=Paper=
{{Paper
|id=Vol-3417/short8
|storemode=property
|title=Quantum Robotic Swarms: What, Why, and How (short paper)
|pdfUrl=https://ceur-ws.org/Vol-3417/short8.pdf
|volume=Vol-3417
|authors=Maria Mannone,Valeria Seidita,Antonio Chella
|dblpUrl=https://dblp.org/rec/conf/aiia/MannoneSC22a
}}
==Quantum Robotic Swarms: What, Why, and How (short paper)==
https://ceur-ws.org/Vol-3417/short8.pdf
Quantum Robotic Swarms: What, Why, and How
Maria Mannone1,2,* , Valeria Seidita1 and Antonio Chella1,3
1
Department of Engineering, University of Palermo, Italy
2
ECLT and DAIS, Ca’ Foscari University of Venice, Italy
3
ICAR CNR National Research Council, Italy
Abstract
What is quantum computing, why do we need it, and how can we use it? Similarly: What is swarm
robotics, why do we need it, and how can we use it? We try to briefly answer these questions, discussing
some possibilities to apply quantum computing to swarm robotics, to get the best out of them. We also
discuss a possible application of sonification as human-friendly feedback, and possible directions to be
undertaken in future research.
Keywords
quantum computing, robotic swarms, sonification
1. Introduction
Nature inspires the brush of the artist and the pen of the scientist. Robotics is a research area
that owes a lot to nature, from the complexity of sensory cognition to the grace of movements.
In particular, the observation and investigation of self-organization in natural swarms paves the
way toward robotic swarm development. Another part of nature, the “physics of the small,”
inspires computational tools. It is the case of quantum computing, whose basics are rooted in the
superposition principle, destructive measure, and entanglement in quantum mechanics.
Here, we provide synthetic explanations of What, Why, and How in quantum computing and in
swarm robotics (Sections 2 and 3, respectively), including some essential references. Then, in
Section 4, we discuss the pros and cons of mixing them up. The article is ended with a discussion
on the possible role of sonification in this endeavor (Section 5), an example of application (Section
6), and some hints toward future research. In sections 2–4, we present with a jargon-free language
the core ideas on these topics. Then, we narrow down the explanation to present our specific
work, discussing its key points in Section 6.
The 9th Italian Workshop on Artificial Intelligence and Robotics – AIRO 2022
" mariacaterina.mannone@unipa.it,maria.mannone@unive.it (M. Mannone); valeria.seidita@unipa.it (V. Seidita);
antonio.chella@unipa.it (A. Chella)
~ http://www.mariamannone.com/ (M. Mannone); https://www.unipa.it/persone/docenti/s/valeria.seidita (V. Seidita);
https://www.icar.cnr.it/en/associati-di-ricerca/esterno-1/ (A. Chella)
0000-0003-3606-3436 (M. Mannone); 0000-0002-0601-6914 (V. Seidita); 0000-0002-8625-708X (A. Chella)
© 2021 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
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2. Quantum computing
What? Quantum Computing is a branch of computer sciences, inspired by the principles of
quantum mechanics. The idea of the classical bit (the basic unit of memory), with the two values
0 or 1, is extended to the qubit, which can assume all possible values between 0 and 1. We can
create a superposition of 0 and 1 with different probability amplitudes. The quantum bit is called
qubit. Logic gates developed in classic computer sciences can be used in quantum computing,
provided their re-writing with reversible gates, in analogy with invertible operators.
Why? Quantum Computing is mostly exploited to speed up algorithms, improving their
efficiency and reducing computational complexity. Current research mainly aims to prove the
fastness of quantum algorithms and develop stronger and safer quantum computers. A specific
branch of research deals with the ‘translation’ itself of classic algorithms in terms of reversible
logic gates, and the definition of completely new ones. Many algorithms are based on applications
of the entanglement [1, 2], that is, the connection between particles, influencing each other
non-locally. The entanglement is one of the most striking quantum effects. Thus, theoretical
knowledge in physics can lead to computational applications. Conversely, research developed
with quantum computers can help better understand the interaction between individual particles,
constituting a benchmark for new theories and experiments.
