Hamiltonian simulation in the low-energy subspace
- URL: http://arxiv.org/abs/2006.02660v2
- Date: Thu, 9 Sep 2021 17:01:15 GMT
- Title: Hamiltonian simulation in the low-energy subspace
- Authors: Burak \c{S}ahino\u{g}lu and Rolando D. Somma
- Abstract summary: 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 $H$.
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 $H$.
- Score: 0.12891210250935145
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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.
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