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Corrected quantum walk for optimal Hamiltonian simulation

Authors:

Leonardo NovoAuthors Info & Claims

Quantum Information & Computation, Volume 16, Issue 15-16

Pages 1295 - 1317

Published: 01 November 2016 Publication History

Abstract

We describe a method to simulate Hamiltonian evolution on a quantum computer by repeatedly using a superposition of steps of a quantum walk, then applying a correction to the weightings for the numbers of steps of the quantum walk. This correction enables us to obtain complexity which is the same as the lower bound up to double-logarithmic factors for all parameter regimes. The scaling of the query complexity is O(τ log log τ/log log log τ + log(1/ε)) where τ := t||H||_maxd, for ε the allowable error, t the time, ||H||_max the max-norm of the Hamiltonian, and d the sparseness. This technique should also be useful for improving the scaling of the Taylor series approach to simulation, which is relevant to applications such as quantum chemistry.

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Digital Library

Cited By

Vazquez AHiptmair RWoerner S(2022)Enhancing the Quantum Linear Systems Algorithm Using Richardson ExtrapolationACM Transactions on Quantum Computing10.1145/34906313:1(1-37)Online publication date: 14-Jan-2022
https://dl.acm.org/doi/10.1145/3490631
Novo LBerry D(2017)Improved hamiltonian simulation via a truncated taylor series and correctionsQuantum Information & Computation10.5555/3179553.317955817:7-8(623-635)Online publication date: 1-Jun-2017
https://dl.acm.org/doi/10.5555/3179553.3179558

Corrected quantum walk for optimal Hamiltonian simulation
1. Theory of computation

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cover image Quantum Information & Computation

Quantum Information & Computation Volume 16, Issue 15-16

November 2016

140 pages

ISSN:1533-7146

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Rinton Press, Incorporated

Paramus, NJ

Publication History

Published: 01 November 2016

Revised: 01 September 2016

Received: 18 June 2016

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Cited By

Vazquez AHiptmair RWoerner S(2022)Enhancing the Quantum Linear Systems Algorithm Using Richardson ExtrapolationACM Transactions on Quantum Computing10.1145/34906313:1(1-37)Online publication date: 14-Jan-2022
https://dl.acm.org/doi/10.1145/3490631
Novo LBerry D(2017)Improved hamiltonian simulation via a truncated taylor series and correctionsQuantum Information & Computation10.5555/3179553.317955817:7-8(623-635)Online publication date: 1-Jun-2017
https://dl.acm.org/doi/10.5555/3179553.3179558

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