Speaker
Description
Gate implementations of Haar-random unitaries are central to randomized benchmarking protocols, quantum cryptography and in simulating black hole dynamics, but exact Haar sampling costs a gate count of $O(4^n)$. Therefore we make do with unitary $k$-designs: ensembles that mimic the Haar measure up to the $k$-th moment. We study an ensemble generated by the chaotic quantum baker map on $n$ qubits, interleaved with Haar-random single-qubit unitaries applied at a fixed site. Using the frame potential to quantify closeness to Haar, we derive an exact expression for the frame potential, involving Catalan numbers, that exhibits two-stage convergence to the Haar value $k!$. The ensemble becomes an approximate k-design with a total gate count of $O(kn³)$, using only $O(3kn)$ random parameters. We further extend this construction to coupled systems, exploring the role of quantum chaos in generating pseudorandomness.
Other Fields of Research (Track) for Abstract
Complex Systems and nonlinear dynamics
| Nature of work | Theoretical |
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