ASTQIT · Applications of the Schur Transform to Quantum Information Theory
FP6 — Marie Curie Actions (Human Resources and Mobility)
- Duration
- 2006-09-01 → 2008-08-31
- EU contribution
- €160,180
- Participants
- 1
- Scheme
- IIF
Lines connect the coordinator with its partners.
Results in brief
Final Activity Report Summary - ASTQIT (Applications of the Schur Transform to Quantum Information Theory)
Quantum computation and communication represent qualitative new methods of information processing, with potentially revolutionary applications to cryptography, algorithms and other tasks. However, many current proposals for quantum communication protocols require impractical amounts of computation on the sending and receiving sides. Our proposal was to use a particular mathematical tool, known as Schur duality, to provide computationally efficient methods for implementing these protocols on quantum computers. During the project we produced a number of efficient new quantum algorithms for use in communication tasks. One of the most significant algorithms was known as the Schur transform. This converted quantum information from a standard form into an alternative form, known as the Schur basis, in which certain manipulations relevant to communication were more readily carried out.
Data: CORDIS, © European Union
Project objective
Quantum computation and quantum information offer qualitatively new capabilities; such as provably secure communication and efficient solutions to computational problems previously believed intractable. However, realizing these possibilities will require techniques for dealing with quantum noise that are efficient in their use of both computational and communication resources. Many information-theoretic solutions achieve the optimal rates of communication but are impossible to apply because they require exponentially large quantum computing resources. One promising new approach to efficiently manipulating quantum information is the Schur transform [1], an algorithm which, similarly to the quantum Fourier transform, allows a quantum computer to efficiently address non-local degrees of freedom in quantum registers.We propose to use the Schur transform to develop practical quantum circuits for a wide range of tasks in quantum information theory, such as remote state preparation, coding for known or unknown quantum channels, mixed state data compression, optimal state estimation and hypothesis testing. In many cases, such as remote state preparation and channel coding, the information-theoretically optimal solutions are known, but we will use the Schur transform to develop novel efficient algorithms to implement them. In others, such as coding for unknown quantum channels, there are not even any computationally inefficient solutions that are currently known, and we hope to use the insights from the Schur transform to solve these problems for the first time. [1] D. Bacon, I. Chuang and A. Harrow, Efficient Quantum Circuits for Schur and Clebsch-Gordan Transforms"; arxiv.org eprint quant-ph/0407082 (2004)."
Original text from CORDIS.
Participants
- UNIVERSITY OF BRISTOL · BRISTOL, CLIFTONCoordinatorUnited Kingdom
Links
Data: CORDIS, © European Union