Quantum Krylov Subspace Diagonalization via Time Reversal Symmetries
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912645476515840 |
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| author | Mariella, Nicola Rico, Enrique Byrne, Adam Zhuk, Sergiy |
| author_facet | Mariella, Nicola Rico, Enrique Byrne, Adam Zhuk, Sergiy |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_22559 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Krylov Subspace Diagonalization via Time Reversal Symmetries Mariella, Nicola Rico, Enrique Byrne, Adam Zhuk, Sergiy Quantum Physics 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. |
| title | Quantum Krylov Subspace Diagonalization via Time Reversal Symmetries |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2507.22559 |