ON-LINE QLunch: Enrique Cervero Martin

Speaker: Enrique Cervero Martin

Title: Streaming implementation of weak Schur sampling

Abstract: 
The Schur transform maps the computational basis of a system of $n$ qudits onto the basis of minimal invariant subspaces given by the representations of the unitary and symmetric groups acting on the state space of $n$ qudits. Previous work shows how to implement the Schur transform on quantum computers and in this text, we develop the theory further by introducing a weak Schur transform that efficiently determines both the Young label, which indexes irreducible representations, and the multiplicity label of the symmetric group. As such, the weak Schur transform is a suitable alternative for processes requiring weak Schur sampling. We present a streaming algorithm decomposing the weak Schur transform on $n$ qubits to accuracy $\epsilon$ into $O(n^3\log_2(\frac{n}{\epsilon}))$ gates from the Clifford+T set, which requires a memory of $O(\log_2n)$ qubits to implement.

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https://ucph-ku.zoom.us/j/64248516479