Measuring Trotter error and its application to precision-guaranteed Hamiltonian simulations

Trotterization is the most common and convenient approximation method for Hamiltonian simulations on digital quantum computers, but estimating its error accurately is computationally difficult for large quantum systems. Here, we develop a method for measuring the Trotter error without ancillary qubi...

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Veröffentlicht in:	arXiv.org 2024-07
Hauptverfasser:	Ikeda, Tatsuhiko N, Kono, Hideki, Fujii, Keisuke
Format:	Artikel
Sprache:	eng
Schlagworte:	Algorithms Circuits Error analysis Physics - Computational Physics Physics - High Energy Physics - Lattice Physics - Materials Science Physics - Quantum Physics Physics - Strongly Correlated Electrons Time dependence Upper bounds
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description	Trotterization is the most common and convenient approximation method for Hamiltonian simulations on digital quantum computers, but estimating its error accurately is computationally difficult for large quantum systems. Here, we develop a method for measuring the Trotter error without ancillary qubits on quantum circuits by combining the $m$th- and $n$th-order (\(m
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Here, we develop a method for measuring the Trotter error without ancillary qubits on quantum circuits by combining the $m$th- and $n$th-order ($m<n$) Trotterizations rather than consulting with mathematical error bounds. Using this method, we make Trotterization precision-guaranteed, developing an algorithm named Trotter$(m,n)$, in which the Trotter error at each time step is within an error tolerance $\epsilon$ preset for our purpose. Trotter$(m,n)$ is applicable to both time- independent and dependent Hamiltonians, and it adaptively chooses almost the largest stepsize $\mathrm{d}t$, which keeps quantum circuits shallowest within the error tolerance. 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subjects	Algorithms Circuits Error analysis Physics - Computational Physics Physics - High Energy Physics - Lattice Physics - Materials Science Physics - Quantum Physics Physics - Strongly Correlated Electrons Time dependence Upper bounds
title	Measuring Trotter error and its application to precision-guaranteed Hamiltonian simulations
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