# Virtual Reality for Understanding Artificial-Intelligence-driven Scientific
Discovery with an Application in Quantum Optics

Philipp Schmidt<EMAIL_ADDRESS>Sören Arlt
<EMAIL_ADDRESS>Max Planck Institute for the Science of Light,
Erlangen, Germany  Carlos Ruiz-Gonzalez  Max Planck Institute for the Science
of Light, Erlangen, Germany  Xuemei Gu  Max Planck Institute for the Science
of Light, Erlangen, Germany  Carla Rodríguez  Max Planck Institute for the
Science of Light, Erlangen, Germany  Mario Krenn<EMAIL_ADDRESS>Max
Planck Institute for the Science of Light, Erlangen, Germany

###### Abstract

Generative Artificial Intelligence (AI) models can propose solutions to
scientific problems beyond human capability. To truly make conceptual
contributions, researchers need to be capable of understanding the AI-
generated structures and extracting the underlying concepts and ideas. When
algorithms provide little explanatory reasoning alongside the output,
scientists have to reverse-engineer the fundamental insights behind proposals
based solely on examples. This task can be challenging as the output is often
highly complex and thus not immediately accessible to humans. In this work we
show how transferring part of the analysis process into an immersive Virtual
Reality (VR) environment can assist researchers in developing an understanding
of AI-generated solutions. We demonstrate the usefulness of VR in finding
interpretable configurations of abstract graphs, representing Quantum Optics
experiments. Thereby, we can manually discover new generalizations of AI-
discoveries as well as new understanding in experimental quantum optics.
Furthermore, it allows us to customize the search space in an informed way -
as a human-in-the-loop - to achieve significantly faster subsequent discovery
iterations. As concrete examples, with this technology, we discover a new
resource-efficient 3-dimensional entanglement swapping scheme, as well as a
3-dimensional 4-particle Greenberger-Horne-Zeilinger-state analyzer. Our
results show the potential of VR for increasing a human researcher’s ability
to derive knowledge from graph-based generative AI that, which is a common
abstract data representation used in diverse fields of science.

## Introduction

Figure 1: Virtual Reality (VR) assisted digital discovery workflow for
obtaining insight from solutions discovered by Artificial Intelligence (AI).
AI results are studied in VR utilizing interactive 3D visualization to
discover interpretable structures. These are used to manually build new graphs
or to direct the AI with smart initial geometries for more efficient searches.

Virtual Reality (VR) describes the full immersion of a human in a simulated
environment, most commonly via the use of a Head Mounted Display, also known
as a VR-Headset or VR-Glasses. Modern headsets feature stereoscopic rendering
on top of the head and gaze tracking combined with gesture controls by
tracking controllers in all spatial degrees of freedom. The applications of
immersive technology are vast and varied [1], including but not limited to
entertainment, education [2, 3, 4], industry and engineering [5, 6, 7], neuro-
and medical science and therapy [8, 9, 10, 11, 12, 13] and data science [14,
15].

In the natural sciences, VR is used to visualize and analyze complex, often
three-dimensional (3D), scientific data, such as molecular or material data
[16, 17, 18, 19, 20], microscopy data [21, 22, 23, 24] or astronomical data
[25, 26, 27]. VR is also used to better visualize neural network models [28,
29, 30] to address the challenge of making Artificial Intelligence (AI)
explainable [31]. In addition, when the AI output is compatible with existing
VR frameworks, it can be studied in an immersive environment such as reviewing
drug candidates [32]. Beyond improved visualization, VR offers natural ways of
interacting with scientific results via intuitive gestures [33], which can be
exploited, for example in interactive molecular simulations [34, 35]. Through
this interactivity, the VR platform enables a variety of ingenious methods
like using interactive simulations to sample data for machine learning tasks
[36, 37] or even manipulating microscopic systems in real-time via in-VR-
interaction [38].

