Efficient Product Formulas for Commutators and Applications to Quantum
Simulation
- URL: http://arxiv.org/abs/2111.12177v1
- Date: Tue, 23 Nov 2021 22:27:20 GMT
- Title: Efficient Product Formulas for Commutators and Applications to Quantum
Simulation
- Authors: Yu-An Chen, Andrew M. Childs, Mohammad Hafezi, Zhang Jiang, Hwanmun
Kim, Yijia Xu
- Abstract summary: We construct product formulas for exponentials of commutators.
We show how to use the product formulas in a digital protocol for counterdiabatic driving.
- Score: 4.523323031658363
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We construct product formulas for exponentials of commutators and explore
their applications. First, we directly construct a third-order product formula
with six exponentials by solving polynomial equations obtained using the
operator differential method. We then derive higher-order product formulas
recursively from the third-order formula. We improve over previous recursive
constructions, reducing the number of gates required to achieve the same
accuracy. In addition, we demonstrate that the constituent linear terms in the
commutator can be included at no extra cost. As an application, we show how to
use the product formulas in a digital protocol for counterdiabatic driving,
which increases the fidelity for quantum state preparation. We also discuss
applications to quantum simulation of one-dimensional fermion chains with
nearest- and next-nearest-neighbor hopping terms, and two-dimensional
fractional quantum Hall phases.
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