Practical numerical integration on NISQ devices

TL;DR

This paper explores implementing a simplified quantum amplitude estimation algorithm for numerical integration on NISQ devices, demonstrating practical circuit optimization and scalability considerations on IBM quantum hardware.

Contribution

It introduces a practical implementation of a QAE algorithm without QPE on NISQ devices, including circuit optimization and scalability analysis.

Findings

Successful implementation on IBM quantum devices

Reduced circuit complexity without QPE

Discussion on scalability to more qubits

Abstract

This paper addresses the practical aspects of quantum algorithms used in numerical integration, specifically their implementation on Noisy Intermediate-Scale Quantum (NISQ) devices. Quantum algorithms for numerical integration utilize Quantum Amplitude Estimation (QAE) (Brassard et al., 2002) in conjunction with Grovers algorithm. However, QAE is daunting to implement on NISQ devices since it typically relies on Quantum Phase Estimation (QPE), which requires many ancilla qubits and controlled operations. To mitigate these challenges, a recently published QAE algorithm (Suzuki et al., 2020), which does not rely on QPE, requires a much smaller number of controlled operations and does not require ancilla qubits. We implement this new algorithm for numerical integration on IBM quantum devices using Qiskit and optimize the circuit on each target device. We discuss the application of this algorithm on two qubits and its scalability to more than two qubits on NISQ devices.