Periodic Reporting for period 4 - RESOURCE Q (Efficient Conversion of Quantum Information Resources)
Reporting period: 2024-06-01 to 2025-11-30
The project studied the conversion of quantum information resources. In contrast to our usual information resources (e.g. internet, hard drive, router, phone), quantum information resources (built e.g. from single photons and single atoms), are fundamentally different and more powerful. The project explored how these new resources can be used to obtain new communication scenarios (faster, more secure, with noisy encoders and decoders) and how they can be used to obtain a better description of larger quantum systems (eg. new materials). The project was theoretical, which means that mathematics was employed to achieve the results. In particular, the theory of matrices and tensors (multidimensional arrays of numbers) played an important role. Tensors are also important in other areas of computer science, for instance the fast multiplication of large matrices, and the project also contributed to this understanding.
We have built a toolbox for making quantum algorithms with quantum input and quantum output run on noisy hardware (fault-tolerance). Traditionally, fault-tolerance has been only considered when taking a classical input and output (e.g. in the famous factoring of large numbers). Our work allows fault-tolerance to be extended to scenarios in quantum communication (where the encoder is preparing a quantum state for transmission through the quantum channel) or as subroutine in quantum algorithms, where state preparation is an important subroutine. We have also shown that one can use quantum particles to better verify the position of a person that pretends to be at a different location (quantum position verification), this could, for instance, be used as an additional security token on the internet.
We have also made progress in the understanding of multiparticle entanglement via research on the mathematics of tensors. Concretely, this has brought tools from algebraic complexity theory to the research on tensor networks, directly relevant in the description of quantum matter (e.g. superconductivity). This has led to the concept of an effective bond dimension (with a concrete example of a better description of the resonating valence bond state) as well as a new numerical procedure for finding better tensor network representations. The quantum information intuition also helped craft new functions for the study of tensors as used in algebraic complexity theory (e.g. as used in the open quest to finding better algorithms for multiplying large matrices). Our "quantum functionals" are the first concrete family of functions, since Strassen proposed their study in the 80s. Our progress has led to barriers (lower bounds) to Strassen's laser method, the state-of-the-art method to build new algorithms. The success in transferring tools from algebraic complexity to tensor network research opened the study of new mathematical structures, such as novel asymptotic orders for tensors.
We have also made progress in the understanding of multiparticle entanglement via research on the mathematics of tensors. Concretely, this has brought tools from algebraic complexity theory to the research on tensor networks, directly relevant in the description of quantum matter (e.g. superconductivity). This has led to the concept of an effective bond dimension (with a concrete example of a better description of the resonating valence bond state) as well as a new numerical procedure for finding better tensor network representations. The quantum information intuition also helped craft new functions for the study of tensors as used in algebraic complexity theory (e.g. as used in the open quest to finding better algorithms for multiplying large matrices). Our "quantum functionals" are the first concrete family of functions, since Strassen proposed their study in the 80s. Our progress has led to barriers (lower bounds) to Strassen's laser method, the state-of-the-art method to build new algorithms. The success in transferring tools from algebraic complexity to tensor network research opened the study of new mathematical structures, such as novel asymptotic orders for tensors.
The proposal of a fault-tolerant toolbox for quantum algorithms with quantum input and quantum output broadens the concept of fault-tolerance from stand-alone quantum computers to quantum computers that interact with other quantum systems. The work has been presented at QIP, the premier series of the field, and may be regarded as opening a new research direction.
The increased understanding of asymptotic tensor parameters obtained in this project (incl. the barriers) has found acclaim in the theoretical computer science community (2x STOC papers). The success in transferring tools from algebraic complexity to tensor network research opened the study of new mathematical structures built from tensors.
The security proof for position-based cryptography that we provided gives, besides QKD, the basis for a second realistically near-term implementation of a quantum cryptographic protocol. This is a very tangible research outcome of the project.
The increased understanding of asymptotic tensor parameters obtained in this project (incl. the barriers) has found acclaim in the theoretical computer science community (2x STOC papers). The success in transferring tools from algebraic complexity to tensor network research opened the study of new mathematical structures built from tensors.
The security proof for position-based cryptography that we provided gives, besides QKD, the basis for a second realistically near-term implementation of a quantum cryptographic protocol. This is a very tangible research outcome of the project.