QC Introductory Seminar: Continuous-variable quantum computing with photonics

Speaker: Olga Solodovnikova (University of Southern Denmark).

Abstract: 
In this seminar, I will introduce continuous quantum variables [1], which are used to describe systems of oscillators, that is, systems with infinite Hilbert spaces such as photonic systems or the vibrational motion of trapped ions. 
To build a universal and fault-tolerant quantum computer with a continuous-variable system, it is necessary to encode a qubit in an oscillator, perform gates from the universal gate set, and measure stabilisers to implement error correction.  

In the second part of the introductory seminar, I will introduce the measurement-based quantum computing framework for optical systems, in which Gottesman-Kitaev-Preskill (GKP) states are injected into a cluster state, and homodyne/heterodyne detectors are used to i) apply gates via teleportation and ii) measure stabilisers [2]. Lastly, I will discuss the experimental progress on building a measurement-based quantum computer [3], where, in particular, the generation of GKP states [4] is a major bottleneck due to photon loss. 

[1] Braunstein and van Loock. “Quantum Information with Continuous Variables.” Rev. Mod. Phys. 77, no. 2 (2005).
[2] Gottesman, et al. “Encoding a Qubit in an Oscillator.” Physical Review A 64, no. 1 (2001): 012310. 
[3] Aghaee Rad, H., T. Ainsworth, R. N. Alexander, et al. “Scaling and Networking a Modular Photonic Quantum Computer.” Nature 638, no. 8052 (2025): 912–19. 
[4] Larsen, M. V., J. E. Bourassa, S. Kocsis, et al. “Integrated Photonic Source of Gottesman–Kitaev–Preskill Qubits.” Nature 642, no. 8068 (2025): 587–91.