More Like this

1. Response properties in phaseless auxiliary field quantum Monte Carlo

   https://doi.org/10.1063/5.0171996  

   Mahajan, Ankit ; Kurian, Jo S. ; Lee, Joonho ; Reichman, David R. ; Sharma, Sandeep ( November 2023 , The Journal of Chemical Physics)

   Unknown (Ed.)

   We present a method for calculating first-order response properties in phaseless auxiliary field quantum Monte Carlo by applying automatic differentiation (AD). Biases and statistical efficiency of the resulting estimators are discussed. Our approach demonstrates that AD enables the calculation of reduced density matrices with the same computational cost scaling per sample as energy calculations, accompanied by a cost prefactor of less than four in our numerical calculations. We investigate the role of self-consistency and trial orbital choice in property calculations. We find that orbitals obtained using density functional theory perform well for the dipole moments of selected molecules compared to those optimized self-consistently.

    

   more » « less
2. Matchgate Shadows for Fermionic Quantum Simulation

   https://doi.org/10.1007/s00220-023-04844-0  

   Wan, Kianna ; Huggins, William J. ; Lee, Joonho ; Babbush, Ryan ( October 2023 , Communications in Mathematical Physics)

   “Classical shadows” are estimators of an unknown quantum state, constructed from suitably distributed random measurements on copies of that state (Huang et al. in Nat Phys 16:1050, 2020,https://doi.org/10.1038/s41567-020-0932-7). In this paper, we analyze classical shadows obtained using random matchgate circuits, which correspond to fermionic Gaussian unitaries. We prove that the first three moments of the Haar distribution over thecontinuousgroup of matchgate circuits are equal to those of thediscreteuniform distribution over only the matchgate circuits that are also Clifford unitaries; thus, the latter forms a “matchgate 3-design.” This implies that the classical shadows resulting from the two ensembles are functionally equivalent. We show how one can use these matchgate shadows to efficiently estimate inner products between an arbitrary quantum state and fermionic Gaussian states, as well as the expectation values of local fermionic operators and various other quantities, thus surpassing the capabilities of prior work. As a concrete application, this enables us to apply wavefunction constraints that control the fermion sign problem in the quantum-classical auxiliary-field quantum Monte Carlo algorithm (QC-AFQMC) (Huggins et al. in Nature 603:416, 2022,https://doi.org/10.1038/s41586-021-04351-z), without the exponential post-processing cost incurred by the original approach.

    

   more » « less
3. Quantification of electron correlation for approximate quantum calculations

   https://doi.org/10.1063/5.0119260  

   Yuan, Shunyue ; Chang, Yueqing ; Wagner, Lucas K. ( November 2022 , The Journal of Chemical Physics)

   State-of-the-art many-body wave function techniques rely on heuristics to achieve high accuracy at an attainable computational cost to solve the many-body Schrödinger equation. By far, the most common property used to assess accuracy has been the total energy; however, total energies do not give a complete picture of electron correlation. In this work, we assess the von Neumann entropy of the one-particle reduced density matrix (1-RDM) to compare selected configuration interaction (CI), coupled cluster, variational Monte Carlo, and fixed-node diffusion Monte Carlo for benchmark hydrogen chains. A new algorithm, the circle reject method, is presented, which improves the efficiency of evaluating the von Neumann entropy using quantum Monte Carlo by several orders of magnitude. The von Neumann entropy of the 1-RDM and the eigenvalues of the 1-RDM are shown to distinguish between the dynamic correlation introduced by the Jastrow and the static correlation introduced by determinants with large weights, confirming some of the lore in the field concerning the difference between the selected CI and Slater–Jastrow wave functions.

