An Amplitude-Based Implementation of the Unit Step Function on a Quantum Computer

TL;DR

This paper presents a novel amplitude-based method for implementing the unit step function on quantum computers, enabling non-linear activation modeling crucial for quantum neural networks, with practical demonstrations on current hardware.

Contribution

It introduces a single-measurement, amplitude-based approach for approximating the unit step function on quantum computers, expanding the toolkit for quantum neural network activation functions.

Findings

High-precision results obtained from up to 8 qubits

Successful implementation on NISQ hardware with error mitigation

Demonstrated feasibility of non-linear functions in quantum circuits

Abstract

Modelling non-linear activation functions on quantum computers is vital for quantum neurons employed in fully quantum neural networks, however, remains a challenging task. We introduce an amplitude-based implementation for approximating non-linearity in the form of the unit step function on a quantum computer. Our approach expands upon repeat-until-success protocols, suggesting a modification that requires a single measurement only. We describe two distinct circuit types which receive their input either directly from a classical computer, or as a quantum state when embedded in a more advanced quantum algorithm. All quantum circuits are theoretically evaluated using numerical simulation and executed on Noisy Intermediate-Scale Quantum hardware. We demonstrate that reliable experimental data with high precision can be obtained from our quantum circuits involving up to 8 qubits, and up to 25 CX-gate applications, enabled by state-of-the-art hardware-optimization techniques and measurement error mitigation.