Quantum Fourier-Transform-enhanced quantum reservoir computing

L’équipe Physique-Mathématique s’intéresse à la description quantique des quatre grandes forces de l’Univers. Plus précisément, elle mène des recherches en gravitation quantique, cosmologie, sur les théories phénoménologiques au-delà du modèle standard et l’interaction lumière-matière. Elle explore également l’impact que la physique et les technologies quantiques pourraient avoir sur le domaine de l’intelligence artificielle.

Scientific Context

Reservoir computing is a machine learning model tailored for sequential and time-series data. Its specificities and interests lie in possible implementations into physical hardware. Reservoir computing has naturally evolved into Quantum Reservoir Computing, for which hardware consists of quantum systems. Quantum Reservoir Computing combines quantum dynamics with the simplicity and robustness of classical machine-learning readout. This framework aims to leverage quantum properties like superposition and entanglement for advanced data processing through machine learning models.

Recent work on the role of spectral methods in machine learning has highlighted a potentially important connection between Fourier analysis and quantum algorithms. In particular, the Quantum Fourier Transform is a fundamental quantum algorithm that transforms the amplitudes of a quantum state into a Fourier basis. For suitable problems, efficient Quantum Fourier Transform algorithms can exploit the structure of quantum states in a way that is not directly available to classical algorithms.

This observation raises an interesting question for quantum reservoir computing. Can the quantum Fourier Transform be a useful tool in the quantum reservoir computing framework?

Internship Topic

This master’s intership will investigate this question that can be refined into the following:

How can the Quantum Fourier Transform be integrated into a quantum reservoir-computing architecture, and under what conditions it can improve or modify the computational properties o the reservoir computing framework ?

First, the student will determine mathematically what should be Fourier transformed in a Quantum Reservoir Computing protocol. The quantum Fourier transform acts on the amplitudes of a quantum state, whereas a conventional reservoir readout generally acts on measured observables or expectation values. It is therefore important to distinguish carefully between:

• the Fourier transform of the classical input signal;

• the Fourier transform of the temporal sequence of reservoir outputs;

• the QFT applied to the amplitudes of the quantum reservoir state;

• measurements performed in the Fourier basis.

Second, the internship will investigate where the Quantum Fourier Transform should be placed in the reservoir-computing algorithm. Several possibilities can be considered, including applying the Quantum Fourier Transform before measurement, using a spectral during the reservoir evolution, or incorporating the Quantum Fourier Transform into the input encoding.

Third, the student will determine whether the resulting architecture provides useful reservoir features that are different from those obtained with a conventional Quantum Reservoir Computing protocol.

Objectives

1. Establish a reference quantum reservoir-computing model
The student will first implement a simple quantum reservoir computing model without a Fourier transform.

2. Implement the Quantum Fourier Transform
The student will study the quantum Fourier transform mathematically and implement it as a quantum circuit.

3. Integrate the Quantum Fourier Transform into Quantum Reservoir Computing
The central part of the thesis will investigate different possible architectures.

4. Evaluate the effect on reservoir computing performance
The QFT-enhanced reservoirs will be evaluated using standard temporal machine-learning tasks

5. Study computational complexity and implementation constraints
An important part of the thesis will be a careful analysis of computational cost.

The Quantum Fourier Transform is often described as a quantum analogue of the classical discrete Fourier transform, but this description can be misleading if interpreted as automatically implying a practical speedup. The relevant comparison depends on what information must be prepared, accessed and measured.

This analysis is particularly important for identifying whether the QFT can provide a meaningful computational benefit within QRC rather than simply increasing the complexity of the reservoir.

We are looking for a Master 2 student with a solid background in one of the following fields:

• Quantum physics

• Theoretical physics or computational physics

• Scientific computing (Python, Julia)

• Data science applied to dynamical systems