Quantum interference enables constant-time quantum information processing

TL;DR

This paper introduces a quantum approach to perform the Kravchuk-Fourier transform in constant time using a single quantum gate, potentially revolutionizing digital signal processing by leveraging quantum interference.

Contribution

It presents a novel quantum algorithm for the fractional Kravchuk-Fourier transform that operates in constant time with a single gate, unlike classical methods.

Findings

Quantum $d$-nary architecture achieves input-size-independent processing time.

The method employs multiphoton Hong-Ou-Mandel effect for gate implementation.

Scalable with existing quantum technologies for diverse applications.

Abstract

It is an open question how fast information processing can be performed and whether quantum effects can speed up the best existing solutions. Signal extraction, analysis and compression in diagnostics, astronomy, chemistry and broadcasting builds on the discrete Fourier transform. It is implemented with the Fast Fourier Transform (FFT) algorithm that assumes a periodic input of specific lengths, which rarely holds true. A less-known transform, the Kravchuk-Fourier (KT), allows one to operate on finite strings of arbitrary length. It is of high demand in digital image processing and computer vision, but features a prohibitive runtime. Here, we report a one-step computation of a fractional quantum KT. A quantum $d$-nary (qudit) architecture we use comprises only one gate and offers processing time independent of the input size. The gate may employ a multiphoton Hong-Ou-Mandel effect. Existing quantum technologies may scale it up towards diverse applications.