Related papers: Quantum Amplitude-Amplification Eigensolver: A State-Learning-Assisted Approach beyond Energy-Gradient-Based Heuristics

Quantum Amplitude-Amplification Eigensolver: A State-Learning-Assisted Approach beyond Energy-Gradient-Based Heuristics

URL: http://arxiv.org/abs/2511.12062v1
Date: Sat, 15 Nov 2025 07:00:00 GMT
Title: Quantum Amplitude-Amplification Eigensolver: A State-Learning-Assisted Approach beyond Energy-Gradient-Based Heuristics
Authors: Kyunghyun Baek, Seungjin Lee, Joonsuk Huh, Dongkeun Lee, Jinhyoung Lee, M. S. Kim, Jeongho Bang,
Abstract summary: Ground-state estimation lies at the heart of a broad range of quantum simulations.<n>We develop the quantum amplitude-amplification eigensolver (QAAE)<n>QAAE coherently drives a trial state toward the ground state via quantum amplitude amplification.
Score: 4.181599718305555
License: http://creativecommons.org/licenses/by-nc-nd/4.0/
Abstract: Ground-state estimation lies at the heart of a broad range of quantum simulations. Most near-term approaches are cast as variational energy minimization and thus inherit the challenges of problem-specific energy landscapes. We develop the quantum amplitude-amplification eigensolver (QAAE), which departs from the variational paradigm and instead coherently drives a trial state toward the ground state via quantum amplitude amplification. Each amplitude-amplification round interleaves a reflection about the learned trial state with a controlled short-time evolution under a normalized Hamiltonian; an ancilla readout yields an amplitude-amplified pure target state that a state-learning step then re-encodes into an ansatz circuit for the next round -- without evaluating the energy gradients. Under standard assumptions (normalized $\hat{H}$, a nondegenerate ground-state, and a learning update), the ground-state overlap increases monotonically per round and the procedure converges; here, a per-round depth bound in terms of the ansatz depth and Hamiltonian-simulation cost establishes hardware compatibility. Cloud experiments on IBMQ processor verify our amplification mechanism on a two-level Hamiltonian and a two-qubit Ising model, and numerical benchmarks on $\mathrm{H}_2$, $\mathrm{LiH}$, and a $10$-qubit longitudinal-and-transverse-field Ising model show that QAAE integrates with chemistry-inspired and hardware-efficient circuits and can surpass gradient-based VQE in accuracy and stability. These results position QAAE as a variational-free and hardware-compatible route to ground-state estimation for near-term quantum simulation.

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