🔹 Ch 5: A sneak peek on our analytical understanding of photon loss correction in superconducting circuits via GKP codes, a question inspired by my first-ever interaction with Steven Girvin circa 2019, and multiple conversations with Vlad Sivak and Baptiste Royer.

🔹 Gaussian Hierarchy (Chapter 2.3, note that the ideas here overlap with a paper from 2003 that I was unaware of: arxiv.org/pdf/quant-ph.... Thanks
@vva.bsky.social
for sharing this article with me today!)

Finally, we also show a compilation for quantum phase estimation using ancillary oscillators with a non-abelian QSP inspired circuit.

Our QSP sequence renders schemes insensitive to Gaussian uncertainty in CV states, bridging the gap between idealized theoretical and realistic finite-energy GKP states. This framework yields a unified framework for finite-energy GKP states.

We then present schemes for universal control of GKP qudits via (i) high-fidelity state preparation, (ii) first end-of-line GKP readout scheme, and (iii) pieceable error-corrected universal gate teleportation

We show improved performance of squeezed vacuum and GKP states against state-of-the-art schemes in literature. Our analytical understanding also yields ways to use mid-circuit ancilla error detection.

Towards its utility in efficient oscillator (CV)-qubit (DV) control, we derive first fully analytical schemes for deterministic preparation of various CV states — squeezed vacuum, cat states, Fock states and GKP states.

We also introduce the concatenation of BB1 and GCR—BB1(GCR) which has a response function closer to a square wave compared to just using BB1.

We introduce the class of composite pulses where the parameters of qubit rotation are non-commuting quantum operators (positions and moments of quantum oscillators). We present the a fundamental composite pulse GCR which is 4.5 times shorter than BB1 with similar performance.