In this work, we show that modern VR technology can be effectively applied to
enhance the interpretability and conceptualization of scientific results
discovered through AI. In particular, we study AI-discovered quantum optics
experimental setups. By representing such experiments as abstract colored
graphs [39, 40, 41], we can map complex setups into networks which in turn
benefit greatly in legibility and interpretability when visualized n a true 3D
environment [15]. We demonstrate the unlocked potential by showcasing (1)
interpretable structures in AI discoveries and (2) generalizations to new
experiments derived from AI results by exploiting their graph geometry.

To this end, we built AriadneVR 111In greek mythology Ariadne is Theseus wife,
assisting him discovering the way out of the labyrinth. AriadneVR assists the
Theseus algorithm [42] in discovery., a webVR tool that allows us to visualize
and edit experimental graphs as well as to dynamically compute their current
state. AriadneVR is hosted online, and does not require any additional
hardware beside of the VR headset and controllers. With it, we discover
previously unknown relations in the construction of different state-generation
experiments for high-dimensional Greenberger-Horne-Zeilinger (GHZ) states [43]
and generalize AI-discovered high-dimensional entanglement swapping
experiments to a new setup for high pair counts. Furthermore, we extend to
human-in-the-loop AI-discovery by intelligently restricting search space based
on observed patterns in a related discovery in the case of a high-dimensional
GHZ-state analyzer to achieve the ability to measure a larger state. The
methods used for these discoveries are conceptually depicted in Fig. 1. Our
techniques are not limited to quantum optics; they can also be applied to
interpret any generative AI outputs involving graph representations.

## AI-driven Discovery in Quantum Physics

AI in Natural Science \- In this work, we leverage the potential of VR to
augment the process of extracting scientific understanding from solutions to
scientific problems discovered by AI. Among other tasks, AI is used to
efficiently search vast configurational spaces to propose testable answers to
research questions [44, 45], such as predicting protein folding patterns [46],
developing drug candidates [47], designing new materials and molecules [48,
49, 50, 51], quantum circuit design [52] or discovering experimental setups
[53, 54].

Even though solutions discovered in this way have value on their own, they
might not generally provide scientific understanding if their discovery does
not lead to new generalizable insights [55, 56, 57]. Achieving such an
understanding can be very challenging when algorithms do not provide
conceptual reasoning alongside the output. In such cases, the scientist has to
deduce the fundamental ideas behind results from examples alone [57].

Discovery in Quantum Optics \- In quantum optics, algorithms are used to
efficiently discover new experiments. In its earliest iterations, this is done
by assembling a setup out of a pre-defined toolbox of elements to solve a
specific task, e.g. designing experiments for quantum state generation,
tranformation or metrology [58, 59, 53]. However, many setups can fulfill the
same task with minor differences between them, which further expands the
already vast search space and decreases search efficiency. This challenge is
mitigated by choosing a more efficient, abstract representation of quantum
optical setups as colored graphs, where a single graph can represent different
setups that yield the same result [39, 40, 41]. Consequently, the search space
for experiments is reduced to the space of graphs. Additionally, such graphs
have been shown to be interpretable, allowing the development of conceptual
understanding and novel methods from AI solutions [42, 60].

The Graph Representation \- Here, we briefly explain the graph representation
of quantum optics for the specific question of finding experimental setups for
generating and measuring photonic quantum systems. In this representation, an
experimental setup is encoded as a colored, weighted graph by identifying
vertices as photon detectors and edges as correlated photon-pair sources [39,
40, 41]. An edge linking two vertices corresponds to the pair-photons
propagating to the corresponding detectors. The complex edge weight encodes
the amplitude and phase of the respective pair. This way, the weights also
account for phase shifts and losses in optical elements like beam splitters
and mirrors, as well as any occurring interference. The color of the edge is
used to specify the internal photon mode, e.g. its polarization, path, spatial
mode, time-bin, or frequency.

Experimentally, quantum states are commonly obtained by relying on
simultaneous detection events across all detectors, known as n-fold
coincidence detection. In the graph picture, such events correspond to subsets
of edges containing each vertex exactly once, called perfect matchings. As an
example, a square graph decomposes into two perfect matchings:

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One such perfect matching corresponds to one term contributing to the final
quantum state. The amplitude and phase associated with the term are computed
as the product of all edge weights in the matching. Thereby, a coherent
superposition of all the perfect matchings in the graph leads to the final
post-selected quantum state.

