Deep reinforcement learning for near-deterministic preparation of cubic- and quartic-phase gates in photonic quantum computing

Cubic-phase states are a sufficient resource for universal quantum computing over continuous variables. We present results from numerical experiments in which deep neural networks are trained via reinforcement learning to control a quantum optical circuit for generating cubic-phase states, with an average success rate of 96%. The only non-Gaussian resource required is photon-number-resolving measurements. We also show that the exact same resources enable the direct generation of a quartic-phase gate, with no need for a cubic gate decomposition.

💡 Research Summary

This paper presents a novel approach to generating the essential non‑Gaussian resources for continuous‑variable quantum computing (CV‑QC) – namely cubic‑ and quartic‑phase gates – by leveraging deep reinforcement learning (DRL) to control a photonic circuit. The authors design a looped optical architecture (Fig. 1) that consists of a variable beamsplitter with transmissivity τ j, a squeezed‑vacuum input with squeezing parameter r j (up to 10 dB), and displacement operations α j applied before each round. The only non‑Gaussian element required is a photon‑number‑resolving (PNR) detector, which can be realized with superconducting transition‑edge sensors or nanowire detectors. After each PNR measurement the circuit’s density matrix is fed to a neural‑network agent that decides the next set of parameters (τ j, r j, α j).

The problem is cast as a finite‑horizon Markov decision process (MDP). The state s j is a flattened representation of the current density matrix ρ j (real and imaginary parts of off‑diagonal elements plus the diagonal). The action a j =