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

• Applicants: Dr. Alessandro Ciani; Professor Sevag Gharibian, Ph.D.
• Subject Area: Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas ; Theoretical Computer Science
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 563388236

Quantum computing promises to augment the computational capabilities of conventional computers, by adding quantum effects, such as coherence and entanglement. While it has been shown theoretically, that the addition of these effects can 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. Additionally, the currently available devices are not capable of fully showing the computational power of quantum systems as they are affected by noise (errors), which affect the computation in a much more fundamental way than in standard computers. Also in this case, the computational power of these noisy devices has been long debated. Quantum error correction promises to solve these issues, but it comes with a considerable overhead. In recent years, cheaper quantum error mitigation techniques have been developed, which are however ultimately not scalable. It can thus be envisioned that in the following years as the error corrected quantum computers will be built, it will be important to complement and combine these techniques with error mitigation in different quantum platforms. In order to address both issues, understanding quantum advantage at a fundamental level and enabling it through measures countering noise effects, this research proposal studies the computational power of quantum systems from two complementary and symbiotic perspectives. On the one hand, we study 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, we aim 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 proposal 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.

• DFG Programme: Priority Programmes
• Subproject of: SPP 2514: Quantum Software, Algorithms and Systems - Concepts, Methods and Tools for the Quantum Software Stack
• Co-Investigators: Dr. Tobias Stollenwerk; Professor Dr. Frank K. Wilhelm-Mauch