Statistical errors in reduced density matrices sampled from quantum circuit simulation and the impact on multireference perturbation theory.

In this work, we present a detailed analysis of statistical errors in reduced density matrices (RDMs) of active space wavefunctions sampled from quantum circuit simulation and the impact on results obtained by the multireference theories. From the sampling experiments, it is shown that the errors in sampled RDMs have a larger value for higher-order RDMs, and that the errors in sampled RDMs for excited states are larger than those for the ground state. We analytically derive the expected value of the sum of squared errors between the true distribution and sample distribution of weights of the electron configurations based on a multinomial distribution model, with which we present an assessment of the dependency of RDM errors on the number of shots for the observation (Nshot) and on the character of the target electronic state. With the benchmark calculations of short polyenes, C4H6 and C6H8, we report the statistical errors in CASCI and complete active space second-order perturbation theory (CASPT2) energies obtained with the sampled 1,2-RDMs and 1,2,3,4-RDMs, respectively. It was found that the standard deviation (SD) of the sampled CASCI energies is proportional to as predicted. It was also found that the dependence of the SD of the second-order correction energies are somewhat different but the errors in the reference CASCI energies are dominant as compared with the corrections and the SD of the resulting CASPT2 energies are proportional to . This suggests that the required Nshot for 3,4-RDMs used only in the second-order perturbative corrections is smaller than that for 1,2-RDM used to calculate the reference CASCI energies. It was also suggested from the analysis of the errors in the sampled energies that the required Nshot for 3-RDM, which is used to calculate the perturbative correction energies, can be smaller than that for 2-RDM to calculate the CASCI energies. In fact, it was shown that the potential energy curve along the isomerization reaction of the {[Cu(NH3)3]2O2}2+ complex as an archetype of metalloenzyme, in which static and dynamical electron correlations are both important, can be reasonably reproduced with Nshot = 106 for 1,2-RDMs but Nshot = 105 for 3-RDM by the sampling simulation.

Post-translational backbone-acyl shift yields natural product-like peptides bearing hydroxyhydrocarbon units.

Hydroxyhydrocarbon (Hhc) moieties in the backbone of peptidic natural products can exert a substantial influence on the bioactivities of the products, making Hhc units an attractive class of building blocks for de novo peptides. However, despite advances in in vitro genetic code reprogramming, the ribosomal incorporation of Hhc units remains challenging. Here we report a method for in vitro ribosomal synthesis of natural-product-like peptides bearing Hhc units. A series of azide/hydroxy acids were designed as chemical precursors of Hhc units and incorporated into the nascent peptide chain by means of genetic code reprogramming. Post-translational reduction of the azide induced an O-to-N acyl shift to rearrange the peptide backbone. This method allows for one-pot ribosomal synthesis of designer macrocycles bearing various ß-, γ- and δ-type Hhc units. We also report the synthesis of a statine-containing peptidomimetic inhibitor of ß-secretase 1 as a showcase example.

Importance of dynamical electron correlation in diabatic couplings of electron-exchange processes.

We demonstrate the importance of the dynamical electron correlation effect in diabatic couplings of electron-exchange processes in molecular aggregates. To perform a multireference perturbation theory with large active space of molecular aggregates, an efficient low-rank approximation is applied to the complete active space self-consistent field reference functions. It is known that kinetic rates of electron-exchange processes, such as singlet fission, triplet-triplet annihilation, and triplet exciton transfer, are not sufficiently explained by the direct term of the diabatic couplings but efficiently mediated by the low-lying charge transfer states if the two molecules are in close proximity. It is presented in this paper, however, that regardless of the distance of the molecules, the direct term is considerably underestimated by up to three orders of magnitude without the dynamical electron correlation, i.e., the diabatic states expressed in the active space are not adequate to quantitatively reproduce the electron-exchange processes.

Rank-one basis made from matrix-product states for a low-rank approximation of molecular aggregates.

An efficient low-rank approximation to complete active space (CAS) wavefunctions for molecular aggregates is presented. Molecular aggregates usually involve two different characteristic entanglement structures: strong intramolecular entanglement and weak intermolecular entanglement. In the method, low-lying electronic states of molecular aggregates are efficiently expanded by a small number of rank-one basis states that are direct products of monomolecular wavefunctions, each of which is written as a highly entangled state such as the matrix product state (MPS). The complexities raised by strong intramolecular entanglement are therefore encapsulated by the MPS and eliminated from the degree of freedom of the effective Hamiltonian of molecular aggregates. It is demonstrated that the excitation energies of low-lying excited states of a pair of bacteriochlorophyll units with CAS(52e, 50o) are accurately reproduced by only five rank-one basis states. Because the rank-one basis states naturally have diabatic character and reproduce the low-lying spectrum of the CAS space, off-diagonal elements of the Hamiltonian are expected to give accurate diabatic couplings. It is also demonstrated that the energy splitting and the diabatic couplings in anthracene dimer systems are improved by augmenting with additional rank-one basis states.