Time Propagation and Spectroscopy of Fermionic Systems Using a Stochastic Technique

Importance-sampling FCIQMC: solving weak sign-problem systems

We investigate the exact FCIQMC algorithm (without the initiator approximation) applied to weak sign-problem fermionic systems, namely systems in which the energy gap to the corresponding sign-free or ``stoquastized" state is small. We show that the minimum number of walkers required to exactly overcome the sign problem can be significantly reduced via an importance-sampling similarity transformation, even though the similarity-transformed Hamiltonian has the same stoquastic gap as the untransformed one. Furthermore, we show that in the off-half-filling Hubbard model at $U/t=8$, the real-space (site) representation has a much weaker sign problem compared to the momentum space representation. By applying importance sampling using a Gutzwiller-like guiding wavefunction, we are able to reduce the minimum number of walkers substantially in the case of $2 \times \ell$ Hubbard ladders, enabling us to get exact energies for sizeable ladders. With these results, we calculate the fundamental charge gap $\Delta E^{\mathrm{fund}}=E(N+1)+E(N-1)-2 E(N)$ for the ladder systems compared to strictly one-dimensional Hubbard chains, and show that the ladder systems have a reduced fundamental gap compared to the 1D chains.

Simulation of adiabatic quantum computing for molecular ground states

Quantum computation promises to provide substantial speedups in many practical applications with a particularly exciting one being the simulation of quantum many-body systems. Adiabatic state preparation (ASP) is one way that quantum computers could recreate and simulate the ground state of a physical system. In this paper, we explore a novel approach for classically simulating the time dynamics of ASP with high accuracy and with only modest computational resources via an adaptive sampling configuration interaction scheme for truncating the Hilbert space to only the most important determinants. We verify that this truncation introduces negligible error and use this new approach to simulate ASP for sets of small molecular systems and Hubbard models. Furthermore, we examine two approaches to speeding up ASP when performed on quantum hardware: (i) using the complete active space configuration interaction (CASCI) wave function instead of the Hartree-Fock initial state and (ii) a nonlinear interpolation between the initial and target Hamiltonians. We find that starting with a CASCI wave function with a limited active space yields substantial speedups for many of the systems examined, while nonlinear interpolation does not. In additional, we observe interesting trends in the minimum gap location (based on the initial state) as well as how state preparation time can depend on certain molecular properties, such as the number of valence electrons. Importantly, we find that the required state preparation times do not show an immediate exponential wall that would preclude an efficient run of ASP on actual hardware.