Practical numerical integration on NISQ devices
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.
Kwangmin Yu Hyunkyung Lim Pooja Rao