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FH Zentralschweiz
Quantum Computing and
Artificial Intelligence in
Finance
Institute of Financial Services Zug IFZ
www.hslu.ch/ifz
1Quantum Computing and Articial Intelligence in Finance
Contents
1 Introduction 2
2 Diving into the Quantum World: Contrasting Quantum and Classical Physics 3
3 Quantum Technologies 4
4 Articial Intelligence and Machine Learning 5
5 Framework: Quantum Machine Learning 6
6 Literature Review 7
7 Use Cases 9
8 Quantum Computing Infrastructure 11
9 Conclusion 13
Authors and Contributors 14
References 15
Introduction 2
1. Introduction
In this report, we investigate the dynamic intersection between Quantum Computing and Articial Intelligence, with a focus
on Machine Learning, tailored for the discerning audience in the nancial industry. Our endeavor involves presenting the
current state of research and applications at this technological crossroads, where quantum principles meet the intricacies
of advanced machine learning algorithms.
To lay the groundwork, we embark on a historical exploration of the transition from classical to quantum paradigms within
the realm of physics. This journey not only unravels the evolution of scientic thought but also delves into the core dis-
tinctions between classical and quantum mechanics. This historical backdrop is instrumental in comprehending the recent
emergence of quantum technologies, including Quantum Computing, Quantum Cryptography, and Quantum Sensing.
Within the realm of Articial Intelligence, we narrow our focus to Machine Learning, a subset that has become integral to the
nancial landscape. Exploring the nuances of quantum and classical machine learning, we elucidate the distinctive features
and capabilities that quantum algorithms bring to the table. As we traverse this technological landscape, we discuss the
benets and limitations inherent in the fusion of quantum computing and machine learning, offering a nuanced perspective
for our esteemed readers in the nancial sector.
To steer our investigation, we introduce a framework crafted for the systematic grouping and analysis of literature. This
framework acts as a roadmap for navigating the diverse aspects of quantum machine learning and its applications in -
nance.
As we venture into the literature review, our focus sharpens on quantum machine learning in the nancial domain. Through
the analysis of existing research and developments, we aim to distill key insights that illuminate the potential transforma-
tions in nancial analytics, risk assessment, and decision-making processes.
We also illuminate implemented use cases that showcase the tangible impact of quantum machine learning in the nancial
industry. From optimizing trading strategies to enhancing fraud detection mechanisms, we unravel the possibilities that
quantum-infused machine learning holds for nancial institutions.
Lastly, we show possible future architectures of quantum computing in banking IT and conclude the report with a summary
in the form of hypotheses.
We would like to thank the research partners of the IFZ FinTech Program, who have supported this condensed study nan-
cially as well as in terms of content. These are e.foresight, Finnova, Inventx, Swiss FinTech Innovations, SIX, Swiss Bankers
Prepaid Services, and Zürcher Kantonalbank.
Thomas Ankenbrand Urs Rhyner A. Ege Yilmaz
HSLU Inventx Lab HSLU
3Quantum Computing and Articial Intelligence in Finance
2. Diving into the Quantum World: Contrasting
Quantum and Classical Physics
Classical and quantum mechanics are the two big frame-
works in physics, where the former mirrors the predictable
patterns we observe in everyday activities, such as the sat-
isfying arc of a basketball in ight or the rhythmic sway of
a swing set in motion. It is the part of physics whose devel-
opment started around the time of Isaac Newton (1642-
1727). During the era of Newton, Leibniz, and Galileo, a
primary focus was on investigating the motion of planets.
Newton’s curiosity was driven by questions about the ap-
parent orbits of Earth around the Sun, the Moon around
Earth, and the downward fall of objects like apples. A
major breakthrough was achieved when Newton recog-
nized that the laws of physics governing Earth are iden-
tical to those determining the motion of planets, which
is described by its position and velocity at different times
(Neumaier & Westra, 2011). Utilizing Newton’s laws, it
became feasible to infer the positions and velocities of
objects at any moment, given precise knowledge of posi-
tions and velocities at a specic moment. This determin-
istic outlook underwent a transformation with the advent
of quantum mechanics in the early 20th century.
The word “quantum” comes from the Latin word “quan-
tus”, which means “how much” or “how great”. In quan-
tum physics, it specically refers to discrete and indivisible
quantities in which certain physical properties, like energy,
can be quantized. This means that certain physical prop-
erties only come in specic amounts, like whole number
multiples of a basic unit known as a “quantum”. The con-
cept of continuity and discreteness has its roots in the con-
templations of ancient Greek philosophers (Editors of En-
cyclopaedia Britannica, 2021; Bell, 2022). In the late 19th
century, classical physics predicted an innite amount
of energy emitted by the so-called blackbodies as wave-
length decreased into the ultraviolet range, where a black-
body is an idealized object that absorbs all incident light.
This “Ultraviolet Catastrophe” was solved by Max Planck
in 1900 (Planck, 1901; Nobel Prize Outreach AB, 2023c),
as he proposed that radiant energy is made up of discrete,
particle-like components termed “quanta”. Subsequently,
in 1905, Einstein elucidated the phenomenon “photoelec-
tric effect” by postulating the existence of such particles,
which we today know as photons (Einstein, 1905; Nobel
Prize Outreach AB, 2023d). This revelation demonstrated
that light, comprising photons, exhibits particle-like be-
havior in conjunction with its wave characteristics estab-
lished in the 19th century (Young, 1804).
