Dissipative quantum algorithms for excited-state quantum chemistry

Electronic excited states are central to a vast array of physical and chemical phenomena, yet accurate and efficient methods for preparing them on quantum devices remain challenging and comparatively underexplored. We introduce a general dissipative algorithm for selectively preparing ab initio electronic excited states. The key idea is to recast excited-state preparation as an effective ground-state problem by suitably modifying the underlying Lindblad dynamics so that the target excited state becomes the unique steady state of a designed quantum channel. We develop three complementary strategies, tailored to different types of prior information about the excited state, such as symmetry and approximate energy. We demonstrate the effectiveness and versatility of these schemes through numerical simulations of atomic and molecular spectra, including valence excitations in prototypical planar conjugated molecules and transition-metal complexes. Taken together, these results provide a new pathway for advancing quantum simulation methods for realistic strongly correlated electronic systems.

💡 Research Summary

This paper introduces a general dissipative quantum algorithm for preparing electronic excited states on quantum computers. The authors recast excited‑state preparation as an effective ground‑state problem by engineering Lindblad dynamics so that the desired excited state becomes the unique steady state of a designed quantum channel. Three complementary strategies are developed, each exploiting different prior information about the target state: (i) a symmetry‑based “dark‑state” approach that restricts both the initial state and the jump operators to a specific symmetry sector, making the target the lowest‑energy state within that sector; (ii) a folded‑spectrum method that applies the transformation (H\rightarrow (H-\mu I)^2) using an approximate energy (\mu) so that the eigenstate closest to (\mu) becomes the effective ground state; and (iii) a spectral‑projector approach that constructs an operator (P_\mu(H)) which approximately projects out all eigenstates with energies below (\mu), thereby confining the dissipative dynamics to the subspace above (\mu). In all cases the jump operators are built from a set of quadratic coupling operators (either the full set (S_{II}) or a reduced set (S’_{II})) together with a filter function that enforces energy‑lowering transitions, guaranteeing that the target state is annihilated by every jump operator and thus a fixed point of the dynamics.

The authors validate the three protocols on a range of systems. For small hydrogen molecules (H₂ in a 6‑31G basis and an H₄ chain in STO‑3G) they prepare the three degenerate triplet states. The symmetry‑based method works directly for the (T_{\pm}) states, which lie in different ((N_\alpha,N_\beta)) sectors from the singlet ground state, while the folded‑spectrum and projector methods successfully prepare the (T_0) state that shares the same symmetry sector as the ground state. All three schemes achieve chemical accuracy (≤1 mHa) in energy, with only a modest performance drop when using the reduced coupling set. Resource analysis shows that the folded‑spectrum approach incurs a substantial overhead due to Hamiltonian squaring, whereas the projector method avoids this cost at the expense of more complex jump‑operator implementation.

Larger, chemically relevant systems are also studied. Using active‑space representations, the authors simulate (\pi)–(\pi^*) excitations in benzene and d–d transitions in ferrocene (Fe(C₅H₅)₂). The algorithms correctly reproduce spin multiplicities, excitation characters, and energies within chemical accuracy. For the ferrocene 2s¹2p³ (⁵S) state, both a high‑spin initial state and a Hartree–Fock ground state are used; the dynamics with the full coupling set (Q\cup S’_{II}) converge faster than with the reduced set alone, but both reach overlaps >0.98 with the target.

The paper compares dissipative state preparation (DSP) with adiabatic state preparation (ASP). ASP can fail when the mean‑field reference Hamiltonian exhibits degenerate excited states or gap closures (e.g., at the Coulson–Fischer point in hydrogen chains), requiring additional tricks such as explicit electron‑photon coupling. In contrast, DSP sidesteps these mean‑field pitfalls because the Lindblad channel directly enforces the desired ordering of eigenstates. Moreover, DSP shows intrinsic robustness to certain noise models; simulations with depolarizing noise demonstrate that convergence and final energy errors remain essentially unchanged, reflecting the contractive nature of the dissipative dynamics.

A detailed resource estimation is provided. The authors quantify the number of T‑gates, circuit depth, and measurement repetitions required for each protocol. The folded‑spectrum method has the highest gate count due to the squared Hamiltonian, while the projector method reduces overall depth but demands more elaborate implementation of the projector operator. The symmetry‑based approach is the most resource‑efficient when applicable, as it avoids both Hamiltonian squaring and projector construction.

In summary, the work establishes dissipative quantum algorithms as a powerful, flexible, and potentially scalable primitive for excited‑state quantum chemistry. By turning excited‑state preparation into a ground‑state‑like problem via engineered Lindblad dynamics, and by offering three practical strategies that leverage symmetry, approximate energies, or spectral projectors, the authors provide a comprehensive toolkit that delivers high accuracy, favorable resource scaling, and noise resilience across a variety of atomic, molecular, and transition‑metal systems.