Quantum Simulation of Molecular Response Properties in the NISQ Era.

Accurate modeling of the response of molecular systems to an external electromagnetic field is challenging on classical computers, especially in the regime of strong electronic correlation. In this article, we develop a quantum linear response (qLR) theory to calculate molecular response properties on near-term quantum computers. Inspired by the recently developed variants of the quantum counterpart of equation of motion (qEOM) theory, the qLR formalism employs "killer condition" satisfying excitation operator manifolds that offer a number of theoretical advantages along with reduced quantum resource requirements. We also used the qEOM framework in this work to calculate the state-specific response properties. Further, through noiseless quantum simulations, we show that response properties calculated using the qLR approach are more accurate than the ones obtained from the classical coupled-cluster-based linear response models due to the improved quality of the ground-state wave function obtained using the ADAPT-VQE algorithm.

Analytic gradients for relativistic exact-two-component equation-of-motion coupled-cluster singles and doubles method.

A first implementation of analytic gradients for spinor-based relativistic equation-of-motion coupled-cluster singles and doubles method using an exact two-component Hamiltonian augmented with atomic mean-field spin-orbit integrals is reported. To demonstrate its applicability, we present calculations of equilibrium structures and harmonic vibrational frequencies for the electronic ground and excited states of the radium mono-amide molecule (RaNH2) and the radium mono-methoxide molecule (RaOCH3). Spin-orbit coupling is shown to quench Jahn-Teller effects in the first excited state of RaOCH3, resulting in a C3v equilibrium structure. The calculations also show that the radium atoms in these molecules serve as efficient optical cycling centers.

Quantum self-consistent equation-of-motion method for computing molecular excitation energies, ionization potentials, and electron affinities on a quantum computer.

Near-term quantum computers are expected to facilitate material and chemical research through accurate molecular simulations. Several developments have already shown that accurate ground-state energies for small molecules can be evaluated on present-day quantum devices. Although electronically excited states play a vital role in chemical processes and applications, the search for a reliable and practical approach for routine excited-state calculations on near-term quantum devices is ongoing. Inspired by excited-state methods developed for the unitary coupled-cluster theory in quantum chemistry, we present an equation-of-motion-based method to compute excitation energies following the variational quantum eigensolver algorithm for ground-state calculations on a quantum computer. We perform numerical simulations on H2, H4, H2O, and LiH molecules to test our quantum self-consistent equation-of-motion (q-sc-EOM) method and compare it to other current state-of-the-art methods. q-sc-EOM makes use of self-consistent operators to satisfy the vacuum annihilation condition, a critical property for accurate calculations. It provides real and size-intensive energy differences corresponding to vertical excitation energies, ionization potentials and electron affinities. We also find that q-sc-EOM is more suitable for implementation on NISQ devices as it is expected to be more resilient to noise compared with the currently available methods.

Quantum Simulation of Molecular Electronic States with a Transcorrelated Hamiltonian: Higher Accuracy with Fewer Qubits.

Simulation of electronic structure is one of the most promising applications on noisy intermediate-scale quantum (NISQ) era devices. However, NISQ devices suffer from a number of challenges like limited qubit connectivity, short coherence times, and sizable gate error rates. Thus, desired quantum algorithms should require shallow circuit depths and low qubit counts to take advantage of these devices. Here, we attempt to reduce quantum resource requirements for molecular simulations on a quantum computer while maintaining the desired accuracy with the help of classical quantum chemical theories of canonical transformation and explicit correlation. In this work, compact ab initio Hamiltonians are generated classically, in the second quantized form, through an approximate similarity transformation of the Hamiltonian with (a) an explicitly correlated two-body unitary operator with generalized pair excitations that remove the Coulombic electron-electron singularities from the Hamiltonian and (b) a unitary one-body operator to efficiently capture the orbital relaxation effects required for accurate description of the excited states. The resulting transcorrelated Hamiltonians are able to describe both the ground and the excited states of molecular systems in a balanced manner. Using the variational quantum eigensolver (VQE) method based on the unitary coupled cluster with singles and doubles (UCCSD) ansatz and only a minimal basis set (ANO-RCC-MB), we demonstrate that the transcorrelated Hamiltonians can produce ground state energies comparable to the reference CCSD energies with the much larger cc-pVTZ basis set. This leads to a reduction in the number of required CNOT gates by more than 3 orders of magnitude for the chemical species studied in this work. Furthermore, using the quantum equation of motion (qEOM) formalism in conjunction with the transcorrelated Hamiltonian, we are able to reduce the deviations in the excitation energies from the reference EOM-CCSD/cc-pVTZ values by an order of magnitude. The transcorrelated Hamiltonians developed here are Hermitian and contain only one- and two-body interaction terms and thus can be easily combined with any quantum algorithm for accurate electronic structure simulations.

Analytic evaluation of energy first derivatives for spin-orbit coupled-cluster singles and doubles augmented with noniterative triples method: General formulation and an implementation for first-order properties.