In 1924, Louis de Broglie hypothesized that the wave-
particle duality was not exclusive to light but was dis-
played by all matter, which was experimentally conrmed
by Clinton Davisson and Lester Germer in 1927 (Davisson
& Germer, 1927; Nobel Prize Outreach AB, 2023b). Later,
Erwin Schrödinger used this result to formulate the wave
mechanics of particles, where he postulated an equation
describing the dynamics in quantum systems (Nobel Prize
Outreach AB, 2023a). This equation can be seen as the
quantum counterpart of Newton’s equation of motion, al-
though here, it does not describe the location of the ob-
ject but the probabilities of the locations, where the ob-
ject might be at. This is precisely where the distinction
in the types of determinism between classical and quan-
tum mechanics becomes evident. Schrödinger’s equation
is deterministic in terms of the potential outcomes upon
measuring the particle, yet it remains indeterministic in
determining the specic result of that measurement.
Emerging from the probabilistic and wave-like nature of
the quantum realm, physicists encountered a plethora
of astonishing quantum properties over the course of
the 20th century. These include Heisenberg’s uncer-
tainty principle, antiparticles, vacuum uctuations, quan-
tum spin, chromodynamics, tunneling, entanglement, and
many others. Richard Feynman was the pioneer in recog-
nizing that some of these properties could be leveraged to
create a more potent form of computing. In 1981, Feyn-
man critically underscored the inadequacies of classical
computers when tasked with simulating intricate quan-
tum systems (Preskill, 2023). This observation laid the
groundwork for a deeper exploration, which will be further
elucidated in the subsequent sections.
Quantum Technologies 4
3. Quantum Technologies
Classical computers employ a binary system composed
of binary digits, known as “bits”, represented as 0s and
1s. These bits serve as the fundamental units of digital
information. In Quantum Computing, quantum bits, or
qubits, are unique in that they can exist in a state of super-
position, simultaneously representing both 0 and 1. This
property arises from their wave-like nature. This implies
that there is a known probability of nding a qubit to be
either 0 or 1, but the actual outcome depends on the act
of measurement. It’s akin to a quantum coin, where the
coin looks like a blend of both heads and tails, as opposed
to a classical coin unambiguously showing either heads or
tails. The crucial point is that the act of observing or mea-
suring the quantum coin forces it to collapse into one of
the states, either heads or tails. The superposition princi-
ple is intimately linked to quantum computing capabilities
such as representing exponentially large feature spaces
with respect to the number of qubits and manipulating
them in parallel to achieve desired probabilities of mea-
surement outcomes. This capability is rooted in quantum
interference, which serves as a foundational element for
crucial quantum algorithms.
Another aspect that Quantum Computing leverages for
computational power is entanglement, a phenomenon in-
timately tied to the particle-like nature of quantum me-
chanics and absent in classical computing. In an entan-
gled two-qubit system, a measurement of a physical prop-
erty of a qubit instantaneously reveals the corresponding
property of the other, regardless of the physical distance
separating them (Nobel Prize Outreach AB, 2023e). This
can be illustrated by considering the scenario of sending a
pair of gloves to two individuals. When one person opens
their box, it immediately provides knowledge about the
handedness of the glove the other person received, form-
ing a direct and instantaneous connection.
Technically, quantum computers can be constructed out
of any quantum technology that allows for dening qubits
and can implement single- and multi-qubit gate opera-
tions with high delity (Qiskit Development Team, 2023).
Today’s gate-based devices’ qubits are based on pho-
tons, trapped atoms, nuclear magnetic resonance, quan-
tum dots, and superconductors (Albareti et al., 2022). Ad-
ditionally, specialized devices called quantum annealers
employ quantum annealing, which is a type of quantum
technology that can be used to nd the best-t solution
for optimization problems (West, 2023). In addition to
quantum computing, a distinction is also made between
quantum communication and quantum sensing.
Quantum Communication is a specialized domain within
the realm of quantum technologies, which includes,
among other things, the areas of clock synchronization,
random number generation, and quantum cryptography.
Shor’s algorithm (Peter W. Shor, 1995) indicates the po-
tential of quantum computers to factor large integers sig-
nicantly faster than the best-known classical algorithms.
Within the contemporary landscape of information tech-
nology, asymmetric encryption, exemplied by the widely
used RSA cryptosystem, stands as a key mechanism for
safeguarding data efciently. Using Shor’s algorithm,
such data can be decrypted, as soon as sufcient quantum
computing power becomes available. Recognizing this im-
minent threat, the US standards authority NIST embarked
on a quest for quantum-safe encryption techniques back
in 2017. In August 2023, four encryption methods were
selected that are currently in the standardization process
(National Institute of Standards and Technology, 2023).
However, time is of the essence, since quantum comput-
ers with appropriate computing power will be available in
the foreseeable future (so-called Q-Day). The threatened
encryption methods must be migrated by this point.
Another area of quantum technology is Quantum Sens-
ing. It refers to the usage of quantum properties such
as entanglement to measure physical quantities with ex-
ceptional precision and sensitivity. Early examples of
quantum sensors include magnetometers using super-
conducting quantum interference devices and atomic va-
pors or atomic clocks. More recently, quantum sensing
has gained prominence as a rapidly progressing discipline
within the realm of quantum science and technology and
is expected to make signicant contributions to applied
physics and various scientic elds (Degen, Reinhard, &
Cappellaro, 2017).
The number of qubits in quantum computers is an im-
portant factor in metrics, which are widely used to mea-
sure their capabilities (Moll et al., 2018). Currently, uni-
versal quantum computers typically possess around two
orders of magnitude, equivalent to hundreds of qubits,
while quantum annealers have three orders of magni-
tude, equating to thousands of qubits. However, to ren-
der the technology genuinely practical for addressing real-
world problems, this number must increase by a fac-
tor of a million. Attaining this milestone is paramount,
alongside advancing other critical performance factors
like state stability and fault tolerance (Yang, Zolanvari,
& Jain, 2023). The present devices fall under the cat-
egory of Noisy Intermediate-Scale Quantum (NISQ) de-
vices, underscoring the current technological landscape.
