The code and data for this work (arxiv.org/abs/2504.19992) are now available with latest arxiv preprint. In addition, we’ve updated the preprint with the table of contents given the feedback on the length of this manuscript!
🔹 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!)
Thrilled to share my PhD thesis is now public! 📖
📎 proquest.com/docview/3225...
Aside from an introduction to quantum computing in CV and DV architectures, some unpublished ideas include:
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.
Take a look at our latest work on non-abelian quantum signal processing: arxiv.org/abs/2504.19992
Excited to share that I’ll be presenting it at #TQC_2025 this year!