Non-Gaussian Resources for Quantum Advantages with Continuous-Variables – NoRdiC

Quantum computers are perhaps the most anticipated of all potential quantum technologies. They provide a quantum advantage that makes it possible to solve problems that lie beyond the reach of classical devices. Yet, the fundamental question “Which physical property lies at the basis of the computation power of a quantum computer?” does not have a clear-cut answer.
In NoRdiC we aim to answer this question for continuous variable platforms, where quantum information is encoded in continuous degrees of freedom. Based on results from computational complexity theory, we formulate the research hypothesis that non-Gaussian quantum correlations play a crucial role in achieving a quantum advantage in such platforms.
To understand the role of this phenomenon in quantum computational protocols, it is essential to explore its fundamental physics. Therefore, the first goal of NoRdic is to develop a theoretical framework to study these quantum correlations and understand their properties in small-scale systems. These small-scale systems serve as building blocks to create the large systems required for quantum protocols. The next step in NoRdiC is to find coarse-grained signatures that provide the means to identify the presence of non-Gaussian quantum correlations in these large systems. To do so, we exploit the idea that, even though the full multimode quantum state is inaccessible, we can extract information of all the two-mode subsystems. This allows us to construct networks, where every node corresponds to a mode, and a connection in the network represents the correlation between these modes. Our aim is to find signatures of non-gaussian entanglement in these network.
Once the fundamental physics of non-Gaussian quantum correlations is unveiled, we can investigate their role in quantum protocols. As a first step, we aim to formally prove that such quantum correlations are necessary to implement of protocol that is hard to simulate with classical resources. Then, we aim to develop protocols that use non-Gaussian quantum correlations to solve graph-theory problems. These problems are narrowly related with the network-based analysis that was carried out to find signature of non-Gaussian quantum correlations. Hence, the same techniques that unveil the fundamental physics of the large non-Gaussian states, will now be fine-tuned to implement computational protocols. Thus, NoRdiC should make it possible to demonstrate a practical quantum advantage on continuous variable platforms.