In response to the challenges posed in the NISQ era, vari-
ous service providers offer quantum simulators as a poten-
tial workaround. As the name implies, these simulators are
employed to simulate quantum computations on classical
devices.
5Quantum Computing and Articial Intelligence in Finance
4. Articial Intelligence and Machine Learning
The term Articial Intelligence (AI) describes the intel-
ligence of machines, which can perform tasks that nor-
mally require human intelligence, such as visual percep-
tion, speech recognition, decision-making, and language
translation (Bildirici, Ozge Zeytin, 2023). In 1950, Alan
Turing transformed the question “Can machines think?”
into the renowned imitation game, which is commonly
known as the “Turing Test”. The test is considered suc-
cessful when a human interrogator, after asking a series
of written questions, cannot discern whether the written
responses originate from a human or a computer. The
computer would need to be able to communicate suc-
cessfully in a human language (Natural Language Pro-
cessing), store what it knows or hears (Knowledge Rep-
resentation), answer questions and draw new conclusions
(Automated Reasoning), and adapt to new circumstances
and detect and extrapolate patterns (Machine Learning).
While Turing did not consider the physical simulation of
a person as essential for showcasing intelligence, other
researchers have put forth the concept of a “total Tur-
ing test”, which necessitates interaction with real-world
objects and individuals. To pass the total Turing test, a
robot will need speech recognition to perceive the world
(Computer Vision) and to manipulate objects and move
about (Robotics). These six disciplines compose most of
AI (Russell & Norvig, 2010).
The goal of Machine Learning is to have learning algo-
rithms devised that can learn automatically without hu-
man intervention or assistance. Instead of programming
the computer directly to solve the task, in machine learn-
ing, methods are sought by which the computer will gen-
erate its own program based on the examples provided
(Grosan & Abraham, 2011). This approach proves useful
for applications where algorithms are unknown, yet ample
data is available.
Recognizing faces, a task we do every day effortlessly, can-
not be written as a computer program, since we are not
able to explain our expertise. Machine learning programs
can accomplish this task by capturing a unique pattern
from different face images of an individual, and subse-
quently identifying the person by detecting this pattern
within a provided image. By identifying regularities and
patterns in historical data, machine learning can gener-
ate valuable predictions. This capability nds applications
in diverse elds, including credit assessment, fraud detec-
tion, and stock market prediction (Alpaydin, 2020).
The process of applying machine learning to discover
knowledge from large databases is called data mining.
Categorically, data mining can be predictive or descrip-
tive, where the former produces the model and the lat-
ter novel information based on the dataset (Kantardzic,
2011). These make up the three basic machine learning
paradigms with the addition of reinforcement learning.
In the eld of predictive data mining, Supervised Learn-
ing is employed to estimate an unknown dependency us-
ing known input-output samples. Essentially, it involves
studying both positive and negative examples of a class
to prociently classify future unseen instances, where the
label of the example has the role of a supervisory signal.
Supervised learning techniques can be employed to min-
imize the risk of credit default, namely by using historical
data on customer credit behavior and training a classi-
cation model to distinguish between customers who are
likely to default on their loans (negative examples) and
those who are not (positive examples). When the vari-
ables in a dataset are numeric rather than discrete, the
analysis involves regression, which is commonly utilized in
nancial time series forecasting.
Unsupervised Learning involves recognizing patterns in
data without explicitly labeled supervisory data points. It
is commonly used to identify clusters or groupings within
the data. For instance, a bank might employ such tech-
niques to analyze customer data, including demographics
and transaction history. This analysis helps identify preva-
lent customer proles and behaviors, facilitating the cus-
tomization of services and products to better meet cus-
tomer needs.
In Reinforcement Learning, “agents” make optimal de-
cisions based on incoming observations from their envi-
ronment. Strategies or “policies” are developed through
interaction, considering the environment’s state and a re-
ward signal inuenced by the agent’s actions (Sutton &
Barto, 2018). In the nancial context, an agent could be
an investment rm optimizing trading decisions based on
market observations.
Framework: Quantum Machine Learning 6
5. Framework: Quantum Machine Learning
A range of applications for Quantum Machine Learning
(QML) in the nancial sector has been suggested in the
existing literature. However, there are disparities in the
executions and anticipated benets of these applications.
These divergences make direct comparisons challenging.
As a solution, a layered framework is introduced to facili-
tate the comparison of QML applications in the nancial
industry. The framework delineates each proposal into
four distinct layers, as depicted in Figure 1. The upper lay-
ers are intricately linked to the specic nancial tasks tar-
geted for resolution, while the lower layers pertain to the
technical facets of QML implementation. The top layer
describes the use case in nance, and the second layer
contains the corresponding ML approach, such as super-
vised learning, unsupervised learning, and reinforcement
learning. Most applications described in the literature are
based on a small set of existing quantum algorithms and
utilize their speedup to enhance the optimization part of
the corresponding ML approach for the designated use
case in the nancial industry. This is depicted in the third
layer. The last layer focuses on the quantum hardware on
which the algorithm has been designed to be executed.
Financial Use Case
ML Approach
Optimization Method
Quantum Hardware
Figure 1: Main layers for the use of QML in nance.
It is important to note that the four layers are not en-
tirely independent. Just as ML approaches must be cho-
sen based on the specic use case, there is not a one-size-
ts-all quantum algorithm. Some algorithms are better
suited for near-term prototype quantum computers, while
others demand the implementation of larger quantum
computers, offering the advantage of theoretically proven
speedups. However, this layering approach enables us to
discern the distinctions among the diverse applications of
quantum computing in nance.