Figure 2:  Optimization flow for a 2-dimensional 4-particle Greenberger-Horne-
Zeilinger (GHZ) state of the PyTheus-algorithm [54]. Starting from a fully
connected initial graph, PyTheus iteratively performs continuous edge weight
optimisation and subsequent pruning of unnecessary edges until a minimal graph
is reached that fulfills the desired output. When translating the resulting
graph to the experimental setup, every vertex represents a detector, and every
edge a correlated photon-pair source emitting towards the connected detectors.
The terms contributing to the final quantum state of the experiment are
conditioned on coincidence detection of all detectors. In the graph picture,
these terms correspond to perfect matchings, subgraphs where each vertex is
only reached by a single edge (see equation (1)).

The colored, weighted graph contains the full information of the quantum
optical experiment and can be translated into several different realizations
using different technologies. The most straightforward way of translation is
using entanglement by path identity, a way of creating superpositions of
emission events by perfectly aligning photon paths [61, 62]. Such an example
is shown in Fig. 2. Measurements can be described in the same way using the
Choi-Jamiołkowski isomorphism [42, 54]. This technique allows for a native
translation of experimental setups to abstract graphs and has been practically
implemented in recent experimental works [63, 64, 65, 66].

PyTheus \- PyTheus is an open-source AI tool for discovering new quantum
optics experimental setups [54]. It can discover a variety of different types
of experiments, such as state generation setups, communication protocols,
measurement devices, or photonic quantum gates.

The initial step in searching for an experiment is to define the desired
experimental task. Subsequently, one specifies the initial parameters such as
the number of detectors, incoming and outgoing photons, and potential
topological constraints. With these parameters, PyTheus constructs the largest
possible setup in graph form. The initial graph is then refined in two
iterative steps: (1) by minimizing the desired loss by optimizing the graph
weights, and (2) by performing topological optimization to remove unnecessary
edges. In this way, PyTheus attempts to find the sparsest graph realizing the
experiment. The optimization loop is depicted in Fig 2.

## Physical Background

We show graphs of experiments for the creation and measurement of GHZ-states
as well as high dimensional entanglement swapping. Both topics are highly
relevant to the fields of quantum communication and quantum computing but are
also used to investigate the fundamental properties of quantum physics [67,
68]. Here, we briefly introduce the quantum physical background of these
experiments.

GHZ-states and GHZ-analyzers \- GHZ-states are a class of highly entangled
multi-particle states originally conceived as a 3-particle generalization of
the well-known bell states [43]. Both classes of states form a multi-particle
orthogonal basis set, where each particle is maximally entangled with all
others. Since their original proposal, they have been generalized both to
particle numbers larger than three and dimensions higher than two [69, 70, 67,
64, 71]. In this work, we discuss graphs relating to the GHZ-state of $n$
particles in $d$ dimensions which is given as:

$|GHZ\rangle_{n}^{d}=\frac{1}{\sqrt{d}}\sum_{i=0}^{d-1}\left|j\right\rangle^{\otimes
n}.$ (2)

GHZ-state analyzers are setups distinguishing one or more GHZ-states out of an
unknown input state [72]. We discuss binary analyzers distinguishing between
the presence or absence of a specific GHZ state given by Equation (2).

High Dimensional Entanglement Swapping \- In its original form, entanglement
swapping refers to the preparation of two Bell pairs and the subsequent
projection of one particle of each pair in a joined Bell state. This
measurement also collapses the remaining two particles in a joined Bell state
of their own, without them ever having interacted [73, 74].
This process can be generalized to multipartite entanglement generation using
GHZ states as the initial entangled states [75]. High-dimensional entanglement
swapping refers to non-locally creating $d$-dimensional Bell-pairs of the
form:

$\left|\Phi^{+}_{d}\right\rangle=\frac{1}{\sqrt{d}}\sum_{j=0}^{d-1}\left|jj\right\rangle.$
(3)

We show graphs creating $n$ such pairs simultaneously between two parties and
refer to it as $n$-pair entanglement swapping.

