Short-Depth Circuits for Dicke State Preparation

Understand

We present short-depth circuits to deterministically prepare any Dicke state |Dn,k>, which is the equal-amplitude superposition of all n-qubit computational basis states with Hamming Weight k.

• Dicke states are an important class of entangled quantum states with a large variety of applications, and a long history of experimental creation in physical systems.
• On the other hand, not much is known regarding efficient scalable quantum circuits for Dicke state preparation on realistic quantum computing hardware connectivities.
• Here we present preparation circuits for Dicke states |Dn,k> with (i) a depth of O(k log(n/k)) for All-to-All connectivity (such as on current ion trap devices); (ii) a depth of O(k sqrt(n/k)) = O(sqrt(nk) for Grid connectivity on grids of size Omega(sqrt(n/s)) x O(sqrt(ns)) with s<=k (such as on current superconducting qubit devices).