The Financial Use Case layer outlines the specic problem
for which quantum computing can offer utility in nance
and species the tangible benets. These benets may
manifest in various forms, such as lower costs, increased
revenue, or reduced risk, ultimately leading to higher prof-
itability in existing business areas or the emergence of
new business opportunities. Achieving this may involve
methods like expedited calculation of nancial product
prices, creating potential arbitrage opportunities. Addi-
tionally, benets may accrue from the mitigation of rep-
utational and nancial risks associated with issues like
fraud.
The ML Approach layer species the machine learning
methodology applied in QML applications for nance, ref-
erencing the types of approaches explained in the pre-
vious chapter. This layer determines the learning strat-
egy, whether it be supervised, unsupervised, or reinforce-
ment learning, tailored to the specic nancial use case.
It acts as a crucial link between the nancial problem at
hand and the technical implementation of quantum algo-
rithms, ensuring alignment with the nuances of nancial
data and decision-making processes.
In the Optimization Method layer, specic strategies are
employed to enhance machine learning processes in QML
applications. Drawing from the ML methodologies, this
layer involves implementing optimization techniques tai-
lored to the nancial use case. Quantum algorithms, par-
ticularly those designed to outperform classical counter-
parts, contribute to this layer’s signicance.
The Quantum Hardware layer straightforwardly ad-
dresses the hardware aspects of QML, providing a critical
parameter for its implementation in the nancial domain.
It is noteworthy that, in this context, the specic imple-
mentation details of qubits are not the focus; instead, the
primary distinction lies in the preference for either gate-
based or annealer-type quantum computing (see Figure
2).
7Quantum Computing and Articial Intelligence in Finance
6. Literature Review
This chapter integrates insights from multiple survey pa-
pers on QML, encompassing analyses and ndings fo-
cused on quantum computing for nance in a broader
context (Orús, Mugel, & Lizaso, 2019; Egger et al., 2020;
Bouland, van Dam, Joorati, Kerenidis, & Prakash, 2020;
Albareti et al., 2022; Gujju, Matsuo, & Raymond, 2023;
Herman et al., 2023), as well as the specic exploration
of QML for nance (Pistoia et al., 2021; Jacquier, Kon-
dratyev, Lipton, & de Prado, 2022). The predominant
content in the analyzed sources comprises theoretical pa-
pers leveraging quantum algorithms at the optimization
level to demonstrate potential speedups in various ML
approaches. Only a limited number of sources provide
real hardware or simulator implementations and not all
contextualize their algorithms for nancial applications.
Nonetheless, our review covers both nancial implemen-
tations and theoretical advancements in QML, recogniz-
ing that the latter can, in principle, be implemented for
the already established use cases in nance.
As highlighted in Chapter 3, quantum computing exhibits
the potential to outperform classical computing by utiliz-
ing quantum mechanical phenomena like quantum inter-
ference. Various essential quantum algorithms, including
Quantum Amplitude Amplication and Estimation (QAE)
(Brassard, Høyer, Mosca, & Tapp, 2000), a generalization
of Grover’s searching algorithm (Grover, 1998), leverage
quantum interference. Additionally, algorithms like Quan-
tum Fourier Transform (QFT) and Quantum Phase Estima-
tion (QPE) (Nielsen & Chuang, 2010), with the latter em-
ployed in the Harrow, Hassidim, and Lloyd (HHL) quantum
algorithm for solving linear equations (Harrow, Hassidim,
& Lloyd, 2009), contribute to the algorithmic landscape
in quantum computing. A substantial portion of the QML
literature relies on these algorithms. Lastly, quantum adi-
abatic optimization plays a pivotal role in QML, predom-
inantly employed by quantum annealers (Rajak, Suzuki,
Dutta, & Chakrabarti, 2022).
The selected literature extensively covers the second and
third layers of our framework, leaving the practical appli-
cation of proposed methodologies open-ended. An impli-
cation of this is that the rst and nal layers in our frame-
work, namely Financial Use Case and Quantum Hardware
are not addressed explicitly in the case of proposals with
theoretical results. However, the majority of these are en-
visioned to be implemented on universal quantum com-
puters, i.e. on gate-based devices. Our literature review
refrains from explicitly discussing quantum hardware for
these theoretical references. Instead, it points out this as-
pect for sources involving implementations on gate-based
devices or algorithms designed for quantum annealers,
also known as adiabatic quantum computers. This dis-
tinction claries the treatment of annealer-based propos-
als within the third layer, Optimization Method, while
highlighting their reliance on the adiabatic optimization
method based on the quantum adiabatic theorem (Born
& Fock, 1928).
The spectrum of ML methodologies (second layer) in the
literature review encompasses regression and classica-
tion (falling under supervised learning), clustering and
feature extraction (categorized as unsupervised learning),
and reinforcement learning. Subsequently, our structured
literature review mirrors this segmentation by aligning
with the distinct ML approaches in the second layer of our
layered framework (see Figure 2).
