A Trotter-Suzuki approximation for Lie groups with applications to Hamiltonian simulation
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
We present a product formula to approximate the exponential of a skew-Hermitian operator that is a sum of generators of a Lie algebra. The number of terms in the product depends on the structure factors. When the generators have large norm with respect to the dimension of the Lie algebra, or when the norm of the effective operator resulting from nested commutators is less than the product of the norms, the number of terms in the product is significantly less than that obtained from well-known results. We apply our results to construct product formulas useful for the quantum simulation of some continuous-variable and bosonic physical systems, including systems whose potential is not quadratic. For many of these systems, we show that the number of terms in the product can be sublinear or even subpolynomial in the dimension of the relevant local Hilbert spaces, where such a dimension is usually determined by the energy scale of the problem. Our results emphasize the power of quantum computers for the simulation of various quantum systems.
- OSTI ID:
- 22596844
- Journal Information:
- Journal of Mathematical Physics, Vol. 57, Issue 6; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
Bounding the costs of quantum simulation of many-body physics in real space
|
journal | June 2017 |
Nearly Optimal Lattice Simulation by Product Formulas
|
journal | August 2019 |
Hamiltonian Simulation by Qubitization
|
journal | July 2019 |
Compilation by stochastic Hamiltonian sparsification
|
journal | February 2020 |
Bounding the costs of quantum simulation of many-body physics in real space | text | January 2016 |
Hamiltonian Simulation by Qubitization | text | January 2016 |
Similar Records
Optimized Lie–Trotter–Suzuki decompositions for two and three non-commuting terms
Theory of Trotter Error with Commutator Scaling