Quantum Krylov Subspace Diagonalization via Time Reversal Symmetries

• URL: http://arxiv.org/abs/2507.22559v1
• Date: Wed, 30 Jul 2025 10:35:36 GMT
• Title: Quantum Krylov Subspace Diagonalization via Time Reversal Symmetries
• Authors: Nicola Mariella, Enrique Rico, Adam Byrne, Sergiy Zhuk,
• Abstract summary: We introduce a novel protocol, which we call Krylov Time Reversal (KTR)<n>We show that it is possible to recover real-valued Krylov matrix elements, which significantly reduces the circuit depth.<n>We validate our method through numerical simulations on paradigmatic Hamiltonians exhibiting time-reversal symmetry.
• Score: 0.562479170374811
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• 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, which we call Krylov Time Reversal (KTR), which avoids these bottlenecks by exploiting the 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. 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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