New innovative solutions have been developed with key components as follows:
• New efficient unbiased phase estimation subroutines
• A better understanding of the cryptanalytic relevance of certain quantum linear algebra techniques
• New natural quantum analogues of classical Monte Carlo methods
Largely building on these advancements, 8 manuscripts have been prepared, 6 of which have already been peer reviewed and published. The main topics of the publications are as follows:
• (Essentially) Optimal purified mixed state tomography
• (Essentially) Optimal quantum algorithms for finding the principal eigenvector
• Improved understanding of the quantum cryptanalysis of multivariate cryptography
• Advanced quantum-inspired classical sampling algorithms (two publications)
• Better understanding of multivariate quantum linear algebra methods
• Demonstrating an exponential speed-up for graph property testing
• Development of new, provably convergent randomized quantum algorithms
The results have been published in leading computer science journals (Journal of the ACM, SIAM Journal on Computing) and conferences (SODA), and a leading community-led quantum journal (Quantum Journal). The two manuscripts not yet peer-reviewed have also been uploaded to the arXiv preprint server and have already attained a high number of citations (19 and 39 respectively according to Google scholar), while one of them have been accepted at QIP'26, the premier venue for presenting theoretical
results in quantum information and computation.
