Digital quantum simulation of Schr\"odinger dynamics using adaptive approximations of potential functions

• URL: http://arxiv.org/abs/2212.04942v1
• Date: Fri, 9 Dec 2022 15:51:27 GMT
• Title: Digital quantum simulation of Schr\"odinger dynamics using adaptive approximations of potential functions
• Authors: Tenzan Araki, James Stokes, Shravan Veerapaneni
• Abstract summary: Digital quantum simulation (DQS) of continuous-variable quantum systems in the position basis requires efficient implementation of diagonal unitaries approxing the time evolution operator generated by the potential energy function. We show how adaptive grids can significantly reduce the total gate count at the cost of introducing a small number of ancillary qubits. We demonstrate the circuit construction with both physically motivated and artificially designed potential functions, and discuss their generalizations to higher dimensions.
• Score: 1.9723551683930771
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Digital quantum simulation (DQS) of continuous-variable quantum systems in the position basis requires efficient implementation of diagonal unitaries approximating the time evolution operator generated by the potential energy function. In this work, we provide efficient implementations suitable for potential functions approximable by piecewise polynomials, with either uniform or adaptively chosen subdomains. For a fixed precision of approximation, we show how adaptive grids can significantly reduce the total gate count at the cost of introducing a small number of ancillary qubits. We demonstrate the circuit construction with both physically motivated and artificially designed potential functions, and discuss their generalizations to higher dimensions.

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