Explicitly correlated plane waves: Accelerating convergence in periodic wavefunction expansions

We present an investigation into the use of an explicitly correlated plane wave basis for periodic wavefunction expansions at the level of second-order M{\o}ller-Plesset perturbation theory (MP2). The convergence of the electronic correlation energy with respect to the one-electron basis set is investigated and compared to conventional MP2 theory in a finite homogeneous electron gas model. In addition to the widely used Slater-type geminal correlation factor, we also derive and investigate a novel correlation factor that we term Yukawa-Coulomb. The Yukawa-Coulomb correlation factor is motivated by analytic results for two electrons in a box and allows for a further improved convergence of the correlation energies with respect to the employed basis set. We find the combination of the infinitely delocalized plane waves and local short-ranged geminals provides a complementary, and rapidly convergent basis for the description of periodic wavefunctions. We hope that this approach will expand the scope of discrete wavefunction expansions in periodic systems.Comment: 15 pages, 13 figure

A regularized second-order correlation method from Green's function theory

We present a scalable single-particle framework to treat electronic correlation in molecules and materials motivated by Green's function theory. We derive a size-extensive Brillouin-Wigner perturbation theory from the single-particle Green's function by introducing the Goldstone self-energy. This new ground state correlation energy, referred to as Quasi-Particle MP2 theory (QPMP2), avoids the characteristic divergences present in both second-order M{\o}ller-Plesset perturbation theory (MP2) and Coupled Cluster Singles and Doubles (CCSD) within the strongly correlated regime. We show that the exact ground state energy and properties of the Hubbard dimer are reproduced by QPMP2 and demonstrate the advantages of the approach for the six-, eight- and ten-site Hubbard models where the metal-to-insulator transition is qualitatively reproduced, contrasting with the complete failure of traditional methods. We apply this formalism to characteristic strongly correlated molecular systems and show that QPMP2 provides an efficient, size-consistent regularization of MP2

The coupled-cluster self-energy

An improved description of electronic correlation in molecules and materials can only be achieved by uncovering connections between different areas of electronic structure theory. A general unifying relationship between the many-body self-energy and coupled-cluster theory has remained hitherto unknown. Here, we present a formalism for constructing the coupled-cluster self-energy from the coupled-cluster ground state energy. Our approach illuminates the fundamental connections between the many-body self-energy and the coupled-cluster equations. As a consequence, we naturally arrive at the coupled-cluster quasiparticle and Bethe-Salpeter equations describing correlated electrons and excitons. This deep underlying structure explains the origin of the connections between RPA, $GW$-BSE and coupled-cluster theory, whilst also elucidating the relationship between vertex corrections and the amplitude equations

Improved CPS and CBS Extrapolation of PNO-CCSD(T) Energies: The MOBH35 and ISOL24 Data Sets

Computation of heats of reaction of large molecules is now feasible using domain-based PNO-CCSD(T) theory. However, to obtain agreement within 1~kcal/mol of experiment, it is necessary to eliminate basis set incompleteness error, which comprises of both the AO basis set error and the PNO truncation error. Our investigation into the convergence to the canonical limit of PNO-CCSD(T) energies with PNO truncation threshold $T$ shows that errors follow the model $E(T) = E + A T^{1/2}$. Therefore, PNO truncation errors can be eliminated using a simple two-point CPS extrapolation to the canonical limit, so that subsequent CBS extrapolation is not limited by residual PNO truncation error. Using the ISOL24 and MOBH35 data sets, we find that PNO truncation errors are larger for molecules with significant static correlation, and that it is necessary to use very tight thresholds of $T=10^{-8}$ to ensure errors do not exceed 1~kcal/mol. We present a lower-cost extrapolation scheme that uses information from small basis sets to estimate PNO truncation errors for larger basis sets. In this way the canonical limit of CCSD(T) calculations on large molecules with large basis sets can be reliably estimated in a practical way. Using this approach, we report complete basis set limit CCSD(T) reaction energies for the full ISOL24 and MOBH35 data sets

Ab initio instanton rate theory made efficient using Gaussian process regression

Ab initio instanton rate theory is a computational method for rigorously including tunnelling effects into calculations of chemical reaction rates based on a potential-energy surface computed on the fly from electronic-structure theory. This approach is necessary to extend conventional transition-state theory into the deep-tunnelling regime, but is also more computationally expensive as it requires many more ab initio calculations. We propose an approach which uses Gaussian process regression to fit the potential-energy surface locally around the dominant tunnelling pathway. The method can be converged to give the same result as from an on-the-fly ab initio instanton calculation but requires far fewer electronic-structure calculations. This makes it a practical approach for obtaining accurate rate constants based on high-level electronic-structure methods. We show fast convergence to reproduce benchmark H + CH4 results and evaluate new low-temperature rates of H + C2H6 in full dimensionality at a UCCSD(T)-F12b/cc-pVTZ-F12 level.Comment: 12 pages, 4 figures; submitted to Faraday Discussion: Quantum effects in small molecular system

Experimental Bayesian Quantum Phase Estimation on a Silicon Photonic Chip

Quantum phase estimation is a fundamental subroutine in many quantum algorithms, including Shor's factorization algorithm and quantum simulation. However, so far results have cast doubt on its practicability for near-term, non-fault tolerant, quantum devices. Here we report experimental results demonstrating that this intuition need not be true. We implement a recently proposed adaptive Bayesian approach to quantum phase estimation and use it to simulate molecular energies on a Silicon quantum photonic device. The approach is verified to be well suited for pre-threshold quantum processors by investigating its superior robustness to noise and decoherence compared to the iterative phase estimation algorithm. This shows a promising route to unlock the power of quantum phase estimation much sooner than previously believed

Grid-based methods for chemistry simulations on a quantum computer

First-quantized, grid-based methods for chemistry modeling are a natural and elegant fit for quantum computers. However, it is infeasible to use today’s quantum prototypes to explore the power of this approach because it requires a substantial number of near-perfect qubits. Here, we use exactly emulated quantum computers with up to 36 qubits to execute deep yet resource-frugal algorithms that model 2D and 3D atoms with single and paired particles. A range of tasks is explored, from ground state preparation and energy estimation to the dynamics of scattering and ionization; we evaluate various methods within the split-operator QFT (SO-QFT) Hamiltonian simulation paradigm, including protocols previously described in theoretical papers and our own techniques. While we identify certain restrictions and caveats, generally, the grid-based method is found to perform very well; our results are consistent with the view that first-quantized paradigms will be dominant from the early fault-tolerant quantum computing era onward