Excited state preparation on a quantum computer through adiabatic light-matter coupling

TL;DR

This work tackles the challenge of preparing excited-state wavefunctions on quantum devices by introducing Excited Adiabatic State Preparation (EXASP), which adiabatically evolves an electronic ground state while explicitly coupling to a single photon mode via the Pauli–Fierz Hamiltonian. By steering the path in the ω–λ plane with ω(s) and λ(s) and leveraging symmetry through photon polarization, EXASP deterministically connects |Ψ0⟩⊗|1⟩ to |Ψ_es⟩⊗|0⟩, circumventing the need for prior excited-state knowledge or variational ansätze. The authors demonstrate high-fidelity excited-state preparation in both a two-level model and more complex many-body Hamiltonians (the Hubbard chain) and molecular CH2, showing convergence with total evolution time T and time step δT and highlighting the beneficial role of photon post-selection. While hardware demonstrations on current noisy devices show the method's practicality for simple models, advancements in fault-tolerant evolution and hardware will enhance scalability to realistic photochemical systems, enabling reliable excited-state simulations on quantum computers.

Abstract

Quantum computing has the potential to transform simulations of quantum many-body problems at the heart of electronic structure theory. Efficient quantum algorithms to compute the eigenstates of fermionic Hamiltonians, such as quantum phase estimation, rely critically on high-accuracy initial state preparation. While several state preparation algorithms have been proposed for fermionic ground states, the preparation of excited states remains a major challenge, limiting the applicability of quantum algorithms to photochemistry and photophysics. In this contribution, we describe a physically motivated adiabatic state preparation technique for low-lying excited states using the explicit coupling between electrons and photons. Our approach systematically converges to the first optically accessible excited state and can target different symmetry sectors by changing the photon polarization. We demonstrate the preparation of high-fidelity excited states for the Hubbard model and methylene molecule across a range of correlation regimes, and perform a successful hardware implementation for a model Hamiltonian.

Figures (8)

• Figure 1: Explicit electron-photon coupling enables adiabatic preparation of an excited-state wavefunction. (a) The electron-photon coupling Hamiltonian for a two-level system is analogous to the Jaynes--Cummings model. (b) The adiabatic states form a conical intersection in the $(\omega,\lambda)$ plane (left). Following a suitable parametrized pathway [Eq. \ref{['eq:path']}] provides a connection between the electronic ground and excited state (right), with $\lambda_{\text{max}}$ controlling the strength of the avoided crossing. (c) Adiabatic time evolution along this parametrized pathway $\hat{H}(s)$ enables the preparation of the excited-state wavefunction, with a success probability that depends on the total evolution time $T$.
• Figure 2: Implementation of EXASP on quantum hardware for a two-level system. (a) Circuit implementation including initial ground state preparation, time-evolution gates, and post-selection for the photon vacuum state. (b) Gate decomposition of the time-evolution step for the two-level system. (c) Electronic energy expectation values for quantum hardware experiments using ibmq_torino with $\delta T = 0.5 \epsilon^{-1}$ (points), compared to a noiseless simulation with $\delta T = 0.01 \epsilon^{-1}$ (solid), showing successful adiabatic preparation of the excited state. The system parameters are $\epsilon = 1$, $g=1$, $\mu = 1$, $T=20$, $\omega_{\text{max}}=5$, and $\lambda_{\text{max}}=1$.
• Figure 3: Convergence of the two-level EXASP final electronic energy with and without post-selection. Comparison of noiseless statevector simulations with hardware calculations on the ibmq_torino quantum chip. Parameters used were $\epsilon=1$, $g=1$, $\omega_{\text{max}} = 5$, $\lambda_{\text{max}} = 1.0$, and $\mu=1$ with $10^5$ measurement shots.
• Figure 4: Convergence of the final energy and success probability of projecting into the $\ket{0}$ photon state for the 4-site Hubbard chain with $U=4t$. (a) Final energy after exact time evolution for different time steps with $U = 4t$, with and without photon state post-selection. (b) Approximating the propagation using a Trotter expansion of the time-evolution operator requires a smaller time step to obtain satisfactory convergence.
• Figure 5: EXASP propagation for the 6-site Hubbard chain. (a) Convergence of the final total energy and probability of measuring the $\ket{0}$ photon state at various $U/t$ values as a function of total evolution time $T$ with $\delta T = 0.1$. Similar convergence is obtained if the propagation is performed exactly or using a first-order Trotter expansion. (b) Adiabatic evolution along the EXASP pathway (purple) for $U/t = 8$, $T = 100$ and $\delta T = 0.1$, shown alongside the eigenvalues of the full system Hamiltonian with the dipole self-energy included (grey). EXASP leads to the first bright excited state as there is no coupling to the lower energy dark states.