Several advantages of quantum computing have been proven, but they come with a main
drawback: decoherence. This is the loss of information due to the interaction of the quantum
system with the environment. Scientists are currently working to minimize the risk of decoherence,
and design error-free quantum computers. Promising results and new algorithms are continuously
appearing. The so-called quantum supremacy is yet to be proven, but it seems that scientists are
on the right track.
How? In the latest years, researchers have had access to a variety of computing centers and
interfaces that would have been unthinkable, let’s say, ten years ago. There are physical quantum
computers, owned by major research centers and companies such as IBM and Amazon. These
companies often allow researchers to remotely access a small portion of their computational
power for free. However, there are some limitations to these free-access options: the number of
possible qubits in a circuit is limited, and there is an online queue to run the circuit.
As an alternative to real computers, there are simulators. The number of available qubits
is higher, and there are limited waiting times. A simulator runs on a classic computer, and it
approximates the behavior of a quantum device. In so doing, the simulator’s outputs present a
lesser quantum rumor than its ‘real’ version. It means that the results obtained with a simulator
are much closer to theoretical expectations than those coming from real quantum computers.
Concerning hardware, a quantum computer is a device different from a classic one. The qubits
are recreated through physical systems: for instance, the orientation of a photon or the spin of an
electron. The initial idea of quantum computers came from physics, with Benioff and Feynman
[1].
3. Swarm Robotics
What? Swarm robotics is a branch of robotics, focusing on hardware and software of small,
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simple, autonomous, interacting, and self-organized multiple robots [3, 4, 5, 6, 7]. In a swarm,
global behavior is a complex phenomenon. It emerges from local interactions of the swarm
members, governed by simple rules. Robotic swarms and their organizational principles are
often inspired by natural swarms, such as flocking birds [8], schooling fish [9], and foraging ants
[10, 11] and termites [12]. Other sources of inspiration are morphogenesis processes, with the
self-organization of cells [13].
Why? Robotic swarms achieve complex goals with several simple robots, where each unit
accomplishes a simple task. Advantages of swarm robotics include autonomy, cooperation,
scalability, cost-effectivity, and adaptability. Robots in a swarm are autonomous because each of
them takes local decisions according to their perception of the environment and the messages
exchanged with their peers. Robots in a swarm cooperate to achieve a complex task, be it search
and rescue or shape formation. Thanks to the scalability, even in the case of loss of a single unit,
the behavior of the whole is not compromised [5, 4]. Thus, they present an economic advantage
with respect to single, less expensive, and complex robots, especially in risky situations, leading
to a cost-effectiveness of the whole system. A robotic swarm can also constitute a model to test
theories on natural swarm formation and behavior. Another application involves small-sized
robots entering the human body and locally and precisely delivering a drug [14].
How? Quantum computing can be approached with real devices and simulators. The same
applies to robotics: there are tangible devices and simulated ones. Working in a simulation
environment allows one to design new robots, check their feasibility, make tests taking into
account the physics of the system without damaging any expensive device, and check the
effectiveness of a prototype or of an algorithm to achieve a task.
4. Quantum + Swarm Robotics
What? Mixing the quantum with swarm robotics means applying quantum algorithms to robotic
controllers. A classic robotic controller can be enhanced with a faster quantum version. We have
to bear in mind that robots live and act in the domain of classical physics: thus quantum effects,
such as the Heisenberg indeterminacy, do not apply. For this reason, the quantum paradigm
can enter details of the decision-making process, or we have to mathematically quantize some
variables, or make some probabilistic assumptions. For instance, we can start with the definition of
probability amplitudes and superposition of different conditions (such as positions and rewards),
in analogy with quantum states (up, down) in quantum mechanics [15].
