Dissipative ground state preparation in ab initio electronic structure theory

TL;DR

A Monte Carlo trajectory-based algorithm is employed for simulating the Lindblad dynamics for full ab initio Hamiltonians, demonstrating its effectiveness on molecular systems amenable to exact wavefunction treatment.

Abstract

Dissipative engineering is a powerful tool for quantum state preparation, and has drawn significant attention in quantum algorithms and quantum many-body physics in recent years. In this work, we introduce a novel approach using the Lindblad dynamics to efficiently prepare the ground state for general ab initio electronic structure problems on quantum computers, without variational parameters. These problems often involve Hamiltonians that lack geometric locality or sparsity structures, which we address by proposing two generic types of jump operators for the Lindblad dynamics. Type-I jump operators break the particle number symmetry and should be simulated in the Fock space. Type-II jump operators preserves the particle number symmetry and can be simulated more efficiently in the full configuration interaction space. For both types of jump operators, we prove that in a simplified Hartree-Fock framework, the spectral gap of our Lindbladian is lower bounded by a universal constant. For physical observables such as energy and reduced density matrices, the convergence rate of our Lindblad dynamics with Type-I jump operators remains universal, while the convergence rate with Type-II jump operators only depends on coarse grained information such as the number of orbitals and the number of electrons. To validate our approach, we employ a Monte Carlo trajectory-based algorithm for simulating the Lindblad dynamics for full ab initio Hamiltonians, demonstrating its effectiveness on molecular systems amenable to exact wavefunction treatment.

Figures (10)

• Figure 1: Conceptual workflow illustrating the proposed dissipative ground state preparation method. We consider the ab initio Hamiltonian in electronic structure theory for molecular systems. The central task in this framework is to construct Lindblad jump operators, derived from either Type-I or Type-II coupling operators. An active-space strategy is employed to reduce the simulation cost. The Lindblad dynamics can be efficiently simulated on quantum devices using only single ancilla qubit, and the approach is classically validated using a wavefunction trajectory method.
• Figure 1: The Lindblad dynamics of the $\rm H_2$ system in the STO-3G basis set, obtained by exactly propagating the many-body density operator and using the quantum-jump unraveling method with 10, 25, 50, 100, and 500 trajectories, respectively. The (a) panel illustrates the energy convergence curves of each simulation. The (b) panel shows the average absolute error of the overlap $\langle \rho_{g}\rangle$ with the exact ground state relative to the exact Lindblad dynamics at each time point. The average error decreases approximately as $1/\sqrt{N_{\mathrm{traj}}}$.
• Figure 2: A conceptual illustration of the "shoveling" process in ground state preparation via Lindbladians. The choice of jump operators ensures that the Lindbladian only allows transitions from high-energy eigenstates to low-energy eigenstates.
• Figure 3: A conceptual illustration of the evolution of the diagonal elements of the 1-RDM for ground state preparation with Type-I set. The occupation numbers on each molecular orbital increase or decrease independently in an exponential rate.
• Figure 4: A conceptual illustration of the evolution of the diagonal elements of the 1-RDM for ground state preparation with Type-II set. It is a "mass transport" process from higher energy orbitals to lower energy orbitals.

Theorems & Definitions (2)

• Theorem 1
• proof