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Trapped Ion Quantum Computing Quantum Simulation

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

arXiv
Authors: Boris Arseniev, Dmitry Guskov, Richik Sengupta, Igor Zacharov

Year

2024

Paper ID

56954

Status

Preprint

Abstract Read

~2 min

Abstract Words

105

Citations

N/A

Abstract

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.

Why This Paper Matters

  • This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
  • It adds a 2024 reference point for readers tracking recent quantum research.
  • We explore the utilization of higher-order discretization techniques in optimizing the gate count needed for quantum computer based solutions of partial differential equations.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2412.19232 [2] arXiv https://arxiv.org/abs/2412.19232 [3] Publisher https://arxiv.org/abs/2412.19232

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