Hamiltonian Simulation in the Interaction Picture
By Guang Hao Low, Nathan Wiebe. 2018
188 citations recorded by the source corpus.
We present a low-space overhead simulation algorithm based on the truncated Dyson series for time-dependent quantum dynamics. This algorithm is applied to simulating time-independent Hamiltonians by transitioning to the interaction picture, where some portions are made time-dependent. This can provide a favorable complexity trade-off as the algorithm scales exponentially better with derivatives of the time-dependent component than the original Hamiltonian. We show that this leads to an exponential improvement in gate complexity for simulating some classes of diagonally dominant Hamiltonian. Additionally we show that this can reduce the gate-complexity scaling for simulating $N$-site Hubbard models for time $t$ with arbitrary long-range interactions as well as reduce the cost of quantum chemistry simulations within a similar-sized plane-wave basis to $\widetilde{\mathcal{O}}(N^2t)$ from $\widetilde{\mathcal{O}}(N^{11/3}t)$. We also show a quadratic improvement in query complexity for simulating sparse time-dependent Hamiltonians, which may be of independent interest.
Subfields: Computer Networks and Communications, Information Systems and Management
View Paper: https://www.semanticscholar.org/paper/a451dd528f431feed65ce76bcff58ef48d5ca8b8
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In Computer Networks and Communications
- William J. Huggins
- Jarrod R. McClean
- Hartmut Neven
- Austin G. Fowler
- Nathan Wiebe
- Craig Gidney
- Ryan Babbush
Citations in the corpus
- Hamiltonian Simulation by Qubitization (2016, background): “More refined simulation algorithms can exploit prior knowledge of geometric locality [44, 45], Hamiltonian induced one-norm [46], spectral norm [47], and separation of energy scales [48].”
- Hartree-Fock on a superconducting qubit quantum computer (2020, background): “Accordingly, the most efficient quantum algorithms for chemistry [12–15] require that one perform the simulation in more structured bases with asymptotically fewer terms [16–18], necessitating that U κ (cid:63) is applied explicitly at the beginning of the computation.”