Hi all,

Next week Moritz Scheer will talk about his master's thesis entitled “Renormalization-Based Preparation of Matrix Product States”. The talk will take place on Monday in HIT K 51 at 14:00. See below for the abstract.

Best, Ladina

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Title:

Renormalization-Based Preparation of Matrix Product States

Abstract:

The preparation of useful quantum states on quantum computers is a crucial subroutine in numerous quantum algorithms. Recently, a novel quantum state preparation protocol has been introduced based on the renormalization-group transformation for matrix product states. With local unitary circuits, this method prepares translation-invariant normal MPS for n sites up to error ϵ in depth O(log n/ϵ), which is asymptotically optimal. During my Master thesis, we implemented the renormalization-based preparation algorithm for a family of normal MPS that correspond to ground states of a one-dimensional spin-1/2 Hamiltonian in both the trivial and symmetry-protected topological phases. We executed this algorithm for the first time on a quantum computer using IBM’s latest QPU ibm_fez, and successfully classified the phase of states with up to 80 qubits. Additionally, we compared the renormalization-based preparation protocol with the sequential preparation algorithm, which prepares MPS in depth O(n). In the trivial phase, we observed a cross-over point at approximately 40 qubits. Beyond that, the renormalization-based protocol outperforms the sequential method, demonstrating its superior asymptotic scaling. In this presentation, I will give an introduction to tensor networks and matrix product states, present the sequential and renormalisation-based preparation protocols, and summarise the results obtained during the project.