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esQueranto: Differentiable Structured Quantum Light for Automated Scientific Discovery

The paper introduces \textsc{esQueranto}, a JAX-based differentiable simulator that unifies photon-number quantum optics and structured-light propagation to enable AI-driven automated discovery of new quantum optical experiments.

Original authors: Marcello Armezzani, Tareq Jaouni, Pontus Lindgren, Sören Arlt, Mario Krenn, Xuemei Gu

Published 2026-10-02

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CC BY 4.0

Original authors: Marcello Armezzani, Tareq Jaouni, Pontus Lindgren, Sören Arlt, Mario Krenn, Xuemei Gu

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

For centuries, the most profound discoveries in physics have come from human ingenuity. A researcher imagines a setup, builds it with mirrors and lasers, and watches to see what the universe reveals. This process relies on the intuition of the scientist to ask the right questions. However, the universe is vast, and the number of possible ways to arrange light and matter is so enormous that a human mind cannot possibly explore them all. There may be brilliant experimental designs hidden in the dark corners of possibility—setups that work perfectly but are so counterintuitive that no person would ever think to build them. To find these hidden gems, scientists are turning to artificial intelligence, teaching computers to design experiments for them. But for a computer to invent a new experiment, it needs a simulator, a virtual laboratory, that is powerful enough to understand the complex rules of nature.

The challenge lies in the fact that light behaves in two very different ways depending on how you look at it. On one hand, light can be treated as a stream of individual particles called photons, where the rules of quantum mechanics apply, and strange things like entanglement occur. On the other hand, light travels as a wave that spreads out, bends around corners, and changes shape as it moves through space. For a long time, computer programs could simulate one of these behaviors well, but not both at the same time. If a program tried to track the quantum nature of the light, it often ignored how the beam's shape changed as it traveled. If it tracked the shape and movement of the beam, it often lost the delicate quantum details. This split meant that computers could not fully explore experiments where the shape of the light beam directly influenced the quantum behavior of the particles inside it.

A team of researchers has now introduced a new software tool called esQueranto that bridges this gap. This program allows scientists to describe both the particle-like quantum nature of light and its wave-like movement through space within a single, unified model. The software is designed to be "differentiable," a technical term that simply means the computer can automatically calculate how small changes in the experiment affect the final result. This capability is crucial because it allows the software to not just simulate an experiment, but to learn from it. The computer can tweak the settings of mirrors, lenses, and light sources, instantly see how those changes alter the outcome, and use that information to find the best possible configuration for a specific goal.

The researchers demonstrated the power of this tool by running it through a wide variety of complex scenarios. In one test, they simulated a setup where four different sources of light interact to create a four-photon state. They found that when the light is very intense, the simple rules that usually predict how these particles cancel each other out no longer apply. The software correctly identified that higher-order effects, which are often ignored in simpler models, shift the point where the interference happens. In another example, the team used the software to design a method for creating a specific type of entangled light known as a NOON state, which is useful for ultra-precise measurements. The computer discovered a new arrangement of beam splitters that produced this state with a success rate five times higher than any previously known human-designed method.

The tool also proved its worth in handling the messy reality of the physical world, where light is never perfect. The researchers simulated an experiment where a single photon travels through two different fiber optic cables separated by a vertical distance of two meters. One cable is higher than the other, meaning the photon in that path experiences a slightly different gravitational pull, which changes its phase. The software successfully calculated how this tiny gravitational effect competes with the loss of photons and the blurring of their quantum properties as they travel. It determined that there is an optimal distance for this experiment—about 44 kilometers—where the signal from gravity is strong enough to be detected before the noise of the environment destroys the information.

Perhaps the most striking demonstration involved the shape of the light itself. The researchers showed that the software could simulate how photons with complex spatial patterns, such as those shaped like a spiral or a ring, interfere with each other. They found that the way these beams spread out and change shape as they travel can be used to sort them into different paths. By carefully arranging lenses and mirrors, the computer showed how to direct photons based on their internal structure, even when the environment introduces noise that tries to scramble the signal. This is significant because it proves that the spatial geometry of an experiment is not just a backdrop for the quantum action; it is an active ingredient that can be tuned to control the outcome.

The paper does not claim to have solved every problem in physics or to have built a physical machine that can do all of this on its own. Instead, it presents a foundational step toward a universal simulator. The authors argue that by combining these different physical descriptions into one language, they have opened up a new design space. This space allows for experiments that mix quantum effects, light propagation, and noise in ways that were previously too difficult to model. The software has already been used to discover new experimental schemes, such as methods for generating entangled states with higher probabilities and new ways to measure gravitational effects. The researchers envision a future where this approach expands beyond light to include atoms, mechanical vibrations, and other forms of matter, creating a single platform where artificial intelligence can design complete experiments from the ground up, uncovering new phenomena that human intuition alone might never have imagined.

Technical Summary: esQueranto – Differentiable Structured Quantum Light for Automated Scientific Discovery

Problem Statement
The design of physics experiments has traditionally been a human endeavor, limited by the intuition and experience of researchers. However, the space of all possible experimental configurations is vast, potentially containing high-performing but unintuitive setups that humans have not envisioned. While artificial intelligence (AI) and computational methods have begun to automate experimental design in quantum optics, existing simulators often lack the necessary expressiveness to model the diverse physical processes and couplings required for true de-novo discovery. Specifically, current tools typically separate photon-number quantum optics (Fock states) from structured-light propagation (spatial modes). This separation prevents the simulation of experiments where the spatial evolution of light directly influences non-classical quantum states and their interference, a capability essential for discovering novel phenomena involving atomic interactions, spatial-mode sorting, and complex interferometry.

