Quantum Krylov Subspace Diagonalization via Time Reversal Symmetries

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.