Regensburg 2025 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 41: Quantum Dynamics, Decoherence, and Quantum Information (joint session DY/TT)
DY 41.4: Talk
Friday, March 21, 2025, 10:15–10:30, H37
Spectral Properties and Magic generation of T-doped Random Clifford Circuits — •Dominik Szombathy — Budapest University of Technology and Economics
We investigate the spectral properties and magic generation of T-doped random Clifford circuits. There is a direct relation between the structure of Pauli string orbits and the eigenvalue spectrum of a Clifford circuit. Operatively, we sample the closed trajectories with brick-wall circuits and determine the distribution of the eigenvalues λ = eiΘ. The autocorrelation function of the phases of the eigenvalues displays peculiar properties: extreme degeneracies as well as some level-repulsion, and features reminiscent of a fractal pattern.
To investigate the stability of orbits and head towards universal quantum computation, we introduce π/4 phase shift gates (T-gates). We find that even a single T-gate completely changes the properties of the circuit. By increasing the number of T-gates (NT), the correlation function rapidly approaches that of the random unitary circuits. Nevertheless, some statistically significant fraction of non-trivial orbits persists at low T-gate densities (NT/N).
We observe a similar phenomenology in the magic generation as a function of T-gate density. In particular, we find universal scaling of the maximum and mean magic as a function of NT/N . We also highlight the structure of magic generated by these circuits. Injecting a few T-gates the distribution is discrete but becomes continuous as NT increases. At large densities NT / N , most of the weight is found in a sharp peak well below the theoretical maximum.
Keywords: Clifford circuit; magic; spectral properties; random matrix theory