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arXiv · 2507.22559

Quantum Krylov Subspace Diagonalization via Time Reversal Symmetries

Nicola Mariella·Enrique Rico·Adam Byrne·Sergiy Zhuk
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Abstract

Krylov quantum diagonalization methods have emerged as a promising use case for quantum computers. However, many existing implementations rely on controlled operations, which pose challenges to near-term quantum hardware. We introduce a novel protocol, termed Krylov Time Reversal (KTR), that circumvents these bottlenecks by leveraging time-reversal symmetry in Hamiltonian evolution. Using symmetric time dynamics, we show that it is possible to recover real-valued Krylov matrix elements, which significantly reduces the circuit depth and enhances compatibility with shallow quantum architectures. Furthermore, the protocol's structure indirectly reduces the total evolution time, benefiting both near-term and long-term architectures. We validate our method through numerical simulations on paradigmatic Hamiltonians exhibiting time-reversal symmetry, including the transverse-field Ising model and a lattice gauge theory, demonstrating accurate spectral estimation and favorable circuit constructions.

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Nicola Mariella, Enrique Rico, Adam Byrne, Sergiy Zhuk. 2025-10-14. Quantum Krylov Subspace Diagonalization via Time Reversal Symmetries. https://arxiv.org/abs/2507.22559

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