Bowtie VarQTE: A Resource-Efficient Quantum State Preparation Primitive

We introduce bowtie Variational Quantum Time Evolution (VarQTE), a resource‑efficient state‑preparation primitive that exploits the causal light‑cone structure of parametrized quantum circuits to enable scalable variational real‑ and imaginary‑time dynamics. By decomposing the metric and gradient quantities arising from McLachlan’s variational principle into independent, parameter‑dependent subcircuits—so‑called bowties—our framework allows for exact, deterministic evaluation of these terms via classical simulation whenever locality permits, eliminating shot noise and improving numerical stability. This causal formulation ensures that quantum resources are used only where necessary, while classical resources are leveraged whenever accurate simulation is feasible. Benchmarking on large‑scale one‑dimensional Heisenberg models demonstrates that bowtie VarQTE, as a circuit compilation technique, attains accuracies comparable to Trotterized approaches with substantially shallower circuits and matches tensor‑network–compiled baselines at fixed depth. We further show how bowtie‑assisted imaginary‑ and real‑time evolution provides an effective front‑end for Sample‑Based Krylov Quantum Diagonalization, enabling high‑quality initial states and efficient generation of informative Krylov subspaces. Overall, bowtie VarQTE establishes a modular and scalable hybrid primitive for quantum state preparation, supporting the efficient integration of classical and quantum resources in near‑term applications.