Why? The two things together, swarms of robots and quantum computing, allow a computa-
tional speed-up for missions of simple, interacting robots. Thus, the advantages of efficiency and
scalability sum up. We may say that, ideally, they help save “time and money”: computational
time and money to buy robots.
More conceptually, the operation of ‘quantum translation’ of classic algorithms does apply
to swarm-robotic controllers as well. Such a translation is based on reversible logic gates and
measurements as the constitutive elements of quantum circuits. We can thus explore potentialities
and applicability limits of quantum computing for swarm robotics. As mentioned while discussing
the advantages of quantum computing, also in the case of the swarm we can use the new tools to
deepen our knowledge of natural phenomena. For instance, we can enhance our understanding of
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complex systems using robots to represent particles and agents, and quantum computing to model
emerging behaviors out of simple local rules. There are already some studies on quantum particle
swarm optimization [16]; however, the aim of future research is broader than just an improved
optimization system. This is why we are not delving here into a detailed comparison with typical
methods for swarm robotics.
Quantum effects such as indeterminacy, superposition, and entanglement may lead to im-
provements in swarm robotics. Entanglement may enhance swarm’s communication strategy
and cohesiveness, letting single robots act as particles of the same system and modifying their
configuration according to the changes made to one of them. Single-robot configurations, such as
space distribution and exploration-success feedback, can be modeled via eigenstate superposi-
tion (Section 6) with suitable probability amplitudes. Their variation for all robots leads to the
emergent behavior. Distributed control may be achieved via a system of quantum gates taking as
inputs the current robotic configurations at 𝑡 and giving as outputs, e.g., positions suggestions at
𝑡 + 1.
How? Some pioneering studies aim to join robotics with the quantum world [17, 18, 19],
and only a few concern swarm-robotic applications [20, 21]. The quantum paradigm can shape
the decision-making system of a single robot, e.g., to make more efficient the path-planning
task [22]. The quantum can also inform pairwise interactions between the elements of the
swarm, influencing their individual decisional process and emerging behavior. In Section 6, we
summarize our approach.
4.1. Caveats
Drawbacks mainly concern the availability of quantum computers or simulators the units (or a
computing center) have (has) to connect with, and the issue of decoherence, that is, the loss of
entanglement due to the interaction with the environment [1]. In addition, the use of quantum
requires the access to online computational resources.
5. Some magic: sonification
Sonification is the transformation of given data into auditory information, using a suitable mapping
strategy. The choice of mapping must be motivated by data typology, properties to be highlighted,
possible auditory limitations, and aesthetic reasons. For scientific applications, sonification is
an alternative or an addition to visualization, enriching data understanding by one more sensory
dimension. There are entire conferences on sonification, for each one of the mentioned research
areas. We are particularly interested in sound renditions of swarm-robotic movements. Existing
examples are limited concerning other sonification applications. They consist of: rhythmic
patterns generated according to neighboring interactions [23]; robotic-role identification through
sound [24] and pre-composed polyphonic music playing; harmonic structures translated into
swarm geometries [25]. There are also studies on the feedback of multi-robot behavior [26] with
user-selected songs played with different timbres according to robots’ proximity. In Section 6,
we discuss our proposed example of sonification for a quantum-driven robotic swarm. Basically,
sound can convey information regarding robots’ position, with convergence as an emerging effect
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from sound superpositions. In addition, sounds can provide feedback in cases of occlusions,
gradually morphing when the robot solves the issue. Sonification is today exploited in different
branches of research. Its application to swarm robotics is promising yet to be fully explored.
6. An example
In our research, we started from the simple definitions of state superposition, probability amplitude
to get an outcome, and destructive measurement to sketch some applications for robotic swarms.
In particular, we defined a circuit modeling pairwise interactions between robots, where the
behavior of the 𝑖-th robot at time 𝑡 + 1 is influenced by the results previously obtained by the
𝑗-th robot at time 𝑡. The swarm behavior emerges from these autonomous pairwise interactions.