Many experiments implementing the tasks mentioned above require additional
photons to realize the desired output. These helper photons are called
$ancillae$, opposed state photons.

## AriadneVR

Here we introduce AriadneVR 222https://github.com/artificial-scientist-
lab/AriadneVR, our web-based virtual reality application for visualizing and
analyzing colored graphs representing quantum optics experiments. It is
developed with the open-source framework A-Frame333https://aframe.io/ using
HTML and JavaScript on an Oculus Quest 2. The tool runs fully locally in the
headset’s browser, requiring neither installation nor a tether to a computer
for 3D rendering.

For preprocessing graphs, we use the igraph Python library [76] and its pre-
implemented Kamada-Kawai-algorithm [77] to obtain a 3D-mapping of vertices.
This creates an initial arrangement to be perfected manually in virtual
reality. The layout-generation step is performed outside the tool and creates
a file containing all relevant information to be stored on the host platform
(e.g. GitHub for hosting via GitHub Pages444https://pages.github.com/). When
running the tool, A-Frame then uses the THREE.js 3D
library555https://threejs.org/ under the hood to construct a model from the
graph information. The VR environment is shown in Fig. 3.

Our tool allows the exploration of graph representations of quantum optics
experiments through visualization and interaction, i.e. manual sorting and
editing the experimental setup in its graph form. Beyond this, it supports the
steering of PyTheus’ searches by generating instruction files based on
constrained geometries defined in VR. Graphs from the library can be spawned
alongside each other and investigated simultaneously. The vertex arrangements
are changed by simply grabbing and dragging them around as desired. When a
user makes functional changes to a graph, e.g. adding a new edge by drawing
with the controller, the changing state is dynamically tracked. The resulting
perfect matchings of a graph are available to be spawned as additional 3D
models. To save the current form of a graph, a file can be downloaded to the
headset, which can then be placed into the host library to make it available
for later sessions. Similarly, the user can download a PyTheus instruction
template, where the current graph is set as the initial graph for the search.
To streamline this process, edges can be drawn without defining their color,
representing a connection where all possible edges are in the initial graph.
The framerate for displaying a typical graph is about 40 per second with an
Oculus Quest 2.

Figure 3: Point of view of an exemplary PyTheus graph analysis inside the
environment of AriadneVR. A PyTheus graph is shown with one perfect matching
subgraph on the right. A rendered version of this graph is depicted in
Fig.4(a).

While AriadneVR is built for analyzing quantum optics experiments, its core
functionality is visualizing and editing small colored graphs, hence can be
applied to other graphs too, assuming they are fed into the pre-processing
pipeline in an appropriate format. As AriadneVR is directly processed at the
computer of the VR glass, the framerate will decrease for large graphs. For
large graphs, with more than 100 nodes (e.g. graphs studied in social science)
a powerful external computer is necessary for rendering the structures. In
that case, different software such as VRnetzer [15] are better suited.

## Applications

Figure 4: Through interactive 3D visualization structure is easily revealed in
complex graphs. (a) I: 2D representation of a 3-particle 4-dimensional GHZ-
state analyzer and its discovered 3D geometry. (a) II: Interference loop
example on the undesired $|311\rangle$ ket. Interactive Figure. (b) I:
3-particle 5-dimensional GHZ-state in 2D and 3D. (b) II: 4-particle
4-dimensional GHZ state in 2D and 3D.Interactive Figure. (b) III: Common core
subgraph highlighted in both previous graphs signifying the nature of both
graphs as generalizations of the $|GHZ\rangle_{4}^{3}$ state. Interactive
Figure. Ancillae are drawn as squares/cubes, detectors as circles/spheres, and
input modes as triangles/tetrahedrons. Colors represent photon modes,
indicators on edges their negative weight. Figure 5: Manual discovery of new
graphs assisted by VR for efficient high dimensional entanglement swapping.
PyTheus discovered graphs are watermarked. Through experimentation with graph
edits, concepts can be easily transferred and tested on new graphs.(a)
Discovered extension mechanism for higher dimensions extracted from efficient
PyTheus discovered 2-dimensional entanglement swapping, represented by the
graph for three 2-dimensional pairs and a single 3-dimensional pair in the
center. Interactive Figure. (b) PyTheus discovered solution for 2-pair
3-dimensional swapping. Interactive Figure.(c) Application of the mechanism
from (a) to a subgraph from (b) to obtain a new swapping graph for 4-pair
3-dimensional swapping. Interactive Figure.

