Piotr Kopszak - High-dimensional quantum Schur transforms Date and time: Thursday 20 November at 10:00 Room

High-dimensional quantum Schur transforms Date and time: Thursday 20 November at 10:00 Room

This seminar, given by Piotr Kopszak, will happend on 20 November 2025, at 9:0. It will take place in Room Not specified.

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Abstract

The quantum Schur transform has become a foundational quantum algorithm, yet even after two decades since the seminal 2004 paper by Bacon, Chuang, and Harrow (BCH), some aspects of the transform remain insufficiently understood. Moreover, an alternative approach proposed by Krovi in 2018 was recently found to contain an error. In this talk, I present a corrected version of Krovi’s algorithm along with a detailed treatment of the high-dimensional version of the BCH Schur transform, based on Clebsch-Gordan transforms of the unitary group. This high-dimensional focus makes the two versions of the transform practical for regimes where the number of qudits $n$ is smaller than the local dimension $d$, with Krovi’s algorithm scaling as $\tilde{O}(n^{3.5})$ and BCH as $\tilde{O}(\min(n^5,nd^4))$. As an application, I will show how high-dimensional Clebsch-Gordan transforms can efficiently simulate Haar random unitaries. Speaker: Piotr Kopszak Title: Entanglement recycling in port-based teleportation Date and time: Thursday 20 November ~ 11:00 Room: 26-00/534 Abstract: We study entangled resource state recycling after one round of probabilistic port-based teleportation. We analytically characterize its degradation and, for the case of the resource state consisting of N EPR pairs, we demonstrate the possibility of reusing it for a subsequent round of teleportation in the N→∞ limit. For the case of an optimized resource state, we compare the protocol’s performance to multi-port-based teleportation, indicating that the resource state reuse is possible. An analogous comparison is made in the case of the deterministic scheme. All the best, Marco