Graph-|Q⟩⟨C|: A Quantum Algorithm with Reduced Quantum Circuit Depth for Electronic Structure

Abstract

The accurate determination of chemical properties is known to have a critical impact on multiple fundamental chemical problems but is deeply hindered by the steep algebraic scaling of electron correlation calculations and the exponential scaling of quantum nuclear dynamics. With the advent of new quantum computing hardware and associated developments in creating new paradigms for quantum software, this avenue has been recognized as perhaps one way to address exponentially complex challenges in quantum chemistry and molecular dynamics. In this paper, we discuss a new approach to drastically reduce the quantum circuit depth (by several orders of magnitude) and help improve the accuracy in the quantum computation of electron correlation energies for large molecular systems. The method is derived from a graph-theoretic approach to molecular fragmentation and enables us to create a family of projection operators that decompose quantum circuits into separate unitary processes. Some of these processes can be treated on quantum hardware and others on classical hardware in a completely asynchronous and parallel fashion. Numerical benchmarks are provided through the computation of unitary coupled-cluster singles and doubles (UCCSD) energies for medium-sized protonated and neutral water clusters using the new quantum algorithms presented here.

Reformulation of All ONIOM-Type Molecular Fragmentation Approaches and Many-Body Theories Using Graph-Theory-Based Projection Operators: Applications to Dynamics, Molecular Potential Surfaces, Machine Learning, and Quantum Computing

“…This method allows access to higher-quality (post-Hartree–Fock) electronic structure methodologies at a lower computational cost. The approach has been used to (a) efficiently compute post-Hartree–Fock Born–Oppenheimer ,− and extended Lagrangian − AIMD trajectories, (b) obtain multidimensional potential energy surfaces for the treatment of nuclear quantum effects where the surfaces are obtained at post-Hartree–Fock accuracy, , (c) provide efficient ML protocols, , (d) derive efficient methods for tensor network-based quantum nuclear dynamics strategies, and (e) obtain efficient, reduced quantum circuit depth algorithms for quantum computing. ,, The cost reduction, robustness, and accuracy demonstrations render great promise to the methods discussed here.…”

“…Thus, the algorithm here envisions spawning out a family of computing processes, and this is shown in Figure . The resultant final energy in eq is closely related to multiple ONIOM-based, ,,,,,, molecular fragmentation methods ,,,,,,,,− of which MIM has proved to be remarkably versatile for a wide range of applications, ,− ,, as well as developments in the many-body theory. ,− ,,,,− Equations , , and have also been actively gas-phase and condensed-phase AIMD, multidimensional potential energy surfaces, ,− and also provide new ways to construct training protocols in ML and for obtaining new quantum computing algorithms. , …”

“…Here, we present an alternate reformulation of all ONIOM-type molecular fragmentation methods and many-body theories from a newly introduced graph-theoretic perspective, ,− which allows us to derive new approaches for post-Hartree–Fock ab initio molecular dynamics ,− for gas- and condensed-phase , systems, computing high-quality molecular potential surfaces for quantum nuclear dynamics, ,, efficient machine learning (ML) transfer learning protocols, , new algorithms for quantum computing, ,, and new algorithms for performing quantum nuclear dynamics with tensor networks . We briefly highlight some of these aspects in this publication.…”

Physical Chemistry of Quantum Information Science

“…We investigate the topic of quantum algorithms tailored for quantum chemistry, molecular dynamics, and statistical mechanics. This includes a quest to enhance the accuracy of classical computations for difficult chemistry problems involving strongly correlated systems in the works by A. Tammaro et al., A. Khamoshi et al, and N. T. Le and L. N. Tran., and calculations of excited states in articles by Y. Kim and A. I. Krylov and by T. Yoshikura et al Outstanding problems of quantum state preparation were discussed by I. Magoulas and F. A. Evangelista, S. G. Mehendale et al, S. E. Ghasempouri et al, J. H. Zhang et al., and L. M. Sager-Smith et al, for near-term quantum algorithms. An equally important topic of quantum measurement is touched upon by Z. P. Bansingh et al and T. Kurita et al In addition, Hamiltonian learning from quantum dynamics is presented by R. Gupta et al, and an interesting and accessible approach to visualization of quantum algorithms is described by I. Ganti and S. S. Iyengar …”

“…A. W. Schlimgen et al investigate the electronic structure of organometallic molecular spin qubits, addressing challenges in modeling due to their complex electronic properties. Furthermore, J. H. Zhang et al present a technique for enhancing accuracy in computing electronic structure energies for large molecular systems by fragmenting the system into overlapping parts, enabling asynchronous processing on classical and quantum hardware. The works by K. M. Duncan et al and N. D. Wright et al explore the electronic properties and excited-state behavior of monomers and aggregates of asymmetric dyes, focusing on maximizing one- and two-exciton interaction energies for potential use in QIS.…”