Quantum Circuit Born Machines (QCBMs) are variational circuits whose goal is to encode a classical probability distribution in the measurement outcomes. With Hierarchical Learning (HL), we exploit the structure of the qubit mapping in this variational circuit to learn gates of a few qubits first before expanding to the whole system. Using adjoint simulation techniques on GPUs, we manage to load a 3 dimensional Gaussian distribution on 27 qubits to within 4% total variational distance (TVD). An additional benefit of this circuit structure is that it can reduce the number of gates required compared to other methods. To demonstrate the use, we benchmark the performance hierarchically learned circuits on IBM hardware with FireOpal optimization.

Optimally encoding classical information in a quantum system is one of the oldest and most fundamental challenges of quantum information theory. Holevo's bound places a hard upper limit on such encodings, while the Holevo-Schumacher-Westmoreland (HSW) theorem addresses the question of how many classical messages can be “packed” into a given quantum system. In this article, we use Sen's recent quantum joint typicality results to prove a one-shot multiparty quantum packing lemma generalizing the HSW theorem. The lemma is designed to be easily applicable in many network communication scenarios. As an illustration, we use it to straightforwardly obtain quantum generalizations of well-known classical coding schemes for the relay channel: multihop, coherent multihop, decode-forward, and partial decode-forward. We provide both finite blocklength and asymptotic results, the latter matching existing classical formulas. Given the key role of the classical packing lemma in network information theory, our packing lemma should help open the field to direct quantum generalization.

We study universal quantum codes for entanglement-assisted quantum communication over compound quantum channels. In this setting, sender and receiver do not know the specific channel that will be used for communication, but only know the set that the channel is selected from. We investigate different variations of the problem: uninformed users, informed receiver, informed sender, and feedback assistance. We derive single-letter formulas for all corresponding channel capacities. Our proofs are based on one-shot decoupling bounds and properties of smooth entropies.