In [15], we also defined a block matrix representing the swarm information from the point of
view of robots. Diagonal blocks contain information about each single robot, and off-diagonal
blocks contain the pairwise information exchange. Our block matrix characterizes a robotic
swarm. Comparing different swarms means comparing different matrices. To this aim, we
presented a formalism based on category theory, allowing comparisons of swarms at the “same
level” (e.g., swarms of the same number of simple flying robots and of simple swimming ones)
and at “different levels” (e.g., swarms of different degrees of complexity and adaptability to
different environments).
In another study [27], we added sonification to get auditory feedback of quantum-driven robots
during their motion, without any pre-composed musical material (except a library of single
pitches). We connect all the presented elements, that is, quantum + swarm + sound. We first start
with the definition of a mission, and how the basics of quantum computing can enter it. We focus
on a search-and-rescue mission, with multiple robots searching for a target. The closer the robot
to the target, the higher the level of ‘success.’ We can model the ‘closeness’ via a probability
amplitude to get ‘success.’ In this way, we can immediately introduce the concept of quantum
superposition: a robot that has no clues on the target is in a balanced superposition of ‘success’
and ‘failure.’ The robot can get information on target proximity through its sensory detection:
infrared light, laser, visible light information, sonar feedback, and so on, according to the nature
of the target, the physics of the scenario, and the characteristics of the robot. For the sake of
simplicity, we consider, as a measure of the robot’s successfulness, the Euclidean distance from
the target. We can extend the quantum analogy to the notion of position, as we call it “reward.”
In fact, we can define probability amplitudes to be in a corner of the 2D (or 3D) space. For the
sake of simplicity, we now consider as ‘positions’ the peaks of the quantum wavefunctions. We
can thus build a logic gate working this way: in a pairwise interaction, robot 1 communicates
to robot 2, telling where it is (probability amplitudes for the position) and what it found (the
reward). If the position of robot 1 is well-defined (a position more likely to be centered on 1
or 0, rather than on an equal superposition of them) and it is successful (reward more toward
1, success), then robot 2 follows robot 1. Otherwise, robot 2 explored other portions of space.
Which ones? Having more than two robots with pairwise interactions, each robot can shape its
decisions by evaluating the feedback of its peers. Or, we can have a computational center that
receives the feedback for each robot, and, according to the output of the quantum circuit for
decision-making, tells each robot where to go. We take the collection of the reached spatial points
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Figure 1: 𝑅1 , 𝑅2 are two robots. The star indicates the target. The visual indication of position is
actually the peak of the probability wavefunction. To each position there corresponds a musical
note. 𝑅1 searches and sends information to 𝑅2 . Case (a): if it is successful (probability amplitude
of success higher than 0.5) and the position is well-defined (probability amplitude of one extreme
of the line higher than 0.5) at 𝑡, then 𝑅2 reaches it at 𝑡1 . Case (b): if it is not successful, 𝑅2
searches elsewhere at 𝑡 + 1, and, in case of success, 𝑅1 reaches it at 𝑡 + 2.
and we map them into sound. Thus, at each time point, we obtain a chord, where the position of
each robot corresponds to a note. The complete simulation is thus transformed into a chorus of
robots. Figure 1 illustrates the core idea two robots approximately moving along a line and their
bichords.
We consider the mapping of robotics positions to pitches at each time point, eventually using
different timbres to distinguish between each robotic element. We discretize pitches using the
Western tuning systems, to easily represent classic scores. The superposition of notes produced
by each robot at each time point constitutes a chord. Observing the robots for four-time points,
we get a harmonic sequence of five chords. A different swarm behavior corresponds to a different
harmonic sequence. The closer the robots, the closer the pitches, and we obtain a harmonic
cluster. If the robots are approaching, their pitches are getting closer. If the robots are all moving
in the same direction in a parallel way, then also the voice leading will be parallel. If the robots
have to find a target and their sound corresponds to the (sonified) position of the target, then the
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mission is successful. If the robots converge on the wrong point, they will lead to another pitch.