We use VR in a threefold manner as shown in Fig. 1. The basis of all our VR
analysis is the discovery and interpretation of structure in an experimental
graph. We provide interactive 3D figures and basic VR environments for all
graphs mentioned in this work at the accompanying website. Through manual
sorting, the majority of PyTheus graphs can be transformed into visually clean
structures, some of which are immediately interpretable, revealing information
on how the respective graph achieves its task. If the mechanism underlying a
graph is understood, we can manually generalize it to new experiments. This is
done directly in VR by drawing new or extending existing graphs. However, in
some cases the underlying structure is not immediately obvious, and it remains
unclear how to generalize the graph. Here we can use VR to propose geometries
of potential generalizations. We then use PyTheus to search for solutions to
confirm or reject our candidates.

Finding interpretable structures in 3D Graphs – In the following, we show
three selected examples from Ref. [54] and Ref. [60] where interpretable
3D-representations were found using AriadneVR. For better visual clarity, we
use renderings made with Blender 4.0666https://www.blender.org/ instead of
screenshots of the VR environment for depictions of 3D-graphs.

Figure 6: Discovering graph generalizations by using AriadneVR to define
initial graph geometries for PyTheus searches based on preexisting
discoveries. I: Discover the structure in the PyTheus discovered graph of a
3-particle 3-dimensional GHZ-state analyzer. Interactive Figure. II: Use
AriadneVR to define a search geometry based on said structure. Interactive
Figure.III: Use PyTheus on the restricted Geometry to discover a 4-particle
generalization. Interactive Figure

Fig. 4(a) shows a 3-particle 4-dimensional GHZ-state analyzer. Beyond the
striking symmetry of the discovered 3D structure, there is a functional
feature exemplified by this highly complex solution. As a measurement graph,
it needs to ensure that all coincidence events produce terms belonging to the
desired state or interfere destructively. A common way to achieve this in the
graph picture is by constructing loops of even edge count with a total
negative sign. Such loops were discovered in this particular graph in VR
simply by superimposing the 3D models of two interfering perfect matchings.

Fig. 4(b) shows (I) $|GHZ\rangle_{3}^{5}$ and (II) $|GHZ\rangle_{4}^{4}$ state
creation graphs. Ancillae are described by cube-shaped vertices and state
photons by spherical vertices. Through their 3D structure discovered in VR, it
is revealed, that both graphs share the same triangular graph structure
highlighted in the center of both graphs. The only difference is the central
vertex being an ancilla in $|GHZ\rangle_{3}^{5}$ and a state photon in
$|GHZ\rangle_{4}^{4}$. In the latter, this core graph creates a 4-particle
3-dimensional GHZ state. The $|GHZ\rangle_{3}^{5}$-graph declares one photon
of this subgraph as an ancilla (vertex 5 in Fig. 4(b) I) to reduce the state
photon count from four to three. Any remaining photon modes are then added by
the outer ancilla structure for both graphs. The examples shown here are
representative of insights made easily accessible just by moving to
stereoscopic rendering and intuitive manual sorting.

Manually discovering new AI-inspired experiments in VR \- AriadneVR allows the
user to modify and edit graph structures and construct completely new ones.
Geometric understanding obtained through the superior rendering in VR combined
with the user’s physical understanding of the experimental mechanisms can then
be used to manually engineer new graphs.

