Complexity of Digital Quantum Simulation in the Low-Energy Subspace: Applications and a Lower Bound

• DOI: 10.22331/q-2024-07-15-1409
• Publication Date: 2024-07-15T14:12:29Z
• Authors: Weiyuan Gong; Shuo Zhou; Tongyang Li
• Keywords: FOS: Computer and information sciences; Quantum Physics; Physics; QC1-999; Computer Science - Data Structures and Algorithms; 0103 physical sciences; FOS: Physical sciences; Data Structures and Algorithms (cs.DS); Quantum Physics (quant-ph); 01 natural sciences

Digital quantum simulation has broad applications in approximating unitary evolution of Hamiltonians. In practice, many tasks for systems focus on states the low-energy subspace instead entire Hilbert space. this paper, we systematically investigate complexity digital based product formulas subspace. We show that error depends effective norm Hamiltonian a variety algorithms and systems, allowing improvements over previous complexities full simulations even imperfect state preparations due to thermalization. particular, simulating spin models subspace, prove randomized such as qDRIFT random permutation require smaller Trotter numbers. Such improvement also persists symmetry-protected simulations. similar dynamics power-law interactions. provide query lower bound general