Finally, we obtain a sequence of chords that is the sonification of the robotic-swarm movement.
Video examples and more technical details can be found in [27].
7. Conclusions and perspectives
Here, we summarized the Whats, Whys, and Hows of swarm robotics, quantum computing,
and the two research fields mixed. Amongst the reasons to undertake such an endeavor, we
may consider the swarm as a classic field [28]. Then, we can discretize the formalism treating
the swarm as a quantum field, toward a future Quantum Swarm Theory, inspired by quantum
fields in advanced quantum mechanics. Another reason is a renewed approach to quantum
cognition through the lens of the swarm. We may try to model a cognitive complex unit through
its decomposition into multiple sub-entities. The brain can be thought of as a collection of
interacting neurons, where each ‘neuron’ is a robotic unit. In this sense, in the future we
may exploit the quantum machinery to shape and support complex operations behind swarm
interaction, such as deep learning.
The connection between the biological world, quantum computing, and robotic models [29] is
yet to be explored. From quantum improvements for path planning, [22, 30], to quantum-based
decision-making systems, to sonification strategies allowing quick comparisons, we can focus on
technical efficiency-related studies and conceptual advancements. The quantum challenge for
robotics and artificial intelligence [31] is just started. Stay tuned!
References
[1] J. Preskill, Quantum computing 40 years later, in: A. Hey (Ed.), Feynman Lectures on
Computation, 2nd ed., Taylor & Francis Group, Abingdon, UK, 2021.
[2] J. Stolze, D. Suter, Quantum Computing: A Short Course from Theory to Experiment,
Wiley, Weinheim, Germany, 2004.
[3] P. Benioff, Quantum robots and environments, Physical Review A 58 (1998) 893.
[4] H. Hamann, Swarm Robotics: A Formal Approach, Springer, Cham, 2018.
[5] M. Schranz, M. Umlauft, M. Sende, W. Elmenreich, Swarm Robotic Behaviors and Current
Applications, Frontiers in Robotics and AI 7 (2020).
[6] R. Eberhart, Y. Shi, J. Kennedy, Swarm Intelligence, The Morgan Kaufmann Series in
Artificial Intelligence, Morgan Kaufman, Burlington, MA, USA, 2001.
[7] F. Zambonelli, N. Bicocchi, G. Cabri, L. Leonardi, M. Puviani, On Self-adaptation, Self-
expression, and Self-awareness in Autonomic Service Component Ensembles, in: 2011
Fifth IEEE Conference on Self-Adaptive and Self-Organizing Systems Workshops, 2011.
[8] C. H. Hemelrijk, H. Hildenbrandt, Schools of fish and flocks of birds: Their shape and
internal structure by self-organization, Interface Focus 2 (2012) 726–737.
[9] K. Zhu, M. Jiang, Quantum Artificial Fish Swarm Algorithm, in: Proceedings of the 8th
World Congress on Intelligent Control and Automation, 2010.
[10] S. Berman, Q. Lindsey, M. S. Sakar, V. Kumar, S. C. Pratt, Experimental Study and
7
Maria Mannone et al. CEUR Workshop Proceedings 1–5
Modeling of Group Retrieval in Ants as an Approach to Collective Transport in Swarm
Robotic Systems, Proceedings of the IEEE 99 (2011) 1470–1481.
[11] W. M. Shen, P. Will, A. Galstyan, C. M. Chuong, Hormone-Inspired Self-Organization and
Distributed Control of Robotic Swarms, Autonomous Robots 17 (2020) 93–105.
[12] C. Noirot, J. P. E. C. Darlington, Termite nests: Architecture, regulation and defence,
in: T. Abe, D. E. Bignell, M. Higashi (Eds.), Termites: Evolution, Sociality, Symbioses,
Ecology, Springer Netherlands, Dordrecht, 2000, pp. 121–139.
[13] I. Slakov, C. Carrillo-Zapata, D. Jansson, H. Kaandorps, J. Sharpe, Morphogenesis in robot
swarms, Science Robotics 3 (2018).