Regression involves establishing a numerical function
based on the training dataset to analyze how values
change with varying attributes. Since the inception of the
HHL algorithm, which advanced the eld of QML, several
other quantum algorithms have been proposed (Wiebe,
Braun, & Lloyd, 2012; Schuld, Sinayskiy, & Petruccione,
2016; Wang, 2017; Zhao, Fitzsimons, & Fitzsimons, 2019)
to handle least squares problems, the traditional method
used in regression analysis. The references mainly make
use of quantum algorithms for solving linear equations,
next to various quantum subroutines, to speed the run-
time of their regression algorithms up. By formulating
the problem as quadratic unconstrained binary optimiza-
tion, which is the natural input of quantum annealers,
they have also been employed for least-squares regression
(Date & Potok, 2021). While the referenced study lacks
an implementation with a real-world dataset, the authors
test their regression algorithm on an annealer. Quan-
tum Neural Networks (QNN) have been proposed with the
aim of leveraging quantum parallelism and a vast feature
space (Mitarai, Negoro, Kitagawa, & Fujii, 2018). They
involve quantum input preparation, parametrized quan-
tum gates, and use gradient-based or gradient-free opti-
mization for training parameters, with the latter being em-
ployed when the objective function’s derivative is unavail-
able or impractical to obtain. It is worth noting that the
optimization, in this case, is usually done by classical op-
timizers (Pellow-Jarman, Sinayskiy, Pillay, & Petruccione,
2021). However, there are proposals exploring QML with
quantum gradient descent for regression tasks (Kerenidis
& Prakash, 2020).
Classication involves assigning objects to predened
categories. It proves benecial in various elds, particu-
larly in extensive data handling, when there is a specic
focus on group information. Within the literature, there
are proposals leveraging quantum algorithms as subrou-
tines to enhance the efciency of established classical al-
gorithms, alongside quantum counterparts of these clas-
sical algorithms. For instance, Quantum Support Vector
Literature Review 8
Financial
Use Case Fraud detection Credit-worthiness
identication Pricing Portfolio
management Trading Hedging
ML
Approach Supervised learning
(e.g. Classication, Regression)
Unsupervised learning
(e.g. Clustering, Feature Extraction) Reinforcement learning
Optimization
Method Adiabatic Gradient-based/free* Solving linear equation
(e.g. HHL, qPCA)
Interference
(e.g. QAE, QPE, QFT)
Quantum
Hardware Annealer Gate-based
Figure 2: Morphological box representing the reviewed QML literature. The box is populated with specic elements or
options for each layer, creating a matrix where different combinations can be examined. Note that gradient-based and
gradient-free optimization predominantly occur on classical computers.
Machines (QSVM) are implemented on both gate-based
devices, optimized by means of quantum algorithms for
solving linear equations (Kariya & Behera, 2021), and an-
nealers (Willsch, Willsch, De Raedt, & Michielsen, 2020).
Additionally, there are gate-based QSVM proposals involv-
ing optimization with interior-point methods (Kerenidis,
Prakash, & Szilágyi, 2021), where the speedup mainly
comes from quantum algorithms for solving linear equa-
tions. Other examples encompass nearest-neighbor learn-
ing accelerated through quantum interference (Basheer,
Afham, & Goyal, 2021), QNNs with theoretical guaran-
tees (Allcock, Hsieh, Kerenidis, & Zhang, 2019), simulator-
based results (Farhi & Neven, 2018) and real gate-based
hardware results (Kerenidis, Landman, & Mathur, 2022).
Again we note that the optimization of QNNs is gradient-
based/free.
Clustering involves the exploration and identication of
the inherent grouping pattern within a dataset. Literature
not only shows that adiabatic optimization can theoreti-
cally be used in gate-based devices to speed known clus-
tering methods up (Lloyd, Mohseni, & Rebentrost, 2013)
but also experimental results obtained with quantum an-
nealers (Arthur & Date, 2020). For the same purpose,
quantum interference is utilized to obtain both theoreti-
cal (Kerenidis, Landman, Luongo, & Prakash, 2018) and ex-
perimental results on gate-based hardware (Khan, Awan,
& Vall-Llosera, 2019). Notably, examples of QNNs in this
context also exist (Bermejo & Orus, 2022).
Feature extraction aims to select and transform the most
relevant and important information or features from raw
data to be used in further analysis or model building, in-
volving the reduction of data dimensionality while main-
taining as much relevant information as possible. One
popular dimensionality reduction technique used in var-
ious elds is Principal Component Analysis (PCA). By en-
coding the principal components within quantum super-
position, diverse quantum iterations of PCA (qPCA) have
been put forward. The rst proposal of qPCA uses quan-
tum algorithms for solving linear equations to accomplish
this (Lloyd, Mohseni, & Rebentrost, 2014). Additionally,
examples of QNNs (Zoufal et al., 2023), as well as an-
nealers (Ferrari Dacrema et al., 2022) involving feature ex-
traction can be found in the literature, where QNNs are
employed in credit-worthiness identication in the former
(see Chapter 7).
In Reinforcement learning an agent learns to make deci-
sions in an environment to maximize cumulative rewards.
Here, quantum interference is utilized to amplify the prob-
ability of observing actions that result in a positive reward,
facilitating a good balance between exploration and ex-
ploitation through probability amplitudes and potentially
accelerating the learning process through quantum par-
allelism (Dong, Chen, Li, & Tarn, 2008). The literature in-
cludes several studies on QNNs for reinforcement learning
implemented by means of simulators (Chen et al., 2020)
and real hardware (Cherrat et al., 2023), yet the benets
of these applications remain unclear. The latter reference
includes a real-world nancial application, namely hedg-
ing (see Chapter 7).
A structured overview of the presented QML literature
from the perspective of our layered framework is shown
in Figure 2. As detailed in Chapter 5, the algorithms from
the literature are examined based on their application in
nance, the selected machine learning approach for task
completion, the optimization method incorporating the
algorithm, and the specic hardware type designed to
support the algorithm. These elements collectively consti-
tute the items in the framework, facilitating the system-
atic classication and comparison of QML applications
across the selected layers. The subsequent chapter sheds
light on the item selection process for the nancial use
case layer.
