{"id":75,"date":"2024-09-03T10:40:29","date_gmt":"2024-09-03T09:40:29","guid":{"rendered":"https:\/\/www.andreadeluca.online\/?p=75"},"modified":"2024-09-03T10:40:29","modified_gmt":"2024-09-03T09:40:29","slug":"new-preprint-about-distribution-of-overlaps-in-the-dynamics-of-quantum-circuits-arxiv2404-10057","status":"publish","type":"post","link":"https:\/\/www.andreadeluca.online\/?p=75","title":{"rendered":"New preprint about distribution of overlaps in the dynamics of quantum circuits (arXiv:2404.10057)"},"content":{"rendered":"\n

I am proud to announce a new work in collaboration with Amos Chan and my PhD student Alexios Christopoulos. We consider the evolution of a wave function starting from a simple product state under a generic quantum circuit. We then analyse the coefficients in the expansion of the wavefunction on the computational basis of q-bits. It is known that for completely random states this distribution has a simple form named Porter-Thomas, which in the thermodynamic limit is simply obtained assuming that the coefficients are complex gaussian numbers. The question we ask is how this distribution is approached. We develop a generic formalism based on replicas and matching of Feynman histories, so that the problem can be rephrased in general terms as the partition function of a 1D gas of domain-walls in the permutation space. This approach highlights a novel kind of universality emerging in these quantities, alike what we had observed in the spectral form factors few years ago. So, we introduce a scaling limit where the shape of this distribution at large t (~ circuit depth) and L (~ system size) becomes completely universal. Only when t>>L, our family of distributions reduces to the known Porter-Thomas. I find this result particularly striking as it is<\/p>\n\n\n\n