[14] X. Dong, M. Sitti, Controlling two-dimensional collective formation and cooperative
behavior of magnetic microrobot swarms, The International Journal of Robotic Research
39 (2020) eabe4385.
[15] M. Mannone, V. Seidita, A. Chella, Categories, Quantum Computing, and Swarm Robotics:
A Case Study, Mathematics 10 (2022) 372.
[16] G. Liu, W. Chen, H. Chen, X. Jiahui, A quantum particle swarm optimization algorithm
with teamwork evolutionary strategy, Mathematical Problems in Engineering 19 (2019)
1805198.
[17] D. Dong, C. Chen, C. Zhang, C. Chen, Quantum robot: structure, algorithms and applica-
tions, Robotica 4 (2006) 513–521.
[18] L. Lamata, M. Quadrelli, C. de Silva, P. Kumar, G. Kanter, M. Ghazinejad, F. Khoshnoud,
Quantum Mechatronics, Electronics 10 (2021) 2483.
[19] P. Atchade-Adelomou, P. Alonso-Linaje, J. Albo-Canals, D. Casado-Fauli, qRobot: A
Quantum Computing Approach in Mobile Robot Order Picking and Batching Problem
Solver Optimization, Algorithms 14 (2021). URL: https://www.mdpi.com/1999-4893/14/7/
194.
[20] A. Koukam, A. Abbas-Turki, V. Hilaire, Y. Ruichek, Towards a Quantum Modeling
Approach to Reactive Agents, in: 2021 IEEE International Conference on Quantum
Computing and Engineering (QCE), 2021.
[21] M. Alvarez-Alvarado, F. Alban-Chacón, E. Lamilla-Rubio, C. Rodríguez-Gallegos,
W. Velásquez, Three novel quantum-inspired swarm optimization algorithms using different
bounded potential fields, Nature Scientific Reports 11 (2021) 11655.
[22] A. Chella, S. Gaglio, G. Pilato, F. Vella, S. Zammuto, A quantum planner for robot motion,
Mathematics 10 (2022) 2475.
[23] T. Blackwell, Swarm music: improvised music with multi-swarms, in: Proc. AISBSympo-
sium in Artificial Intelligence and Creativity Arts Science, 2003, pp. 41–49.
[24] J. McLurkin, Stupid robot tricks: A behavior-based distributed algorithm library forpro-
gramming swarms of robots (Master’s Thesis), 2004.
[25] J. McLurkin, The Swarm Orchestra: Temporal Synchronization and Spatial Division of
Labor for Large Swarms of Autonomous Robots, https://groups.csail.mit.edu/mac/projects/
amorphous/6.978/final-papers/jamesm-final.pdf, 2022.
[26] F. Santos, Musical abstractions for multi-robot coordination (2016). URL: https://smartech.
gatech.edu/handle/1853/55049.
[27] M. Mannone, V. Seidita, A. Chella, Quantum RoboSound: Auditory Feedback of a Quantum-
Driven Robotic Swarm, in: RO-MAN 2022 Proceedings, IEEE, Naples, Italy, 2022, pp.
8
Maria Mannone et al. CEUR Workshop Proceedings 1–5
287–292.
[28] V. Edwards, P. deZonia, M. A. Hsieh, J. Hindes, I. Triandaf, I. B. Schartz, Delay induced
swarm pattern bifurcations in mixed reality experiments, Chaos 30 (2020) 073126.
[29] P. S. Emani, J. Warrell, A. Anticevic, et al., Quantum computing at the frontiers of biological
sciences, Nature Methods 18 (2021) 701–709.
[30] Z. Li, W. Liu, G. Li-E, L. Li, Path Planning Method for AUV Docking Based on Adaptive
Quantum-Behaved Particle Swarm Optimization, IEEE Access Multidisciplinary 7 (2019)
78665–78674.
[31] A. Wichert, Principles of Quantum Artificial Intelligence, World Scientific, Singapore,
2020.
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