Dr. Shantanav Chakraborty and his students, Aditya Morolia, a dual degree student,
(CCSNB) and Anurudh Peduri, Computer Science and Engineering – dual degree student who graduated recently and currently a Ph.D student at Ruhr University, Bochum published a paper on Quantum Regularized Least Squares in the journal Quantum. Research work as explained by the authors:
Linear regression is a widely used technique to fit linear models and finds widespread applications across different areas such as machine learning and statistics. In most real-world scenarios, however, linear regression problems are often ill-posed or the underlying model suffers from overfitting, leading to erroneous or trivial solutions. This is often dealt with by adding extra constraints, known as regularization. In this paper, we use the frameworks of block-encoding and quantum singular value transformation (QSVT) to design the first quantum algorithms for quantum least squares with general ℓ2-regularization. These include regularized versions of quantum ordinary least squares, quantum weighted least squares, and quantum generalized least squares. Our quantum algorithms substantially improve upon prior results on
quantum ridge regression (polynomial improvement in the condition number and an exponential improvement in accuracy), which is a particular case of our result.
To this end, we assume approximate block-encodings of the underlying matrices as input and use robust QSVT algorithms for various linear algebra operations. In particular, we develop a variable-time quantum algorithm for matrix inversion using QSVT, where we use quantum eigenvalue discrimination as a subroutine instead of gapped phase estimation. This ensures that substantially fewer ancilla qubits are required for this procedure than prior results. Owing to the generality of the block-encoding framework, our algorithms are applicable to a variety of input models and can also be seen as improved and generalized versions of prior results on standard (non-regularized) quantum least squares algorithms.
Full paper: https://quantum-journal.org/papers/q-2023-04-27-988/
Quantum is a non-profit and open access peer-reviewed journal that provides high visibility for quality research on quantum science and related fields. It is an effort by researchers and for researchers to make science more open and publishing more transparent and efficient.
It addresses the growing dissatisfaction in the community with traditional, profit driven and impact factor focused models of scientific publishing, their disproportionate effect on academics’ careers, and the recent call for immediate open access publishing by the European Council.
Quantum is an online journal that provides a rigorous curating and peer-review service, and publishes high quality research, both theoretical and experimental. The main editorial criteria are correctness, significance, and clarity. By focusing on the essential, Quantum dramatically speeds up the publication process, reducing costs and hassle for authors, referees, and editors. For exceptional publications, Quantum features editorial highlights and publicity through traditional and social media.
April 2023