2019/02/28 by Ian D. Kivlichan, Craig Gidney, Dominic W. Berry +9 · 2 citations
Physics and Astronomy · #quant-ph #physics.chem-ph
paper · pdf · doi:10.22331/q-2020-07-16-296
published as Quantum 4, 296 (2020) · 45 pages, 15 figures. Only difference from v3 is change to CC BY 4.0 license
arxiv created 2020/07/13 · arxiv updated 2020/07/20
Recent work has deployed linear combinations of unitaries techniques to reduce the cost of fault-tolerant quantum simulations of correlated electron models. Here, we show that one can sometimes improve upon those results with optimized implementations of Trotter-Suzuki-based product formulas. We show that low-order Trotter methods perform surprisingly well when used with phase estimation to compute relative precision quantities (e.g. energies per unit cell), as is often the goal for condensed-phase systems. In this context, simulations of the Hubbard and plane-wave electronic structure models with N < 105 fermionic modes can be performed with roughly O(1) and O(N2) T complexities. We perform numerics revealing tradeoffs between the error and gate complexity of a Trotter step; e.g., we show that split-operator techniques have less Trotter error than popular alternatives. By compiling to surface code fault-tolerant gates and assuming error rates of one part per thousand, we show that one can error-correct quantum simulations of interesting, classically intractable instances with a few hundred thousand physical qubits.