9Quantum Computing and Articial Intelligence in Finance
7. Use Cases
Our review reveals that the algorithms in the QML litera-
ture, whether directly or indirectly, cover a diverse range
of use cases in nance through the integration of various
ML techniques. Even when a particular item in the liter-
ature does not explicitly present a nancial use case, its
ML approach can be repurposed to fulll a relevant task.
To elucidate this point, we provide an overview of the ap-
plicable tasks for the ML approaches encountered in the
literature (Herman et al., 2023):
•Regression stands as a cornerstone in nancial
forecasting, offering invaluable insights into asset
pricing and volatility forecasting. By leveraging re-
gression models, analysts and investors gain a so-
phisticated tool to discern and predict future nan-
cial trends.
•Classication, a fundamental ML technique, nds
multifaceted applications in the nancial domain,
particularly in risk management. Tasks such as
credit-worthiness identication and fraud detection
benet signicantly from classication methodolo-
gies, contributing to enhanced nancial security.
•Clustering in the nancial domain nds application
in devising a trading strategy aimed at assisting in-
vestors in constructing a diversied portfolio. More-
over, clustering facilitates the examination of var-
ious stocks, grouping those with signicant return
correlations into distinct categories.
•Feature extraction can sometimes lead to data
transformations that are not easily interpretable by
humans, which can pose challenges for use in the
tightly regulated nancial sector. Consequently, in
nance, there is a need to identify effective, valu-
able, and interpretable feature extraction methods.
One such straightforward approach is PCA. Regret-
tably, extracting useful classical information from
the quantum output of qPCA is notably challeng-
ing. However, the results can be utilized as input for
other machine learning models based on quantum
linear algebra.
•Reinforcement learning has found application in
various nancial domains, such as pricing and hedg-
ing of contingent claims, portfolio allocation, auto-
mated trading in the presence of market frictions,
market making, asset liability management, and
optimization of tax consequences.
The proposed nancial use cases, implicitly or explicitly
featured in the literature, constitute the elements in the
top layer of Figure 2. It is important to reiterate that our
use case determination process includes theoretical nd-
ings without implementation, as the literature for nance-
specic QML techniques remains sparse. Among the se-
lected literature, there are a total of ve references with
nancial use cases implemented on actual quantum hard-
ware. These use cases are described in more detail below.
In classical machine learning, Generative Adversarial Net-
works (GANs) excel at generative modeling, an unsuper-
vised learning approach that involves a generator and
a discriminator engaged in a competitive training pro-
cess. The introduction of quantum systems, replacing
the generator, discriminator, or both, extends this frame-
work into the domain of quantum computing. An exem-
plary application is demonstrated in the work by Zoufal,
Lucchi, and Woerner (2019), where quantum-classical hy-
brid GANs are employed to learn and transfer approxi-
mations of probability distributions from classical data to
gate-based quantum computers. This is an efcient, ap-
proximate data loading scheme that requires signicantly
fewer gates than existing methods. Specically, a log-
normal distribution is learned that models the spot price
of an underlying asset for a European call option. Finally,
QAE is used to estimate the expected payoff of the op-
tion, given the efcient, approximate data loading by the
quantum GANs (qGANs). The training and loading are run
on an actual quantum computer, the IBM Q Boeblingen
chip with 20 qubits, with the gradient-based optimization
of the qGAN parameters taking place on a classical com-
puter.
The Heath-Jarrow-Morton (HJM) model, extensively ap-
plied in nance for interest rate derivatives valuation
(Heath, Jarrow, & Morton, 1992), faces a signicant chal-
lenge due to its substantial degrees of freedom when de-
scribing yield curve evolution. One potential approach
to address this issue involves employing principal com-
ponent analysis to select factors. It is demonstrated by
Martin et al. (2021) that the number of noisy factors can
be effectively reduced by qPCA, facilitating the determi-
nation of fair prices for interest rate derivatives. The esti-
mation of the principal components of 2×2and 3×3
cross-correlation matrices based on historical data for two
and three time-maturing forward rates is performed us-
ing the 5-qubit IBMQX2 quantum processor. The results
show that the algorithm can provide reasonable approx-
imations for the 2×2case, but the quantum proces-
sor is limited by gate delities, connectivity, and number
of qubits. Concurrently, the experimental outcomes with
simulators suggest that improved results could be attain-
able by the availability of a lower-level programming in-
terface, enabling the customization of the quantum algo-
rithm optimization to align with chip constraints.
Use Cases 10
A hybrid system of quantum and classical machine learn-
ing algorithms for detecting phishing attacks in nancial
transaction networks based on the Ethereum blockchain
is proposed by Ray, Guddanti, Ajith, and Vinayagamurthy
(2022). The Etherscan1block explorer is utilized to ac-
cess data from the open-source public blockchain platform
Ethereum. The labeled data of phishing accounts is ob-
tained from public reports on phishing activities. A total
of 3 million nodes is collected, revealing 1165 phishing
nodes (0.039%) and 2972324 non-phishing nodes, indi-
cating a high class-imbalance scenario. For this classica-
tion task, QNNs and QSVMs are employed, with the former
undergoing testing with a diverse array of parametriza-
tion schemes and the latter implemented on both anneal-
ers and gate-based devices. Optimal congurations of the
models are determined through simulators, and a key con-
tribution of the study involves exhaustive experimenta-
tion with these optimally congured models on IBM’s 5-
and 27-qubit chips, as well as a DWave annealer with 5617
qubits. The results do not demonstrate an improvement
in performance that comes with an increased number of
qubits. For the optimization of the QNNs, the gradient-
free algorithm called constrained optimization by linear
approximation is chosen as the classical optimizer. It is
shown that improved results can be obtained by means
of stacking and bagging, techniques that allow leverag-
ing the complementary strengths of (quantum and clas-
sical) models. Overall, gate-based QSVMs are reported to
consistently yield lower false positives, resulting in higher
precision when compared to other classical and quantum
models. This characteristic is particularly desirable in any
anomaly detection problem.
