Hamiltonian Encoding for Quantum Approximate Time Evolution of Kinetic Energy Operator

TL;DR

This paper introduces a novel quantum encoding method called QATE for simulating kinetic energy evolution, achieving lower gate complexity and improved fidelity on quantum hardware.

Contribution

The paper presents a new quantum encoding technique for time evolution that reduces gate complexity and enhances fidelity compared to existing methods.

Findings

Gate complexity is sub-quadratic in the number of qubits.

Experimental results show improved fidelity in simulating Gaussian wave packets.

Method successfully implemented on IBM quantum hardware.

Abstract

The time evolution operator plays a crucial role in the precise computation of chemical experiments on quantum computers and holds immense promise for advancing the fields of physical and computer sciences, with applications spanning quantum simulation and machine learning. However, the construction of large-scale quantum computers poses significant challenges, prompting the need for innovative and resource-efficient strategies. Traditional methods like phase estimation or variational algorithms come with certain limitations such as the use of classical optimization or complex quantum circuitry. One successful method is the Trotterization technique used for quantum simulation, specifically in atomic structure problems with a gate complexity of approximately O(n^2) for an n-qubit realization. In this work, we have proposed a new encoding method, namely quantum approximate time evolution (QATE) for the quantum implementation of the kinetic energy operator as a diagonal unitary operator considering the first quantization level. The theoretical foundations of our approach are discussed, and experimental results are obtained on an IBM quantum machine. Our proposed method offers gate complexity in sub-quadratic polynomial with qubit size $n$ which is an improvement over previous work. Further, the fidelity improvement for the time evolution of the Gaussian wave packet has also been demonstrated.