Dataset Information

Destructive Error Interference in Product-Formula Lattice Simulation.

ABSTRACT: Quantum computers can efficiently simulate the dynamics of quantum systems. In this Letter, we study the cost of digitally simulating the dynamics of several physically relevant systems using the first-order product-formula algorithm. We show that the errors from different Trotterization steps in the algorithm can interfere destructively, yielding a much smaller error than previously estimated. In particular, we prove that the total error in simulating a nearest-neighbor interacting system of n sites for time t using the first-order product formula with r time slices is O(nt/r+nt^{3}/r^{2}) when nt^{2}/r is less than a small constant. Given an error tolerance ϵ, the error bound yields an estimate of max{O(n^{2}t/ϵ),O(n^{2}t^{3/2}/ϵ^{1/2})} for the total gate count of the simulation. The estimate is tighter than previous bounds and matches the empirical performance observed in Childs et al. [Proc. Natl. Acad. Sci. U.S.A. 115, 9456 (2018)PNASA60027-842410.1073/pnas.1801723115]. We also provide numerical evidence for potential improvements and conjecture an even tighter estimate for the gate count.

SUBMITTER: Tran MC

PROVIDER: S-EPMC7693083 | biostudies-literature | 2020 Jun

REPOSITORIES: biostudies-literature

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Destructive Error Interference in Product-Formula Lattice Simulation.

Tran Minh C MC Chu Su-Kuan SK Su Yuan Y Childs Andrew M AM Gorshkov Alexey V AV

Physical review letters 20200601 22

Quantum computers can efficiently simulate the dynamics of quantum systems. In this Letter, we study the cost of digitally simulating the dynamics of several physically relevant systems using the first-order product-formula algorithm. We show that the errors from different Trotterization steps in the algorithm can interfere destructively, yielding a much smaller error than previously estimated. In particular, we prove that the total error in simulating a nearest-neighbor interacting system of n ...[more]

PMID: 32567903

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Project description:Ionic transport in solid electrolytes can often be approximated as ions performing a sequence of hops between distinct lattice sites. If these hops are uncorrelated, quantitative relationships can be derived that connect microscopic hopping rates to macroscopic transport coefficients; i.e. tracer diffusion coefficients and ionic conductivities. In real materials, hops are uncorrelated only in the dilute limit. At non-dilute concentrations, the relationships between hopping frequency, diffusion coefficient and ionic conductivity deviate from the random walk case, with this deviation quantified by single-particle and collective correlation factors, f and fI, respectively. These factors vary between materials, and depend on the concentration of mobile particles, the nature of the interactions, and the host lattice geometry. Here, we study these correlation effects for the garnet lattice using lattice-gas Monte Carlo simulations. We find that, for non-interacting particles (volume exclusion only), single-particle correlation effects are more significant than for any previously studied three-dimensional lattice. This is attributed to the presence of two-coordinate lattice sites, which causes correlation effects intermediate between typical three-dimensional and one-dimensional lattices. Including nearest-neighbour repulsion and on-site energies produces more complex single-particle correlations and introduces collective correlations. We predict particularly strong correlation effects at xLi=3 (from site energies) and xLi=6 (from nearest-neighbour repulsion), where xLi=9 corresponds to a fully occupied lithium sublattice. Both effects are consequences of ordering of the mobile particles. Using these simulation data, we consider tuning the mobile-ion stoichiometry to maximize the ionic conductivity, and show that the 'optimal' composition is highly sensitive to the precise nature and strength of the microscopic interactions. Finally, we discuss the practical implications of these results in the context of lithium garnets and other solid electrolytes.

Dataset Information

Destructive Error Interference in Product-Formula Lattice Simulation.

Publications

Destructive Error Interference in Product-Formula Lattice Simulation.

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