Dave Bacon: Enlarging the 'IS' in NISQ

Abstract: Before we build fault-tolerant quantum computers, can we use ideas from quantum error correction to build larger quantum programs on NISQ processors?  In this talk I will cover two recent results from Google's team on this topic.  The first pertains to simulating fermions on a two dimensional lattice.  Here one can show that there are encodings of fermions onto qubits that also have error correcting properties.  But how would one use the error correcting properties without doing full fault-tolerant quantum computing?  In the second result we discuss how one can project onto error correcting code space while avoiding traditional fault-tolerant syndrome measurement using ancillas.  This comes at the cost of increasing the repetitions.  We provide a general construction equipped with a simple stochastic sampling scheme that does not depend explicitly on a number of terms that we extend to approximate projectors within a subspace. This theory then allows one to generalize to the correction of some logical errors in the code space, correction of some physical unencoded Hamiltonians without engineered symmetries, and corrections derived from approximate symmetries.