Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Near-deterministic production of universal quantum photonic gates enhanced by machine learning

Krishna Kumar Sabapathy, Haoyu Qi, Josh Izaac, Christian Weedbrook

Published Sep 12, 2018• 3 citations
OpenAlex

Abstract

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 $\geq 10^{-2}$, an increase by a factor of $10^4$ 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 $\sim {\rm 100 kHz}$ 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.

Related papers

Production of photonic universal quantum gates enhanced by machine learning

Krishna Kumar Sabapathy, Haoyu Qi, Josh Izaac +1 more

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 ${10}^{4}$ 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.

arXiv:1809.04680•Physical Review A•Jul 17, 2019•62 citations

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 +1 more

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.

arXiv:2506.07859•Physical Review Research•Feb 10, 2026•1 citation

ON states as resource units for universal quantum computation with photonic architectures

Krishna Kumar Sabapathy, Christian Weedbrook

Universal quantum computation using photonic systems requires gates the Hamiltonians of which are of order greater than quadratic in the quadrature operators. We first review previous proposals to implement such gates, where specific non-Gaussian states are used as resources in conjunction with entangling gates such as the continuous-variable versions of controlled-phase and controlled-not gates. We then propose ON states which are superpositions of the vacuum and the $N\mathrm{th}$ Fock state, for use as non-Gaussian resource states. We show that ON states can be used to implement the cubic and higher-order quadrature phase gates to first order in gate strength. There are several advantages to this method such as reduced number of superpositions in the resource state preparation and greater control over the final gate. We also introduce useful figures of merit to characterize gate performance. Utilizing a supply of on-demand resource states one can potentially scale up implementation to greater accuracy, by repeated application of the basic circuit.

arXiv:1802.05220•Physical Review A•Jun 11, 2018•47 citations

Repeat-until-success cubic phase gate for universal continuous-variable quantum computation

Kevin Marshall, Raphael C. Pooser, George Siopsis +1 more

To achieve universal quantum computation using continuous variables, one needs to jump out of the set of Gaussian operations and have a non-Gaussian element, such as the cubic phase gate. However, such a gate is currently very difficult to implement in practice. Here we introduce an experimentally viable ``repeat-until-success'' approach to generating the cubic phase gate, which is achieved using sequential photon subtractions and Gaussian operations. We find that our scheme offers benefits in terms of the expected time until success, as well as the fact that we do not require any complex off-line resource state, although we require a primitive quantum memory.

arXiv:1412.0336•Physical Review A•Mar 24, 2015•78 citations

General Photon Subtraction from a Gaussian Perspective

Niklas Budinger, Ulrik L. Andersen, Peter van Loock

A near-deterministic source of non-Gaussianity is the missing piece to reach universal and fault-tolerant quantum computing with continuous-variable optics. Due to a lack of strong non-linearities, the probabilistic photon-subtracted Gaussian states remain the most promising contender. In combination with Gaussian measurements and single-mode feed-forward operations, they have been shown to provide sufficient non-Gaussianity at high rates. However, these existing breeding protocols lack the necessary loss tolerance to be experimentally feasible. In this work, we introduce a mathematical formalism based on the application of a Gaussian blur and filter on the measured Fock Wigner function to describe general photon-subtracted Gaussian states. Within our representation, the initial squeezing, Gaussian measurements, and photon loss can all be understood as contributions to the total blurring and interchanged accordingly. We find that this intuitive approach can be used to find improvements to cat, cubic phase, and GKP state generation by compromising between success rates, feed-forward compatibility, and loss tolerance. In the case of multiple photon subtractions, this is achieved by introducing a hybrid setup variant bridging the gap between protocols based on breeding and post-selection. Finally, we establish a general lower bound on the resources needed to generate a given target state near-deterministically by introducing the expected Wigner logarithmic negativity as an additive monotone of non-Gaussianity.

quant-pharXiv:2609.34803•Sep 29, 2026•0 citations

Machine learning for efficient generation of universal photonic quantum computing resources

Amanuel Anteneh, F. Brunel, Olivier Pfister

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.

arXiv:2310.03130•Optica Quantum•Jun 28, 2024•4 citations
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 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.
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.
Universal quantum computation using photonic systems requires gates the Hamiltonians of which are of order greater than quadratic in the quadrature operators. We first review previous proposals to implement such gates, where specific non-Gaussian states are used as resources in conjunction with entangling gates such as the continuous-variable versions of controlled-phase and controlled-not gates. We then propose ON states which are superpositions of the vacuum and the NthN\mathrm{th}Nth Fock state, for use as non-Gaussian resource states. We show that ON states can be used to implement the cubic and higher-order quadrature phase gates to first order in gate strength. There are several advantages to this method such as reduced number of superpositions in the resource state preparation and greater control over the final gate. We also introduce useful figures of merit to characterize gate performance. Utilizing a supply of on-demand resource states one can potentially scale up implementation to greater accuracy, by repeated application of the basic circuit.
To achieve universal quantum computation using continuous variables, one needs to jump out of the set of Gaussian operations and have a non-Gaussian element, such as the cubic phase gate. However, such a gate is currently very difficult to implement in practice. Here we introduce an experimentally viable ``repeat-until-success'' approach to generating the cubic phase gate, which is achieved using sequential photon subtractions and Gaussian operations. We find that our scheme offers benefits in terms of the expected time until success, as well as the fact that we do not require any complex off-line resource state, although we require a primitive quantum memory.
A near-deterministic source of non-Gaussianity is the missing piece to reach universal and fault-tolerant quantum computing with continuous-variable optics. Due to a lack of strong non-linearities, the probabilistic photon-subtracted Gaussian states remain the most promising contender. In combination with Gaussian measurements and single-mode feed-forward operations, they have been shown to provide sufficient non-Gaussianity at high rates. However, these existing breeding protocols lack the necessary loss tolerance to be experimentally feasible. In this work, we introduce a mathematical formalism based on the application of a Gaussian blur and filter on the measured Fock Wigner function to describe general photon-subtracted Gaussian states. Within our representation, the initial squeezing, Gaussian measurements, and photon loss can all be understood as contributions to the total blurring and interchanged accordingly. We find that this intuitive approach can be used to find improvements to cat, cubic phase, and GKP state generation by compromising between success rates, feed-forward compatibility, and loss tolerance. In the case of multiple photon subtractions, this is achieved by introducing a hybrid setup variant bridging the gap between protocols based on breeding and post-selection. Finally, we establish a general lower bound on the resources needed to generate a given target state near-deterministically by introducing the expected Wigner logarithmic negativity as an additive monotone 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.