and properties that are more complex than tractable at present on classical architectures. Here, we discuss computational frameworks to carry out electronic structure calculations of solids on noisy intermediate-scale quantum computers using embedding theories, and we give examples for a specific class of materials, that is, solid materials hosting spin defects. These are promising systems to build future quantum technologies, such as quantum computers, quantum sensors and quantum communication devices. Although quantum simulations on quantum architectures are in their infancy, promising results for realistic systems appear to be within reach.

Quantum algorithms for electronic structures: basis sets and boundary conditions

The advantages of quantum computers are believed to significantly change the research paradigm of chemical and materials sciences, where computational characterization and theoretical design play an increasingly important role. It is especially desirable to solve the electronic structure problem, a central problem in chemistry and materials science, efficiently and accurately with well-designed quantum algorithms. Various quantum electronic-structure algorithms have been proposed in the literature. In this article, we briefly review recent progress in this direction with a special emphasis on the basis sets and boundary conditions. Compared to classical electronic structure calculations, there are new considerations in choosing a basis set in quantum algorithms. For example, the effect of the basis set on the circuit complexity is very important in quantum algorithm design. Electronic structure calculations should be performed with an appropriate boundary condition. Simply using a wave function ansatz designed for molecular systems in a material system with a periodic boundary condition may lead to significant errors. Artificial boundary conditions can be used to partition a large system into smaller fragments to save quantum resources. The basis sets and boundary conditions are expected to play a crucial role in electronic structure calculations on future quantum computers, especially for realistic systems.

Fermi.jl: A Modern Design for Quantum Chemistry

Approximating molecular wave functions involves heavy numerical effort; therefore, codes for such tasks are written completely or partially in efficient languages such as C, C++, and Fortran. While these tools are dominant throughout quantum chemistry packages, the efficient development of new methods is often hindered by the complexity associated with code development. In order to ameliorate this scenario, some software packages take a dual approach where a simpler, higher-level language, such as Python, substitutes the traditional ones wherever performance is not critical. Julia is a novel, dynamically typed, programming language that aims to solve this two-language problem. It gained attention because of its modern and intuitive design, while still being highly optimized to compete with "low-level" languages. Recently, some chemistry-related projects have emerged exploring the capabilities of Julia. Herein, we introduce the quantum chemistry package Fermi.jl, which contains the first implementations of post-Hartree-Fock methods written in Julia. Its design makes use of many Julia core features, including multiple dispatch, metaprogramming, and interactive usage. Fermi.jl is a modular package, where new methods and implementations can be easily added to the existing code. Furthermore, it is designed to maximize code reusability by relying on general functions with specialized methods for particular cases. The feasibility of the project is explored through evaluating the performance of popular ab initio methods. It is our hope that this project motivates the usage of Julia within the community and brings new contributions into Fermi.jl.

Mechanistic photophysics and photochemistry of unnatural bases and sunscreen molecules: insights from electronic structure calculations

Photophysics and photochemistry are basic subjects in the study of light-matter interactions and are ubiquitous in diverse fields such as biology, energy, materials, and environment. A full understanding of mechanistic photophysics and photochemistry underpins many recent advances and applications. This contribution first provides a short discussion on the theoretical calculation methods we have used in relevant studies, then we introduce our latest progress on the mechanistic photophysics and photochemistry of two classes of molecular systems, namely unnatural bases and sunscreens. For unnatural bases, we disclose the intrinsic driving forces for the ultrafast population to reactive triplet states, impacts of the position and degree of chalcogen substitutions, and the effects of complex environments. For sunscreen molecules, we reveal the photoprotection mechanisms that dissipate excess photon energy to the surroundings by ultrafast internal conversion to the ground state. Finally, relevant theoretical challenges and outlooks are discussed.

Equation-of-Motion Theory to Calculate Accurate Band Structures with a Quantum Computer

Band structure is a cornerstone to understand the electronic properties of materials. Accurate band structure calculations using a high-level quantum chemistry theory can be computationally very expensive. It is promising to speed up such calculations with a quantum computer. In this study, we present a quantum algorithm for band structure calculations based on the equation-of-motion (EOM) theory. First, we introduce a new variational quantum eigensolver algorithm named ADAPT-C for ground-state quantum simulation of solids, where the wave function is built adaptively from a complete set of anti-Hermitian operators. Then, on top of the ADAPT-C ground state, quasiparticle energies and the band structure can be calculated using the EOM theory in a quantum-subspace-expansion style, where the projected excitation operators guarantee that the killer condition is satisfied. As a proof of principle, such an EOM-ADAPT-C protocol is used to calculate the band structures of silicon and diamond using a quantum computer simulator.