This process is shown on an example in Fig. 5. Here, we show the discovery
method in the case of resource-efficient high-dimensional multi-pair
entanglement swapping. The discovery is based on the PyTheus-generated
solution for 2-pair 3-dimensional entanglement swapping without requiring a
3-dimensional Bell-state measurement (graph 78 in Ref. [54]) shown in Fig.
5(a). By combining it with an AI-inspired construction method (see Fig. 5(b))
of generating high-dimensional non-locally entangled pairs derived from a
different AI-discovered graph for 3-pair 2-dimensional entanglement swapping
(graph 77 in Ref. [54]) we can generalize to a new, previously unknown 4-pair
3-dimensional entanglement swapping graph. The result is shown in Fig. 5(c).
It effectively creates one whole 3-dimensional pair with no additional
resource cost in ancillae by superimposing additional creation processes from
single-pair experiments. It is an alternative setup to stacking two of the
2-pair AI solutions showing the same novel decrease in required ancillae.
AriadneVR assists this discovery process by firstly providing easy access to
graph structures and secondly offering an intuitive method of defining new
graphs through manual drawing.

Steering AI discoveries through VR via customized search spaces \- Potentially
useful generalizations to quantum optical experiments can involve the increase
in particle count, dimensionality, or both [67, 68]. Searching for such
generalizations from scratch can be inefficient as the corresponding initial
graphs, i.e. the search spaces, quickly increase in size. For example, the
initial graph for 4-particle 2-dimensional GHZ-state generation has 24 edges.
Searching for a 3-dimensional generalization more than doubles this amount to
54 edges, and attempting a 4-dimensional state without additional ancilla
raises the size to 96 edges.

We can use AriadneVR to customize our search spaces and decrease the size of
the initial graph to steer PyTheus to more efficiently discover desired
solutions. We achieve this by analyzing existing solutions for lower graph
sizes and defining candidate geometries of extensions based on observed
patterns. In Fig. 6 we show this process for the generalization of a
3-particle 3-dimensional to a 4-particle 3-dimensional GHZ-state analyzer. The
3-particle analyzer is highly symmetric. Our candidate for a 4-particle
geometry keeps this symmetry and follows the same patterns observed in the
smaller solution. By restricting the initial graph to this geometry, the
search for the 4-particle analyzer is reduced from 124 edges down to 74. In
this way, we can use human intelligence to assist PyTheus in its discovery
task, which in turn can provide the human scientist with the example cases
needed for concept extraction.

## Conclusion and Outlook

In this work, we presented ways to leverage the unique potential of immersive
technology in the AI-driven discovery process for quantum optics experiments
using PyTheus and our purpose-built VR-tool AriadneVR. By interactively
exploring the graph representations of quantum optics, a new approach to
learning from AI to develop new experiments and insight is opened. Beyond
furthering the understanding of existing solutions for GHZ-state creation and
measurement, we achieved substantial machine-inspired discoveries with our
tool. We engineered a new alternative 4-pair 3-dimensional entanglement
swapping setup, where one pair is created at no additional photon cost with
knowledge derived from AI discoveries. We also showed the human-assisted AI
discovery of a 4-particle 3-dimensional GHZ-state analyzer. To further exploit
the potential of VR our prototype could be expanded to include multi-user
support for cooperative analysis and direct access to PyTheus within VR.
Additionally, a variety of potential visualization features and tools could be
added to streamline the analysis process. Examples include computational
operations on vertices as well as support for more post-selection conditions.
Beyond PyTheus’ discoveries, the methods developed here can potentially also
prove useful in other AI-discovery fields where graph-based representations
are used, such as in quantum computing (quantum circuits [52], especially ZX-
graphs [78]), material or protein design (involving crystal structures and
molecular graphs [79]) and DNA-origami design [80, 81] in material science and
biochemistry. We believe that enhancing human researchers’ capabilities to
comprehend complex data with technologies like VR is crucial to fully utilize
the power of AI for scientific discovery. Beyond task-specific applications,
immersive technologies also have the potential to fundamentally transform the
scientific workspace by allowing remote collaboration and experimental control
[82].

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