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In this work, we developed and showcased the occ-RI-K algorithm to compute the exact exchange contribution in density functional calculations of solids near the basis set limit. Within the gaussian planewave (GPW) density fitting, our algorithm achieves a 1-2 orders of magnitude speedup compared to conventional GPW algorithms. Since our algorithm is well-suited for simulations with large basis sets, we applied it to 12 hybrid density functionals with pseudopotentials and a large uncontracted basis set to assess their performance on band gaps of 25 simple solids near the basis set limit. The largest calculation performed in this work involves 16 electrons and 350 basis functions in the unit cell utilizing a 6x6x6 k-mesh. With 20-27\% exact exchange, global hybrid functionals (B3LYP, PBE0, revPBE0, B97-3, SCAN0) perform similarly with a root-mean-square-deviation (RMSD) of 0.61-0.77 eV while other global hybrid functionals such as M06-2X (2.02 eV) and MN15 (1.05 eV) show higher RMSD due to their increased fraction of exact exchange. A short-range hybrid functional, HSE achieves a similar RMSD (0.76 eV) but shows a noticeable underestimation of band gaps due to the complete lack of long-range exchange. We found that two combinatorially optimized range-separated hybrid functionals, $\omega$B97X-rV (3.94 eV) and $\omega$B97M-rV (3.40 eV), and the two other range separated hybrid functionals, CAM-B3LYP (2.41 eV) and CAM-QTP01 (4.16 eV), significantly overestimate the band gap because of their high fraction of long-range exact exchange. Given the failure of $\omega$B97X-rV and $\omega$B97M-rV, we have yet to find a density functional that offers consistent performance for both molecules and solids. Our algorithm development and density functional assessment will serve as a stepping stone towards developing more accurate hybrid functionals and applying them to practical applications.

In this work, we present an overview of the phaseless auxiliary-field quantum Monte Carlo (ph- AFQMC) approach from a computational quantum chemistry perspective, and present a numerical assessment of its performance on main group chemistry and bond-breaking problems with a total of 1004 relative energies. While our benchmark study is somewhat limited, we make recommendations for the use of ph-AFQMC for general main-group chemistry applications. For systems where single determinant wave functions are qualitatively accurate, we expect the accuracy of ph-AFQMC in conjunction with a single determinant trial wave function to be between that of coupled-cluster with singles and doubles (CCSD) and CCSD with perturbative triples (CCSD(T)). For these applications, ph-AFQMC should be a method of choice when canonical CCSD(T) is too expensive to run. For systems where multi-reference (MR) wave functions are needed for qualitative accuracy, ph-AFQMC is far more accurate than MR perturbation theory methods and competitive with MR configuration interaction (MRCI) methods. Due to the computational efficiency of ph-AFQMC compared to MRCI, we recommended ph-AFQMC as a method of choice for handling dynamic correlation in MR problems. We conclude with a discussion of important directions for future development of the ph-AFQMC approach.

We develop a time-dependent second-order Green's function theory (GF2) for calculating neutral excited states in molecules. The equation of motion for the lesser Green's function (GF) is derived within the adiabatic approximation to the Kadanoff-Baym (KB) equation, using the second-order Born approximation for the self-energy. In the linear response regime, we recast the time-dependent KB equation into a Bethe-Salpeter-like equation (GF2-BSE), with a kernel approximated by the second-order Coulomb self-energy. We then apply our GF2-BSE to a set of molecules and atoms and find that GF2-BSE is superior to configuration interaction with singles (CIS) and/or time-dependent Hartree-Fock (TDHF), particularly for charge-transfer excitations, and is comparable to CIS with perturbative doubles (CIS(D)) in most cases.

We developed and implemented a method-independent, fully numerical, finite difference approach to calculating nuclear magnetic resonance shieldings, using gauge-including atomic orbitals. The resulting capability can be used to explore non-standard methods, given only the energy as a function of finite-applied magnetic fields and nuclear spins. For example, standard second-order Møller-Plesset theory (MP2) has well-known efficacy for 1H and 13C shieldings and known limitations for other nuclei such as 15N and 17O. It is, therefore, interesting to seek methods that offer good accuracy for 15N and 17O shieldings without greatly increased compute costs, as well as exploring whether such methods can further improve 1H and 13C shieldings. Using a small molecule test set of 28 species, we assessed two alternatives: κ regularized MP2 (κ-MP2), which provides energy-dependent damping of large amplitudes, and MP2.X, which includes a variable fraction, X, of third-order correlation (MP3). The aug-cc-pVTZ basis was used, and coupled cluster with singles and doubles and perturbative triples [CCSD(T)] results were taken as reference values. Our κ-MP2 results reveal significant improvements over MP2 for 13C and 15N, with the optimal κ value being element-specific. κ-MP2 with κ = 2 offers a 30% rms error reduction over MP2. For 15N, κ-MP2 with κ = 1.1 provides a 90% error reduction vs MP2 and a 60% error reduction vs CCSD. On the other hand, MP2.X with a scaling factor of 0.6 outperformed CCSD for all heavy nuclei. These results can be understood as providing renormalization of doubles amplitudes to partially account for neglected triple and higher substitutions and offer promising opportunities for future applications.

Measurement has a special role in quantum theory1: by collapsing the wavefunction it can enable phenomena such as teleportation2 and thereby alter the "arrow of time" that constrains unitary evolution. When integrated in many-body dynamics, measurements can lead to emergent patterns of quantum information in space-time3-10 that go beyond established paradigms for characterizing phases, either in or out of equilibrium11-13. On present-day NISQ processors14, the experimental realization of this physics is challenging due to noise, hardware limitations, and the stochastic nature of quantum measurement. Here we address each of these experimental challenges and investigate measurement-induced quantum information phases on up to 70 superconducting qubits. By leveraging the interchangeability of space and time, we use a duality mapping9,15-17 to avoid mid-circuit measurement and access different manifestations of the underlying phases—from entanglement scaling3,4 to measurement-induced teleportation18—in a unified way. We obtain finite-size signatures of a phase transition with a decoding protocol that correlates the experimental measurement record with classical simulation data. The phases display sharply different sensitivity to noise, which we exploit to turn an inherent hardware limitation into a useful diagnostic. Our work demonstrates an approach to realize measurement-induced physics at scales that are at the limits of current NISQ processors.