Quantum signal processing in a Hilbert-space fragmented system

Quantum Signal Processing (QSP) is known as a powerful quantum algorithm framework that enables polynomial transformations of block-encoded signals [1]. QSP can be applied as a powerful analog quantum emulator to control the nonequilibrium dynamics of the target Hamiltonian. For integrable quantum many-body systems, a proposal has been made to implement QSP as the dynamics of the one-dimensional transverse-field Ising model, which is experimentally feasible in quantum simulators [2]. To further extension, we propose a QSP protocol that can be implemented in non-integrable quantum many-body systems. Generic quantum many-body systems are generally non-integrable, leading to thermalization caused by increasing entanglement. However, we show that Hilbert-space fragmentation arising from dynamically constrained subspaces plays a vital role in suppressing thermalization and preserving the QSP protocol even in the non-integrable regime [3]. Our method enables the construction of Krylov subspaces that exhibit SU(2) dynamics in momentum space, and we further clarify the relationship with thermalization.

[1] G. H. Low and I. L. Chuang, Optimal Hamiltonian Simulation by Quantum Signal Processing, Phys. Rev. Lett. 118, 010501 (2017).

[2] V. M. Bastidas et al., Quantum signal processing with the one-dimensional quantum Ising model, Phys. Rev. B 109, 014306 (2024).

[3] S. Moudgalya et al., Thermalization and its Absence within Krylov Subspaces of a Constrained Hamiltonian, arXiv:1910.14048 (2019).