JQI

In recent years, the use of Gottesman-Kitaev-Preskill (GKP) Codes to  implement fault-tolerant quantum computation has gained significant traction and evidence for their experimental utility has steadily grown.  But what does it even mean for quantum computation with the GKP code to be fault tolerant?  In this talk, we discuss the structure of logical Clifford gates for the GKP code and how their understanding leads to a classification of the space of all GKP Codes.

Abstract: We create honeycomb superlattice structures in TMD moiré materials as model systems to
study magnetism, electronic correlations and topology. In twisted MoTe 2 , we realize topological flat
bands that closely resemble the lowest Landau level but in the absence of an external magnetic field.
We present evidence for integer and fractional Chern states [1], which are the lattice analogues of
integer and fractional quantum Hall states at zero magnetic field. We further explore correlated states in

In this work we present fast constructions for the quantum Fourier transform and quantum integer multiplication, using few ancilla qubits compared to the size of the input. For the approximate QFT we achieve depth O(log n) using only n + O(n / log n) total qubits, by applying a new technique we call "optimistic quantum circuits." To our knowledge this is the first circuit for the AQFT with space-time product O(n log n), matching a known lower bound.

Dissertation Committee Chair: Prof. Mohammad Hafezi

Committee: 

Professor Kartik Srinivasan

Professor Yanne Chembo

Professor Carlos A. Rios Ocampo

Professor Miao Yu (Dean’s Representative)