Periodic Reporting for period 2 - AlgoQIP (Beyond Shannon: Algorithms for optimal information processing)
Reporting period: 2022-07-01 to 2023-12-31
Quantum technologies have the potential to revolutionise computation and communication. However, a major bottleneck in achieving this potential is the difficulty and cost of dealing with unwanted noise affecting quantum devices. Despite important research activity in designing better error correcting codes and fault-tolerant schemes, the fundamental limits of computation and communication in the presence of noise are far from being understood.
The objective of this project is to develop mathematical and algorithmic tools to determine optimal ways of encoding quantum information in imperfect devices. These tools will impact the development of quantum technologies by identifying the minimal resources needed to achieve information-processing tasks.
The objective of this project is to develop mathematical and algorithmic tools to determine optimal ways of encoding quantum information in imperfect devices. These tools will impact the development of quantum technologies by identifying the minimal resources needed to achieve information-processing tasks.
We have designed algorithms to obtain certified bounds on the security of protocols in quantum cryptography. This tool can be used to automatically search for protocols that are adapted to the actual quantum devices, for example protocols that can tolerate higher levels of noise. In addition, at the mathematical level, we have significantly generalised the tool known as "entropy accumulation" to be applicable to analyse the security of a wider class of protocols. We expect that entropy accumulation will become one of the main tools used to establish security of a given scheme. In terms of communication networks, we gave evidence that quantum entanglement has the potential of significantly increasing the communication capacities of a classical communication network.
Regarding quantum computation in the presence of faults, we have established fundamental limitations on the tradeoff between memory, time and the geometry of the quantum computation architecture. Moreover, we developed an algorithmic tool to determine bounds on how much information can be stored in a quantum device given a mathematical model of this device.
Regarding quantum computation in the presence of faults, we have established fundamental limitations on the tradeoff between memory, time and the geometry of the quantum computation architecture. Moreover, we developed an algorithmic tool to determine bounds on how much information can be stored in a quantum device given a mathematical model of this device.
For the remaining time in the project, we expect to further improve the efficiency of the tools we have introduced and make further progress in determining optimal ways of encoding quantum information in a device.