A formulation of analytic energy first derivatives for the coupled-cluster singles and doubles augmented with noniterative triples [CCSD(T)] method with spin-orbit coupling included at the orbital level and an implementation for evaluation of first-order properties are reported. The standard density-matrix formulation for analytic CC gradient theory adapted to complex algebra has been used. The orbital-relaxation contributions from frozen core, occupied, virtual, and frozen virtual orbitals to analytic spin-orbit CCSD(T) gradients are fully taken into account and treated efficiently, which is of importance to calculations of heavy elements. Benchmark calculations of first-order properties including dipole moments and electric-field gradients using the corresponding exact two-component property integrals are presented for heavy-element containing molecules to demonstrate the applicability and usefulness of the present analytic scheme.

Mapping the Electronic Structure of the Uranium(VI) Dinitride Molecule, UN2.

A combined anion photoelectron spectroscopic and relativistic coupled-cluster computational study of the electronic structure of the UN2 molecule is presented. Because the photoelectron spectrum of the uranium dinitride negative ion, UN2-, directly reflects the electronic structure of neutral UN2, we have measured and relied upon the photoelectron spectrum of the UN2- anion as a means of mapping the electronic structure of neutral UN2. In addition to the electron affinity of the UN2 ground state, energy levels of the UN2 excited states were well characterized by the close interplay between the experiment and high-level theory. We found that both electron attachment and electronic excitation significantly bend the UN2 molecule and elongate its U≡N bond. Implications for the activation of UN2 are discussed.

Exact two-component equation-of-motion coupled-cluster singles and doubles method using atomic mean-field spin-orbit integrals.

A new semi-atomic-orbital- based algorithm for a two-component spin-orbit (SO) equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) method using mean-field SO integrals is reported. The new algorithm removes the major computational bottlenecks of a SO-EOM-CCSD calculation associated with the evaluation, storage, and processing of the H¯ab,cd elements in the similarity-transformed Hamiltonian involving four virtual orbital labels. The partial recovery of spin symmetry in the present algorithm reduces the storage requirement by an order of magnitude and the floating point operation count for the evaluation of the ladder-like term by a factor of three to four. EOM-CCSD calculations of excited states in the triiodide ion (I3 -) using the exact two-component Hamiltonian in combination with atomic mean-field SO integrals (X2CAMF) are reported as a validation of the implementation and also as a demonstration of the capability of the new algorithm to correlate extended virtual spaces. X2CAMF-EOM-CCSD calculations of the ground and excited states in As2, Sb2, and Bi2 are also presented and compared with the available experimental studies. An analysis based on the computed spectroscopic constants as well as the compositions of the excited-state wavefunctions strongly supports a new assignment for the lowest 2u and 0u - levels in the photoelectron spectrum of Bi2.

Unitary coupled-cluster based self-consistent polarization propagator theory: A third-order formulation and pilot applications.

In this article, the development of a third-order self-consistent polarization propagator method based on unitary coupled-cluster (UCC) parametrization of the ground-state wavefunction and the excitation manifold comprising unitary-transformed excitation operators, hereafter referred to as UCC3, is reported. The UCC3 method is designed to provide excitation energies correct up to the third order for excited states dominated by single excitations. An expansion for the UCC transformed Hamiltonian involving Bernoulli numbers as expansion coefficients is adopted in the derivation of UCC3 working equations. Interestingly, UCC-based polarization propagator theory offers an alternative derivation for the strict version of the third-order algebraic diagrammatic construction [ADC(3)-s] method. The UCC3 results for the excitation energies of excited states in H2O, HF, N2, Ne, CH2, BH, and C2 molecules are compared with benchmark full configuration interaction values as well as ADC(3) and equation-of-motion coupled-cluster singles and doubles results to demonstrate the accuracy of the UCC3 method. UCC-based self-consistent polarization propagator theory appears to be a promising framework for developing non-perturbative hermitian formulations for treating electronically excited states.

Two-component relativistic coupled-cluster methods using mean-field spin-orbit integrals.

A novel implementation of the two-component spin-orbit (SO) coupled-cluster singles and doubles (CCSD) method and the CCSD augmented with the perturbative inclusion of triple excitations [CCSD(T)] method using mean-field SO integrals is reported. The new formulation of SO-CCSD(T) features an atomic-orbital-based algorithm for the particle-particle ladder term in the CCSD equation, which not only removes the computational bottleneck associated with the large molecular-orbital integral file but also accelerates the evaluation of the particle-particle ladder term by around a factor of 4 by taking advantage of the spin-free nature of the instantaneous electron-electron Coulomb interaction. Benchmark calculations of the SO splittings for the thallium atom and a set of diatomic 2Π radicals as well as of the bond lengths and harmonic frequencies for a set of closed-shell diatomic molecules are presented. The basis-set and core-correlation effects in the calculations of these properties have been carefully analyzed.