QM Research Seminar: Circumventing the no-go theorems: self-correcting qubits and protected non-Clifford gates with driven-dissipative superconducting resonators

Speaker: Frederik Nathan (University of Copenhagen).

Abstract: 
The current main paradigm for quantum computing — active quantum error correction (AEC) with overhead qubits — faces two challenges: Realizing long-lived logical qubits at reasonable resource cost, and achieving universal fault-tolerant quantum gates. At the root of these challenges lie two no-go theorems: The Braviy-Terhal theorems, which forbids passively-stabilized, or self-correcting, qubits in <4 dimensions, and the Eastin-Knill theorem which dictates that fault-tolerant non-Clifford gates must be generated with costly magic distillation or cultivation routines. Together, these theorems imply that even simple quantum information processing operations require continuous readout, data processing, and feedback control of very large numbers of overhead qubits. 

Here I illustrate how the no-go-theorems above are not as far-reaching as one could fear, but can be circumvented via an alternative paradigm for quantum computing currently gaining experimental maturity: bosonic codes (BC), which redundantly encodes a qubit in the infinite-dimensional Fock state of a single continuous variable. In particular, I will demonstrate how tuning the impedance of a simple driven-dissipative superconducting resonator to a “magic” value given by a constant of nature can lead to a self-correcting Gottesman-Kitaev-Preskill qubit that supports exponentially-robust Clifford and non-Clifford gates [1,2]. 

[1] FN, L. O’Brien, K. Noh, M.H. Matheny, A.L. Grimsmo, L. Jiang, G. RefaelPRX Quantum 6 (3), 030352 (2025)[2] L. O'Brien, G. Refael, FN arXiv:2507.19713 (2025)