Speaker
Description
Quantum states generated from random tensor networks have been the subject of intense interest across a broad range of fields. In high-energy physics, random tensor networks constitute a tractable toy model of holographic dualities [Hayden et al 2016, Vasseur et al 2019]. In the theory of quantum computing, they describe the states generated by random quantum circuits, which have emerged as an important setting for exploring quantum computational advantage [Boixo et al 2017, Arute et al 2019].
In this talk, I will describe a series of results that pertain to phase transitions in entanglement arising in random tensor networks. As various parameters are tuned (e.g. the bond dimension of the tensor network), the quantum states described by these tensor networks can undergo an abrupt change in their entanglement scaling, from weak "area-law" entanglement, to strong "volume-law" entanglement. We provide the first mathematically rigorous results on these transitions, and relate these to the computational complexity of contracting the tensor network, and of simulating random shallow circuits. I will also describe a new prediction regarding the statistical properties of these states, which suggests that the distribution of states arising in the volume-law phase is captured by the so-called Scrooge ensemble [Josza et al 1994].
Based in part on M. McGinley, W. W. Ho, D. Malz, PRX 15, 021059 (2025)