A Blueprint for a Photonic Quantum Computer

• Applicant: Dr. Farzin Salek Shishavan
• Subject Area: Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas ; Mathematics
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 524058134

Quantum communication allows to transmit information with physical security guarantees at rates exceeding the capacities of classical links and quantum computers provide a means to speed up certain computations solving certain problems faster than any (present or future) classical computer. Quantum computation with a discrete-variable system such as a two-level electron spin demands temperatures colder than those found in deep space. However, continuous-variable systems, such as photons (particles of light) can operate at room temperatures and are more robust against decoherence, allowing for full miniaturization and mass manufacturing. The theory of quantum error-correcting codes (QEC) provides a new set of techniques to run a quantum algorithm with an arbitrary level of accuracy despite using imperfect noisy photons. Photonic quantum codes exhibit either translational or rotational symmetry in phase space. Significant development of translational-symmetric codes is the result of existence of a standard stabilizer framework for these codes. However, there is a lack of theoretical understanding and unification of techniques in defining phase-number codes in a systematic way. As such, the questions about upscaling, formulating decoding algorithms and performing universal computation with phase-number codes have remained unanswered or ambiguous. This project aims to understand the interplay between rotational symmetry in phase space and QECs resistance to rotations and photon shifts in phase space. Such an understanding is prerequisite to build a fault-tolerant and universal photonic quantum computer with rotational symmetric codes for two reasons: First for upscaling and constructing new rotational symmetric codes and second devising a universal set of operations. Concerning the first, my goal is to find a stabilizer formalism for rotational-symmetric codes and study its properties; that is, either to convert already existing continuous-variable codes to rotational symmetric codes, or to concatenate single-mode rotational-symmetric codes with qubit codes such as surface code. For the second, implementation of Clifford operations is rather straightforward; nonetheless to build a universal gate set, I will work out efficient protocols for magic state distillation. We are at the dawn of the quantum computing age and the quantum codes and techniques developed in PhoQC will bring (photonic) quantum computation closer to industrial deployment.

• DFG Programme: WBP Position