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Hamiltonian simulation in the low energy subspace

Thursday February 18, 2021
3:30 pm

 Presenter:  Burak Sahinoglu, Los Alamos National Lab
 Series:  CQuIC Seminars
 Abstract:  In this talk we will be concerned with 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 novel 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.

This is a joint work with Rolando D. Somma.

Check https://arxiv.org/abs/2006.02660 for the preprint, and https://youtu.be/iz4jihYShEg for a shorter version of the talk at QIP 2021.
 Host:  Elizabeth Crosson
 Location:  Zoom

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