Project description
Study investigates noise stability for noisy quantum systems
The noise sensitivity of Boolean functions, which indicates whether a specific random Boolean network constructed from those functions is ordered or chaotic, and applications to percolation have been extensively studied over the last two decades. The EU-funded SensStabComp project aims to extend the study to various stochastic and combinatorial models and explore connections with computer science and quantum information amongst others. Researchers will extend the use of high-dimensional Fourier analysis, an important tool in mathematics, to develop discrete Fourier methods. Another goal is to further develop the ‘argument against quantum computers’, which relates to the feasibility of quantum computing, revealing what governs the behaviour of noisy quantum systems.
Objective
Noise sensitivity and noise stability of Boolean functions, percolation, and other models were introduced in a paper by Benjamini, Kalai, and Schramm (1999) and were extensively studied in the last two decades. We propose to extend this study to various stochastic and combinatorial models, and to explore connections with computer science, quantum information, voting methods and other areas.
The first goal of our proposed project is to push the mathematical theory of noise stability and noise sensitivity forward for various
models in probabilistic combinatorics and statistical physics. A main mathematical tool, going back to Kahn, Kalai, and Linial (1988),
is applications of (high-dimensional) Fourier methods, and our second goal is to extend and develop these discrete Fourier methods.
Our third goal is to find applications toward central old-standing problems in combinatorics, probability and the theory of computing.
The fourth goal of our project is to further develop the ``argument against quantum computers'' which is based on the insight that noisy intermediate scale quantum computing is noise stable. This follows the work of Kalai and Kindler (2014) for the case of noisy non-interacting bosons. The fifth goal of our proposal is to enrich our mathematical understanding and to apply it, by studying connections of the theory with various areas of theoretical computer science, and with the theory of social choice.
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Funding Scheme
ERC-ADG - Advanced GrantHost institution
4610101 Herzliya
Israel