Feature selection is a challenging and important task in
machine learning. It is a process of selecting a subset of
relevant features in the dataset from the original set of
features, setting it apart from feature extraction, which
creates new features derived from the original while cap-
turing the essential information from the data in a lower-
dimensional space. A novel quantum algorithm for fea-
ture selection is introduced by Zoufal et al. (2023), lever-
aging QNNs. More precisely, QNNs are trained to produce
feature subsets that maximize the performance of a pre-
dictive model. While the utilization of any arbitrary classi-
er and scoring function is possible, logistic regression and
log-loss are specically chosen as the classier and perfor-
mance score, respectively. The effectiveness of the QNN
1https://etherscan.io/
feature selection method is evaluated using a publicly
available real-world credit risk dataset comprising 1000
data points that ascertain the credit-worthiness of a cus-
tomer based on 20 attributes. A version of the gradient-
free method called simultaneous perturbation stochastic
approximation is chosen as the optimizer for the train-
ing of the parameters of the QNNs. The feature selection
algorithm is implemented on actual quantum hardware
equipped with 27 qubits showing results that are compet-
itive with state-of-the-art classical methods and, in some
experiments, outperform them.
An important problem in the nancial securities industry
is pricing and hedging portfolios of derivatives. Recently,
an approach addressing this problem in the absence of
frictionless and complete market assumptions has been
put forward (Buehler, Gonon, Teichmann, & Wood, 2019),
where the trading decisions in hedging strategies are
modeled as neural networks in a reinforcement learning
setting. Expanding on this, Cherrat et al. (2023) trans-
forms the problem studied by Buehler et al. (2019) into
a quantum-native setup. Here, market states are encoded
into quantum states, and policies are represented using
QNNs. The implementation takes place on the 20-qubit
trapped-ion quantum processor, Quantinuum H1, and in-
volves training through gradient descent. The efcacy of
this method is assessed against the Black-Scholes delta
hedge model, revealing that the QNN policies signicantly
outperform the traditional model.
It remains uncertain whether the proposed QML ap-
proaches can yield a tangible end-to-end quantum ad-
vantage in addressing practical problems today. In the
nancial domain, the computational time and accuracy
signicantly impact the prot and loss of businesses, em-
phasizing the potential impact that any actual accelera-
tion and model performance improvement from new com-
puting methods could have on the industry. For instance,
swift and precise assessment of risk metrics in derivatives
trading is crucial for effective risk hedging, especially amid
volatile market conditions. Another time-critical use case
in nance is fraud detection, where early and accurate
identication of fraudulent activities can prevent substan-
tial monetary loss and protect the reputation of nancial
institutions. Consequently, the nancial industry stands in
an opportune position to be an early adopter, fully lever-
aging quantum computing in the realm of computational
nance (Herman et al., 2023).
11 Quantum Computing and Articial Intelligence in Finance
8. Quantum Computing Infrastructure
A solid foundation is imperative for the nancial indus-
try to truly benet from quantum computing and QML.
Therefore, we focus on the elements essential for an ef-
fective quantum computing infrastructure in this chapter.
We start by discussing the key features of a quantum com-
puter.
David DiVincenzo, an American physicist, formulated the
following ve necessary criteria for a quantum com-
puter and two criteria regarding quantum communication
in 1996, known as the DiVincenzo criteria (DiVincenzo,
1996):
• A scalable physical system with well-characterized
qubits
• The ability to initialize the state of the qubits to a
simple ducial state
• Long relevant decoherence times
• A “universal” set of quantum gates
• A qubit-specic measurement capability
These ve criteria are not fully met today. But devel-
opment has increased signicantly, particularly in recent
years, which is also reected in increased business activi-
ties and investments. However, there are still challenges
to be solved for widespread adoption in the economy. This
is primarily due to the following two aspects:
A) Scalability: High-performance computers are neces-
sary to carry out complex calculations. Similar to classi-
cal chips (CPU/GPU), the performance of quantum com-
puters is described using qubits. We currently can assume
that hundreds of thousands of qubits will be necessary for
practical use. The industry is working hard to develop new
and scalable hardware, but it will still take a few years be-
fore a service is available in the required quantities. In
practice, this point in time is referred to as “Q-Day”. Like-
wise, the use of quantum computing is still complicated
and not user-friendly today. Further innovations can also
be expected in the area of quantum-related software.
B) Reliability: A sticking point in the operation of a quan-
tum computer is decoherence (Schlosshauer, 2005). De-
coherence effects arise when a quantum system inter-
acts with its environment and the superposition is lost. In
quantum computers, an attempt is made to delay these
decoherence effects for as long as possible by cooling
them to a few millikelvins above absolute zero (approx.
-273 ◦C). Decoherence cannot be avoided and has an in-
uence on the possible running time of a quantum algo-
rithm. This is where error-correcting quantum codes come
into play. In the classical world, an algorithm can be di-
vided into individual steps, the partial results can be saved
and processed in further steps. In the quantum world, this
is not possible because a partial result means a measure-
ment of the quantum state, and the quantum mechanical
superposition is therefore lost.
