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arXiv:2506.07859 · Physical Review Research

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

Amanuel Anteneh, F. Brunel, Carlos González-Arciniegas, Olivier Pfister

Published Feb 10, 2026• 1 citation
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Abstract

Cubic-phase states are a sufficient gate 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 by leveraging quantum interference in phase space, with an unprecedented 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.

DOI
10.1103/wkfp-tf74

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Cubic-phase states are a sufficient gate 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 by leveraging quantum interference in phase space, with an unprecedented 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.
We introduce architectures for near-deterministic implementation of fully tunable weak cubic phase gates requisite for universal quantum computation. The first step is to produce a resource state which is a superposition of the first four Fock states with a probability ≥10−2\geq 10^{-2}≥10−2, an increase by a factor of 10410^4104 over standard sequential photon-subtraction techniques. The resource state is produced from a quantum gadget that uses displaced squeezed states, interferometers and photon-number resolving detectors. The parameters of this gadget are trained using machine learning algorithms for variational circuits. Stacking these gadgets in parallel we build quantum resource farms in a scalable manner depending on the error tolerance. Using conventional teleportation techniques we can implement weak cubic phase gates, in principle, at a rate ∼100kHz\sim {\rm 100 kHz}∼100kHz dictated by the photon number resolving detectors. Our proposal is realizable with current photonic technologies without the need for quantum memories. The methods for non-Gaussian state preparation is of independent interest to the resource theory of non-Gaussianity.
We present numerical results from simulations using deep reinforcement learning to control a measurement-based quantum processor—a time-multiplexed optical circuit sampled by photon-number-resolving detection—and find it generates squeezed cat states quasi-deterministically, with an average success rate of 98%, far outperforming all other proposals. Since squeezed cat states are deterministic precursors to the Gottesman–Kitaev–Preskill (GKP) bosonic error code, this is a key result for enabling fault tolerant photonic quantum computing. Informed by these simulations, we also discovered a one-step quantum circuit of constant parameters that can generate GKP states with high probability, though not deterministically.
We introduce photonic architectures for universal quantum computation. The first step is to produce a resource state which is a superposition of the first four Fock states with a probability greater than or equal to ${10}^{\ensuremath{-}2}$, an increase by a factor of 104{10}^{4}104 over standard sequential photon-subtraction techniques. The resource state is produced with near-perfect fidelity from a quantum gadget that uses displaced squeezed vacuum states, interferometers, and photon-number-resolving detectors. The parameters of this gadget are trained using machine learning algorithms for variational circuits. We discuss in detail various aspects of the non-Gaussian state preparation resulting from the numerical experiments. We then propose a notion of resource farms where these gadgets are stacked in parallel, to increase the success probability further. We find a trade-off between the success probability of the farm, the error tolerance, and the number of gadgets. Using the resource states in conventional gate teleportation techniques, we can then implement weak tunable cubic phase gates. The numerical tools that have been developed could potentially be useful for other applications in photonics as well.
Quantum computers may solve some computing tasks more efficiently than classical computers, but to do so requires the design of appropriate quantum circuits. However, it is hard to design even simple quantum programs. Recent results have shown that deep learning augmented search has the potential to discover good circuits for a problem, but it is not yet sufficiently understood how well deep learning is able to model such a complex domain: the search space and output space grow exponentially. This work explores the ability of neural networks to encode quantum circuits for tasks that require knowledge about the unitary representation of the circuit. To this end, we trained neural networks to directly learn to predict the unitary of a circuit and applied reinforcement learning to train neural networks to solve circuit based quantum state preparation. This work finds that encoding quantum circuits is quite difficult especially with regards to the amount of entanglement applied in both application domains. The use of intermediate states and structure in quantum circuits combined with a reasonable inductive bias, where applicable, can alleviate these problems to some extent. The use of intermediate states also greatly improves the results of Deep Reinforcement Learning for quantum state preparation. Based on these results, we discuss the next set of challenges to address if we are to design neural network-based approaches for the automatic generation of quantum circuits. Add sentence on how it improves things in the end.