Generalized Unitary Coupled Cluster Wavefunctions for Quantum Computation

We introduce a unitary coupled-cluster (UCC) ansatz termed $k$-UpCCGSD that is based on a family of sparse generalized doubles (D) operators which provides an affordable and systematically improvable unitary coupled-cluster wavefunction suitable for implementation on a near-term quantum computer. $k$-UpCCGSD employs $k$ products of the exponential of pair coupled-cluster double excitation operators (pCCD), together with generalized single (S) excitation operators. We compare its performance in both efficiency of implementation and accuracy with that of the generalized UCC ansatz employing the full generalized SD excitation operators (UCCGSD), as well as with the standard ansatz employing only SD excitations (UCCSD). $k$-UpCCGSD is found to show the best scaling for quantum computing applications, requiring a circuit depth of $\mathcal O(kN)$, compared with $\mathcal O(N^3)$ for UCCGSD and $\mathcal O((N-\eta)^2 \eta)$ for UCCSD where $N$ is the number of spin orbitals and $\eta$ is the number of electrons. We analyzed the accuracy of these three ans\"atze by making classical benchmark calculations on the ground state and the first excited state of H$_4$ (STO-3G, 6-31G), H$_2$O (STO-3G), and N$_2$ (STO-3G), making additional comparisons to conventional coupled cluster methods. The results for ground states show that $k$-UpCCGSD offers a good tradeoff between accuracy and cost, achieving chemical accuracy for lower cost of implementation on quantum computers than both UCCGSD and UCCSD. Excited states are calculated with an orthogonally constrained variational quantum eigensolver approach. This is seen to generally yield less accurate energies than for the corresponding ground states. We demonstrate that using a specialized multi-determinantal reference state constructed from classical linear response calculations allows these excited state energetics to be improved

QMCPACK: Advances in the development, efficiency, and application of auxiliary field and real-space variational and diffusion Quantum Monte Carlo

We review recent advances in the capabilities of the open source ab initio Quantum Monte Carlo (QMC) package QMCPACK and the workflow tool Nexus used for greater efficiency and reproducibility. The auxiliary field QMC (AFQMC) implementation has been greatly expanded to include k-point symmetries, tensor-hypercontraction, and accelerated graphical processing unit (GPU) support. These scaling and memory reductions greatly increase the number of orbitals that can practically be included in AFQMC calculations, increasing accuracy. Advances in real space methods include techniques for accurate computation of band gaps and for systematically improving the nodal surface of ground state wavefunctions. Results of these calculations can be used to validate application of more approximate electronic structure methods including GW and density functional based techniques. To provide an improved foundation for these calculations we utilize a new set of correlation-consistent effective core potentials (pseudopotentials) that are more accurate than previous sets; these can also be applied in quantum-chemical and other many-body applications, not only QMC. These advances increase the efficiency, accuracy, and range of properties that can be studied in both molecules and materials with QMC and QMCPACK

Photoionization of few electron systems with a hybrid Coupled Channels approach

We present the hybrid anti-symmetrized coupled channels method for the calculation of fully differential photo-electron spectra of multi-electron atoms and small molecules interacting with strong laser fields. The method unites quantum chemical few-body electronic structure with strong-field dynamics by solving the time dependent Schr\"odinger equation in a fully anti-symmetrized basis composed of multi-electron states from quantum chemistry and a one-electron numerical basis. Photoelectron spectra are obtained via the time dependent surface flux (tSURFF) method. Performance and accuracy of the approach are demonstrated for spectra from the helium and berryllium atoms and the hydrogen molecule in linearly polarized laser fields at wavelength from 21 nm to 400 nm. At long wavelengths, helium and the hydrogen molecule at equilibrium inter-nuclear distance can be approximated as single channel systems whereas beryllium needs a multi-channel description

Increasing the representation accuracy of quantum simulations of chemistry without extra quantum resources

Proposals for near-term experiments in quantum chemistry on quantum computers leverage the ability to target a subset of degrees of freedom containing the essential quantum behavior, sometimes called the active space. This approximation allows one to treat more difficult problems using fewer qubits and lower gate depths than would otherwise be possible. However, while this approximation captures many important qualitative features, it may leave the results wanting in terms of absolute accuracy (basis error) of the representation. In traditional approaches, increasing this accuracy requires increasing the number of qubits and an appropriate increase in circuit depth as well. Here we introduce a technique requiring no additional qubits or circuit depth that is able to remove much of this approximation in favor of additional measurements. The technique is constructed and analyzed theoretically, and some numerical proof of concept calculations are shown. As an example, we show how to achieve the accuracy of a 20 qubit representation using only 4 qubits and a modest number of additional measurements for a simple hydrogen molecule. We close with an outlook on the impact this technique may have on both near-term and fault-tolerant quantum simulations

Efficient calculation of electronic structure using O(N) density functional theory

We propose an efficient way to calculate the electronic structure of large systems by combining a large-scale first-principles density functional theory code, Conquest, and an efficient interior eigenproblem solver, the Sakurai-Sugiura method. The electronic Hamiltonian and charge density of large systems are obtained by \conquest and the eigenstates of the Hamiltonians are then obtained by the Sakurai-Sugiura method. Applications to a hydrated DNA system, and adsorbed P2 molecules and Ge hut clusters on large Si substrates demonstrate the applicability of this combination on systems with 10,000+ atoms with high accuracy and efficiency.Comment: Submitted to J. Chem. Theor. Compu

Tensor Numerical Methods in Quantum Chemistry: from Hartree-Fock Energy to Excited States

We resume the recent successes of the grid-based tensor numerical methods and discuss their prospects in real-space electronic structure calculations. These methods, based on the low-rank representation of the multidimensional functions and integral operators, led to entirely grid-based tensor-structured 3D Hartree-Fock eigenvalue solver. It benefits from tensor calculation of the core Hamiltonian and two-electron integrals (TEI) in $O(n\log n)$ complexity using the rank-structured approximation of basis functions, electron densities and convolution integral operators all represented on 3D $n\times n\times n$ Cartesian grids. The algorithm for calculating TEI tensor in a form of the Cholesky decomposition is based on multiple factorizations using algebraic 1D ``density fitting`` scheme. The basis functions are not restricted to separable Gaussians, since the analytical integration is substituted by high-precision tensor-structured numerical quadratures. The tensor approaches to post-Hartree-Fock calculations for the MP2 energy correction and for the Bethe-Salpeter excited states, based on using low-rank factorizations and the reduced basis method, were recently introduced. Another direction is related to the recent attempts to develop a tensor-based Hartree-Fock numerical scheme for finite lattice-structured systems, where one of the numerical challenges is the summation of electrostatic potentials of a large number of nuclei. The 3D grid-based tensor method for calculation of a potential sum on a $L\times L\times L$ lattice manifests the linear in $L$ computational work, $O(L)$, instead of the usual $O(L^3 \log L)$ scaling by the Ewald-type approaches

Extensions of the siesta dft code for simulation of molecules

We describe extensions to the siesta density functional theory (dft) code [30], for the simulation of isolated molecules and their absorption spectra. The extensions allow for: - Use of a multi-grid solver for the Poisson equation on a finite dft mesh. Non-periodic, Dirichlet boundary conditions are computed by expansion of the electric multipoles over spherical harmonics. - Truncation of a molecular system by the method of design atom pseudo- potentials of Xiao and Zhang[32]. - Electrostatic potential fitting to determine effective atomic charges. - Derivation of electronic absorption transition energies and oscillator stren- gths from the raw spectra produced by a recently described, order O(N3), time-dependent dft code[21]. The code is furthermore integrated within siesta as a post-processing option