IQIM Postdoctoral and Graduate Student Seminar

Abstract: I'll describe a construction for a family of constant depth quantum circuits that output states whose entanglement entropy across a given cut cannot be efficiently estimated (to within constant additive error), based on plausible cryptographic assumptions. Previous works were only able to achieve this with either log-depth circuits or constant depth circuits having gates of unbounded fan-out. In contrast, this construction uses a constant depth circuit with local single and two-qubit gates. 

Since constant depth quantum circuits can be learned efficiently, the resulting pseudoentangled states are public key (the circuits preparing them are known in advance) and not pseudorandom (the states can be efficiently distinguished from Haar random). Nevertheless, their entanglement structure is intractable to learn both quantumly and
classically.

I'll also discuss a potential classical analog of this result, as well as implications to the hardness of learning the entanglement structure of ground-states of local Hamiltonians.

The talk is based on unpublished work and I welcome comments, feedback and suggestions for potential improvements or for applications of this result.

Following the talk, lunch will be provided on the lawn outside East Bridge.