Hamiltonian simulation in the low-energy subspace

Journal Article · 26 July 2021 · npj Quantum Information

DOI: https://doi.org/10.1038/s41534-021-00451-w · OSTI ID:1810422

Şahinoğlu, Burak; Somma, Rolando D.

Abstract We study the problem of simulating the dynamics of spin systems when the initial state is supported on a subspace of low energy of a Hamiltonian H . This is a central problem in physics with vast applications in many-body systems and beyond, where the interesting physics takes place in the low-energy sector. We analyze error bounds induced by product formulas that approximate the evolution operator and show that these bounds depend on an effective low-energy norm of H . We find improvements over the best previous complexities of product formulas that apply to the general case, and these improvements are more significant for long evolution times that scale with the system size and/or small approximation errors. To obtain these improvements, we prove exponentially decaying upper bounds on the leakage to high-energy subspaces due to the product formula. Our results provide a path to a systematic study of Hamiltonian simulation at low energies, which will be required to push quantum simulation closer to reality.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States); Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Quantum Science Center (QSC)
• Sponsoring Organization: USDOE; USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Office of Science (SC), High Energy Physics (HEP)
• Grant/Contract Number: 89233218CNA000001
• OSTI ID: 1810422
• Report Number(s): LA-UR-20-23338; 119; PII: 451
• Journal Information: npj Quantum Information, Journal Name: npj Quantum Information Journal Issue: 1 Vol. 7; ISSN 2056-6387
• Publisher: Nature Publishing GroupCopyright Statement
• Country of Publication: United Kingdom
• Language: English