Symmetric Finite-Time Preparation of Cluster States via Quantum Pumps

TL;DR

This paper demonstrates a method to prepare cluster-like states in finite time using symmetry-preserving Hamiltonian evolution, leveraging topological protection and measurement-based corrections.

Contribution

It introduces a higher-dimensional Hamiltonian protocol that pumps cluster states to the boundary without symmetry breaking, enabling robust, finite-time state preparation.

Findings

Finite-time cluster state preparation via Hamiltonian pumping.

Protection against symmetric perturbations using measurements and feedforward.

Application to 1D and 2D cluster states with symmetry considerations.

Abstract

It has recently been established that cluster-like states -- states that are in the same symmetry-protected topological phase as the cluster state -- provide a family of resource states that can be utilized for Measurement-Based Quantum Computation. In this work, we ask whether it is possible to prepare cluster-like states in finite time without breaking the symmetry protecting the resource state. Such a symmetry-preserving protocol would benefit from topological protection to errors in the preparation. We answer this question in the positive by providing a Hamiltonian in one higher dimension whose finite-time evolution is a unitary that acts trivially in the bulk, but pumps the desired cluster state to the boundary. Examples are given for both the 1D cluster state protected by a global symmetry, and various 2D cluster states protected by subsystem symmetries. We show that even if unwanted symmetric perturbations are present in the driving Hamiltonian, projective measurements in the bulk along with feedforward correction is sufficient to recover a cluster-like state.