Methodology
The authors introduce esQueranto, a differentiable software framework implemented in JAX that unifies photon-number quantum optics with structured-light propagation within a single computational description.

Unified Representation: esQueranto represents optical states in the Fock basis $|n\rangle = |n_1, n_2, \dots, n_M\rangle$ , where modes are indexed by optical path ( $j$ ) and transverse spatial indices (Laguerre-Gaussian radial $p$ and azimuthal $\ell$ ). This allows the simulation of mixed states, coherent states, and squeezed states within a common Hilbert space.
Differentiable Workflow: The framework follows a workflow of space → state → circuit → simulate → measure. Crucially, it supports automatic differentiation with respect to continuous parameters (source amplitudes, phases, squeezing strengths, loss, dephasing, and geometric quantities). This enables gradient-based optimization and automated search within a fixed experimental topology.
Structured Light Propagation: The framework incorporates scalar paraxial optics using the ABCD formalism. It tracks the complex beam parameter $q(z)$ , beam waist, and wavefront curvature. A key feature is the handling of Gouy phases, which are mode-dependent and accumulate differently for different transverse orders. When fields with different beam parameters interfere, esQueranto analytically transforms them into a common transverse basis before applying beam-splitter operations, ensuring that spatial mismatches affect interference visibility physically rather than via phenomenological factors.
Noise and Open Systems: The framework models photon loss and dephasing via quantum channels acting on the optical modes, allowing for the simulation of open-system dynamics and noisy propagation.
Implementation: Built in JAX, esQueranto leverages just-in-time (JIT) compilation, vectorization, and hardware acceleration (GPU/TPU) for efficient evaluation and differentiation.

Key Contributions

Integration of Physical Domains: esQueranto is the first framework to combine Fock-state quantum optics (photon-number dynamics) with structured-light propagation (spatial modes, diffraction, Gouy phase) in a single differentiable simulator.
Differentiable Quantum Optics: It provides a unified interface for optimizing continuous experimental parameters (e.g., lens positions, fiber lengths, squeezing strengths) to maximize scientific objectives like fidelity or Fisher information.
Basis Transformation for Interference: The framework explicitly handles the change of basis required when interfering photons with different spatial beam parameters (e.g., different Gouy phases or beam waists), a critical step often overlooked in simplified models.
Demonstration Across Six Applications: The authors validate the framework across a broad range of scenarios:
- Multiphoton Interference: Simulating four-photon interference between nonlinear pair sources, capturing high-gain effects beyond perturbative low-gain approximations.
- NOON-like State Generation: Generating high-photon-number NOON states by interfering coherent light with squeezed vacuum.
- Heralded State Preparation: Reproducing an automatically discovered high-probability heralding scheme for path-entangled states (NOON8), achieving unit fidelity and a 500% improvement in heralding probability over previous human-designed schemes.
- High-Precision Interferometry: Modeling gravity-sensitive interferometry with simultaneous photon loss and dephasing, identifying an optimal fiber length (~44 km) where signal accumulation balances noise.
- Structured HOM Interference: Demonstrating how spatial mode mismatch and Gouy phases modulate Hong–Ou–Mandel interference visibility.
- Radial-Mode Sorting: Combining squeezing, heralding, and spatial-mode sorting with dephasing noise to show how coherence loss affects mode-dependent routing.

Results
The paper demonstrates that esQueranto can successfully simulate complex quantum-optical phenomena that require the interplay of spatial and quantum degrees of freedom.

In the multiphoton interference example, the simulator correctly predicts the shift in interference minima at high squeezing strengths due to higher-order Fock components, matching analytical high-gain treatments.
In heralded state preparation, the framework successfully models the circuit that produces a NOON8 state with unit fidelity, validating its ability to handle conditional measurements and complex interferometer topologies.
In interferometric sensing, the framework quantifies the trade-off between phase accumulation and noise (loss/dephasing), identifying a specific optimal propagation length that maximizes Fisher information.
In structured HOM interference, the results confirm that spatial mismatch reduces visibility and that the Gouy phase can be used to sort radial modes, with the simulator accurately capturing the transition from indistinguishable to distinguishable photon behavior based on geometry.

Significance and Claims
The authors position esQueranto as a significant step toward the "dream of a foundational simulator in physics." By bringing photon-number quantum optics and structured-light propagation into a common, differentiable description, the framework enables the automated discovery of experiments that combine physical effects previously treated in separate modeling domains.

The paper claims that esQueranto does not aim to replace specialized simulators (like MrMustard for Gaussian states or XLuminA for classical wave optics) but rather to create a shared design space where diverse physical processes can interact consistently. This capability allows researchers to explore experimental setups where spatial evolution directly influences non-classical quantum states, opening new directions for automated experimental design in quantum optics. The authors view this as a foundational step toward a universal simulator that could eventually integrate other physical domains, such as optomechanics, matter-wave optics, and atomic systems, into a single differentiable search space for scientific discovery.

Technical Summary: esQueranto – Differentiable Structured Quantum Light for Automated Scientific Discovery

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