    

   more » « less
4. In silico prediction of annihilators for triplet–triplet annihilation upconversion via auxiliary-field quantum Monte Carlo

   https://doi.org/10.1039/d0sc03381b  

   Weber, John L. ; Churchill, Emily M. ; Jockusch, Steffen ; Arthur, Evan J. ; Pun, Andrew B. ; Zhang, Shiwei ; Friesner, Richard A. ; Campos, Luis M. ; Reichman, David R. ; Shee, James ( January 2021 , Chemical Science)

   null (Ed.)

   The energy of the lowest-lying triplet state (T1) relative to the ground and first-excited singlet states (S0, S1) plays a critical role in optical multiexcitonic processes of organic chromophores. Focusing on triplet–triplet annihilation (TTA) upconversion, the S0 to T1 energy gap, known as the triplet energy, is difficult to measure experimentally for most molecules of interest. Ab initio predictions can provide a useful alternative, however low-scaling electronic structure methods such as the Kohn–Sham and time-dependent variants of Density Functional Theory (DFT) rely heavily on the fraction of exact exchange chosen for a given functional, and tend to be unreliable when strong electronic correlation is present. Here, we use auxiliary-field quantum Monte Carlo (AFQMC), a scalable electronic structure method capable of accurately describing even strongly correlated molecules, to predict the triplet energies for a series of candidate annihilators for TTA upconversion, including 9,10 substituted anthracenes and substituted benzothiadiazole (BTD) and benzoselenodiazole (BSeD) compounds. We compare our results to predictions from a number of commonly used DFT functionals, as well as DLPNO-CCSD(T 0 ), a localized approximation to coupled cluster with singles, doubles, and perturbative triples. Together with S1 estimates from absorption/emission spectra, which are well-reproduced by TD-DFT calculations employing the range-corrected hybrid functional CAM-B3LYP, we provide predictions regarding the thermodynamic feasibility of upconversion by requiring (a) the measured T1 of the sensitizer exceeds that of the calculated T1 of the candidate annihilator, and (b) twice the T1 of the annihilator exceeds its S1 energetic value. We demonstrate a successful example of in silico discovery of a novel annihilator, phenyl-substituted BTD, and present experimental validation via low temperature phosphorescence and the presence of upconverted blue light emission when coupled to a platinum octaethylporphyrin (PtOEP) sensitizer. The BTD framework thus represents a new class of annihilators for TTA upconversion. Its chemical functionalization, guided by the computational tools utilized herein, provides a promising route towards high energy (violet to near-UV) emission. 

   more » « less
5. Markov chain Monte Carlo enhanced variational quantum algorithms

   https://doi.org/10.1088/2058-9565/aca821  

   Patti, Taylor L ; Shehab, Omar ; Najafi, Khadijeh ; Yelin, Susanne F ( December 2022 , Quantum Science and Technology)

   Abstract Variational quantum algorithms have the potential for significant impact on high-dimensional optimization, with applications in classical combinatorics, quantum chemistry, and condensed matter. Nevertheless, the optimization landscape of these algorithms is generally nonconvex, leading the algorithms to converge to local, rather than global, minima and the production of suboptimal solutions. In this work, we introduce a variational quantum algorithm that couples classical Markov chain Monte Carlo techniques with variational quantum algorithms, allowing the former to provably converge to global minima and thus assure solution quality. Due to the generality of our approach, it is suitable for a myriad of quantum minimization problems, including optimization and quantum state preparation. Specifically, we devise a Metropolis–Hastings method that is suitable for variational quantum devices and use it, in conjunction with quantum optimization, to construct quantum ensembles that converge to Gibbs states. These performance guarantees are derived from the ergodicity of our algorithm’s state space and enable us to place analytic bounds on its time-complexity. We demonstrate both the effectiveness of our technique and the validity of our analysis through quantum circuit simulations for MaxCut instances, solving these problems deterministically and with perfect accuracy, as well as large-scale quantum Ising and transverse field spin models of up to 50 qubits. Our technique stands to broadly enrich the field of variational quantum algorithms, improving and guaranteeing the performance of these promising, yet often heuristic, methods. 

   more » « less