P4: Bridging finite dimensional and infinite dimensional quantum systems — simulations and computational power

Members: Dr. Alessandro Ciani (FZ Juelich), Prof. Dr. Sevag Gharibian (Paderborn University)

Quantum computing promises to augment the computational capabilities of the standard computers we have in our houses, by adding quantum effects, such as coherence and entanglement. While the addition of these effects has been shown, at the theory level, to provide a so-called quantum advantage, i.e., an improvement over the best classical methods, in several scenarios, the source of this quantum advantage has remained elusive. The worldwide research effort underway for designing experimental quantum computers has attracted large investments. A prerequisite for investing such resources is arguably a solid theoretical backing for why such devices should outperform classical devices for useful tasks to begin with, at least in ideal, noise-free setups. As several quantum platforms are being developed based on different quantum systems, it is thus paramount to clearly demark the computational power of these systems.

This project studies the computational power of quantum systems from two complementary and symbiotic perspectives: On the one hand, the project studies lower bounds on computational power in discrete versus continuous systems (and hybrid), in the form of connections between the classical simulatability of finite dimensional (i.e. qubit) and continuous variable quantum systems. On the other hand, the project aims to upper bound and more generally characterize the power of polynomial-time photonic quantum computation, to complement the existing knowledge of polynomial-time quantum computation on qubits. Moreover, the project studies how the addition of noisy quantum resources gradually allows us to gain computational power by means of quantum error correction and mitigation techniques for both continuous and discrete variable systems.