High-order schemes for solving partial differential equations on a quantum computer

被引：0
作者：
Arseniev, Boris [1 ]
Guskov, Dmitry [1 ]
Sengupta, Richik [1 ,2 ]
Zacharov, Igor [1 ]
机构：
[1] Skolkovo Institute of Science and Technology, Moscow
[2] Artificial Intelligence Research Institute, Moscow
来源：
Physical Review A | 2025年 / 111卷 / 04期
关键词：
Hamiltonians - Numerical methods - Quantum channel - Wave equations;
D O I：
10.1103/PhysRevA.111.042625
中图分类号：
学科分类号：
摘要：
We explore the utilization of higher-order discretization techniques in optimizing the gate count needed for quantum computer based solutions of partial differential equations. To accomplish this, we present an efficient approach for decomposing d-band diagonal matrices into Pauli strings that are grouped into mutually commuting sets. Using numerical simulations of the one-dimensional wave equation, we show that higher-order methods can reduce the number of qubits necessary for discretization, similar to the classical case, although they do not decrease the number of Trotter steps needed to preserve solution accuracy. This result has important consequences for the practical application of quantum algorithms based on Hamiltonian evolution. © 2025 American Physical Society.
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