Dissipative Preparation of Quantum Ground States and Excited States in Electronic Structure Theory

Dissipative engineering has emerged as a powerful tool for quantum state preparation, attracting growing attention in quantum algorithms and many-body physics. We present a Lindblad dynamics–based approach to efficiently prepare both ground and excited states for general ab initio electronic structure problems on quantum computers, without variational parameters. These problems often involve Hamiltonians lacking geometric locality or sparsity, which we address by introducing two generic classes of jump operators. Type-I operators break particle-number symmetry and are simulated in Fock space, while Type-II operators preserve particle-number symmetry and are simulated efficiently within the full configuration interaction space.

For ground-state preparation, we prove that for both types of jump operators, the spectral gap of the corresponding Lindbladian—within a simplified Hartree–Fock framework—is lower-bounded by a universal constant. For observables such as energy and reduced density matrices, the convergence rate with Type-I operators remains universal, whereas that with Type-II operators depends only on coarse-grained parameters such as the number of orbitals and electrons. To validate our approach, we employ a Monte Carlo trajectory-based algorithm to simulate the Lindblad dynamics for ab initio Hamiltonians, demonstrating its effectiveness on molecular systems tractable by exact wavefunction methods.

We further extend this approach to excited-state preparation using three complementary strategies: a symmetry-based targeting scheme, a folded-spectrum method, and a spectral projection approach. We demonstrate the applicability of these methods on examples like atomic spectra and small molecular systems within the regime of exact wavefunction treatment. Finally, we highlight potential advantages of dissipative state preparation over adiabatic algorithms in electronic structure theory.