Descrizione del progetto
Alcuni studi esaminano la stabilità del rumore per sistemi quantistici rumorosi
La sensibilità al rumore delle funzioni booleane, che indica se una specifica rete booleana casuale costruita a partire da tali funzioni sia ordinata o caotica, e le applicazioni alla percolazione sono state ampiamente studiate nel corso degli ultimi due decenni. Il progetto SensStabComp, finanziato dall’UE, si propone di estendere lo studio a vari modelli stocastici e combinatori ed esplora, tra l’altro, le connessioni con l’informatica e l’informazione quantistica. I ricercatori amplieranno l’uso dell’analisi di Fourier ad alta dimensione, uno strumento importante in matematica, per sviluppare metodi di Fourier discreti. Un altro obiettivo consiste nell’ulteriore sviluppo dell’«argomentazione contro i computer quantici», correlata alla fattibilità del calcolo quantistico, svelando i fattori che regolano il comportamento dei sistemi quantistici rumorosi.
Obiettivo
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.
Campo scientifico
Parole chiave
Programma(i)
Argomento(i)
Meccanismo di finanziamento
ERC-ADG - Advanced GrantIstituzione ospitante
4610101 Herzliya
Israele