Efficient Operator Selection and Warm-Start Strategy for Excitations in Variational Quantum Eigensolvers

TL;DR

The paper tackles the bottleneck of efficiently preparing ground states with VQE by pairing Energy Sorting with the ExcitationSolve optimizer to construct a near-ground-state from a UCCSD pool in a single operator-selection sweep, aided by classical pre-processing and warm-started parameters. It demonstrates that this hybrid approach yields substantial reductions in quantum resource costs, achieves quadratic speedups in operator-selection workload, and remains effective when extended to higher-order excitations (e.g., UCCSDT) and to OVP-CEOs, with trade-offs between circuit depth and pool size. Across a suite of molecules, the method delivers faster convergence and the possibility of fixed-like compact ansätze, while maintaining chemical accuracy, and reduces overall compute times from days to minutes, enabling larger-scale quantum chemistry simulations on NISQ devices. The work also outlines extensions to broader Hamiltonian variational methods and potential integrations with future adaptive frameworks, signaling a practical path toward quantum advantage in chemistry."

Abstract

We present a novel approach for efficient preparation of electronic ground states, leveraging the optimizer ExcitationSolve [Jäger et al., Comm. Phys. (2025)] and established variational quantum eigensolver-based operator selection methods, such as Energy Sorting. By combining these tools, we demonstrate a computationally efficient protocol that enables the construction of an approximate ground state from a unitary coupled cluster ansatz via a single sweep over the operator pool. Utilizing efficient classical pre-processing to select the majority of relevant operators, this approach reduces the computational complexity associated with traditional optimization methods. Furthermore, we show that this method can be seamlessly integrated with one-variational-parameter couple exchange operators, thereby further reducing the number of required CNOT operations. Overall, we empirically observe a quadratic convergence speedup beyond state-of-the-art methods, advancing the realization of quantum advantage in quantum chemistry.

Figures (7)

• Figure 1: Comparison of ExcitationSolve + ES (green) to ADAPT VQE (yellow), naive adaptive ExcitationSolve (red), and a fixed ansatz UCCSD optimization (blue). Lighter colors signal quantum resources spent on operator selection, darker colors mean quantum resources spent on VQE optimization. The light blue area marks chemical accuracy.
• Figure 2: Evaluations to convergence over pool size on log-log scale, comparing ExcitationSolve + ES (green) to ADAPT VQE (yellow) and adaptive ExcitationSolve (red). An unweighted linear fit to the log-log data is used as guide to the eye. As the pool size grows, the number of evaluations required on the QC grows exponentially in all cases, but the exponent when using ExcitationSolve + ES is reduced significantly.
• Figure 3: Fixed ansatz (blue) convergence compared to ExcitationSolve + ES (green) for the LiI molecule. Even though the convergence process begins earlier for the fixed ansatz, the optimization using ES is faster, because all unnecessary operators are removed from the ansatz. The light blue area marks chemical accuracy.
• Figure 4: ExcitationSolve and Energy Sorting for a UCCSDT pool (purple) for a LiH molecule compared to a UCCSD pool (green). First double excitations are appended to the ansatz, then singles and lastly triples, followed by the optimization of the complete circuit. The light blue area marks chemical accuracy.
• Figure 5: Adaptive optimization of an OVP-CEO pool (blue) compared to a UCCSD pool (red) of LiH. Convergence is reached with the same number of operators, but for OVP-CEOs twice as many evaluations are needed due to the increased pool size. The light blue area marks chemical accuracy.