Quantum Krylov Subspace Diagonalization via Time Reversal Symmetries

TL;DR

The paper introduces Krylov Time Reversal (KTR), a quantum algorithm leveraging time-reversal symmetry to efficiently perform Krylov subspace diagonalization with reduced circuit depth, suitable for near-term quantum hardware.

Contribution

It presents a novel KTR protocol that avoids controlled operations by exploiting time-reversal symmetry, enabling more hardware-friendly quantum diagonalization methods.

Findings

KTR reduces circuit depth compared to traditional methods.

Numerical simulations show accurate spectral estimation on symmetric Hamiltonians.

The protocol is compatible with shallow quantum architectures.

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.