But in the eld of quantum computing, there are other
variants than gate-based computers. Quantum gate com-
puters are based on so-called logic gates. Quantum an-
nealers, on the other hand, use the adiabatic theorem of
quantum mechanics for the calculation. Further, there are
also quantum-inspired systems or quantum simulators,
which are based on classic microchips. All of these tech-
nologies have different advantages. Quantum-inspired
systems or quantum simulators can already be easily used
today (e.g. via several public cloud providers) to evaluate
Figure 3: Quantum Computing as part of a multi-cloud platform. Source: Own illustration.
Quantum Computing Infrastructure 12
the benets of quantum computing. Quantum annealers
(e.g. from D-Wave) can today be used for optimization
problems and have already proven some benets in prac-
tice (Yarkoni, Raponi, Bäck, & Schmitt, 2022).
What role do quantum computers play in the future IT
platform of the nancial industry? We assume that only a
portion of the business application landscape will benet
from quantum computers. Therefore, there is no motiva-
tion to migrate traditional workloads to quantum comput-
ers, as today’s cloud provider with highly scalable infras-
tructure and platform services (IaaS/PaaS) based on CPU
and GPU provide a very cost-effective and stable solution.
We believe that quantum computing will be mainly con-
sumed as a cloud service and therefore needs to be inte-
grated into the IT infrastructure as part of a multi-cloud
strategy. Figure 3 illustrates possible infrastructure com-
ponents that might be interconnected in a wide area net-
work (WAN) of a corporation. Medium-sized companies,
in particular, must be aware that the pre-investment vol-
ume for quantum hardware will be very high, especially at
the beginning of the adoption, so a service model is ad-
vantageous.
However, quantum computers also pose a real threat.
Quantum computers have the ability to crack the very
common asymmetric encryption methods (Kumar, 2022).
This signicant cybersecurity risk means that the nan-
cial industry must already deal with Quantum Computing
today and address the migration to Quantum-Safe Cryp-
tography.
13 Quantum Computing and Articial Intelligence in Finance
9. Conclusion
In presenting this report, we aim to equip the banking
community with an understanding of the symbiotic re-
lationship between Quantum Computing and Machine
Learning, unraveling the potential opportunities and chal-
lenges that lie ahead in this groundbreaking technological
convergence. The core ndings are summarised in the fol-
lowing statements and theses:
Quantum computing is changing the paradigms of tra-
ditional computer science. Just as quantum physics has
shaken traditional physics to its foundations, quantum
computing is establishing new rules in computer science.
The potential power of quantum computers will push the
boundaries of computing, especially in the eld of arti-
cial intelligence.
Superposition and entanglement are difcult to mas-
ter. Quantum computers leverage quantum principles
such as superposition and entanglement to perform com-
putation. Various hardware architectures and congura-
tions are possible. Scalability and reliability pose major
problems. For this reason, the quantum computers cur-
rently available are often still too small for real applica-
tions.
Solution design is crucial. Not every quantum computer
is suitable for every AI or machine learning model, just as
not every machine learning model is suitable for every use
case in the nancial industry. Knowledge of the advan-
tages and disadvantages of the various quantum comput-
ers and algorithms, as well as AI and ML models, is a pre-
requisite for high-performance solutions. We have devel-
oped a corresponding framework in this report to provide
assistance.
Expectations for quantum computing are high. How-
ever, the literature review shows that little has been im-
plemented to date, and even then mostly in the form
of prototypes. In principle, however, the potential is in-
tact and requires further research. Although, at the mo-
ment, quantum advantage on classical problems by using
quantum-native methods appears to be unlikely, there is
still signicant algorithmic research that needs to be done
to be certain (Hoeer, Häner, & Troyer, 2023). Further-
more, as quantum hardware advances, one will eventually
be able to benchmark these heuristic algorithms on real-
world problems.
Potential applications are widely distributed. The litera-
ture review shows that potential applications of quantum
computing span across different ML approaches and AI
models. This means that many use cases in banking and
nance can potentially benet from quantum computing.
Quantum-Safe Cryptography is of current importance.
Quantum computers have the ability to crack the very
common asymmetric encryption methods (Kumar, 2022).
This signicant cybersecurity risk means that the nan-
cial industry must already deal with Quantum Computing
today and address the migration to Quantum-Safe Cryp-
tography.
Quantum computing (such as AI) is used in multi-cloud
infrastructures. We believe that quantum computing will
be mainly consumed as a cloud service and therefore
needs to be integrated into the IT infrastructure as part
of a multi-cloud strategy.
Authors and Contributors 14
Authors and Contributors
This condensed study was prepared in collaboration with the following individuals who contributed in the form of text,
discussion, document reviews, and other forms of feedback (in alphabetical order).
Authors
Thomas Ankenbrand Urs Rhyner
Head of the Competence Center for Investments Head of ix.Lab
Lucerne University of Applied Sciences and Arts Inventx Lab AG
A. Ege Yilmaz
Research Associate
Lucerne University of Applied Sciences and Arts
Acknowledgements
We would like to thank the following project members for their support in the form of valuable discussions, stimulating input,
partial reviews and technical support.
Denis Bieri Fabian Keller
Lecturer Co-Lead Foresight & Innovation
Lucerne University of Applied Sciences and Arts Zurich Cantonal Bank
Attila Makra Levin Reichmuth
Co-Lead Foresight & Innovation Master’s Assistant
Zurich Cantonal Bank Lucerne University of Applied Sciences and Arts
Marcel Schöngens
Senior Data Scientist
SIX Financial Information AG
Contact
For more information about this study, please contact us at:
Thomas Ankenbrand Urs Rhyner
Lucerne University of Applied Sciences and Arts Inventx Lab AG
thomas.ankenbrand@hslu.ch urs.rhyner@inventx.ch
15 Quantum Computing and Articial Intelligence in Finance
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