Periodic Reporting for period 1 - QuantOrder (Finding Order in Large-scale Structures by Quantum Computing)
Berichtszeitraum: 2021-09-01 bis 2023-08-31
The project aimed at pursuing new approaches and ideas for quantum algorithms development with a particular focus on finding large-scale structures in various objects. This is a very timely topic as the first quantum computers that are large and precise enough to provide a practical advantage are expected to arrive in 5-10 years, yet we only know a handful of algorithms that one may want to run on them. The project significantly enhanced the state of the art with the development of novel efficient quantum algorithmic subroutines.
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 The two manuscripts not yet peer-reviewed have also been uploaded to the arXiv preprint server and have already attained a high number of citations (19 and 39 respectively according to Google scholar),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.
• 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.
The first applications of quantum computers will likely involve the simulation of quantum systems. For such problems it is crucially important to prepare the physically relevant states that one wishes to study. Here, our new provably convergent randomized quantum algorithms would be invaluable. Additionally, for learning properties of the arising quantum states our new (essentially) optimal purified mixed state tomography algorithms could yield significant savings and thus effectively speed up the study and potential discovery of new exotic materials. The resulting newfound simulation ability may lead, for example, to the development of new high-temperature superconductors, with potentially very far-reaching implications.