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Results for “Off-diagonal series expansion”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Quantum Algorithm for Simulating Hamiltonian Dynamics with an Off-diagonal Series Expansion

We propose an efficient quantum algorithm for simulating the dynamics of general Hamiltonian systems. Our technique is based on a power series expansion of the time-evolution operator in its off-diagonal terms. The expansion decouples the dynamics due to the diagonal component of the Hamiltonian from the dynamics generated by its off-diagonal part, which we encode using the linear combination of unitaries technique. Our method has an optimal dependence on the desired precision and, as we illustrate, generally requires considerably fewer resources than the current state-of-the-art. We provide an analysis of resource costs for several sample models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Calculating the divided differences of the exponential function by addition and removal of inputs

We introduce a method for calculating the divided differences of the exponential function by means of addition and removal of items from the input list to the function. Our technique exploits a new identity related to divided differences recently derived by F. Zivcovich. We show that upon adding an item to or removing an item from the input list of an already evaluated exponential, the re-evaluation of the divided differences can be done with only O(sn) floating point operations and O(sn) bytes of memory, where [z 0 ,...,z n ] are the inputs and s ∝ max i,j |z i – z j |. We demonstrate our algorithm’s ability to deal with input lists that are orders-of-magnitude longer than the maximal capacities of the current state-of-the-art. Here, we discuss in detail one practical application of our method: the efficient calculation of weights in the off-diagonal series expansion quantum Monte Carlo algorithm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Permutation matrix representation quantum Monte Carlo

We present a quantum Monte Carlo algorithm for the simulation of general quantum and classical many-body models within a single unifying framework. The algorithm builds on a power series expansion of the quantum partition function in its off-diagonal terms and is both parameter-free and Trotter error-free. In our approach, the quantum dimension consists of products of elements of a permutation group. As such, it allows for the study of a very wide variety of models on an equal footing. To demonstrate the utility of our technique, we use it to clarify the emergence of the sign problem in the simulations of non-stoquastic physical models. We showcase the flexibility of our algorithm and the advantages it offers over existing state-of-the-art by simulating transverse- field Ising model Hamiltonians and comparing the performance of our technique against that of the stochastic series expansion algorithm. Furthermore, we also study a transverse-field Ising model augmented with randomly chosen two-body transverse-field interactions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