ABOUT THE PROJECT

Advances in Quantum Computing hardware technology in recent years have been accompanied by the acceleration on the development of quantum computing algorithms with applications across many different use cases in different industry sectors: Automotive, Energy, Logistics, Pharma, Chemical/Manufacturing and the Financial Services Industry. One of the use cases in Finance comes from the application of Quantum Computing for Derivative Pricing and Derivative Risk Management. The purpose of this document is to provide a summary of the “state of the art” for these applications.

NEASQC Use Case 5 (UC5) works on the development and evaluation of quantum algorithms for financial applications. More specifically, the main line of research in UC5 focuses on Pricing and Value at Risk (VaR) problems. These two problems are computationally demanding tasks that are classically solved using Monte Carlo (MC) techniques. As Quantum Accelerated Monte Carlo (QAMC) techniques promise a quadratic speedup over Classical Monte Carlo (CMC) this roughly motivates why and how this field could benefit from the recent advances in Quantum Computing.

This report summarises the development of a new pricing algorithm as well as its experimental assessment. In the first part of the report there is a brief summary of the classical and quantum techniques used to tackle both financial challenges. In the second part of the report the new method is explained in detail and evaluated. This new method includes two well defined parts: a new encoding for the quantum oracle and a new Amplitude Estimation (AE) technique.

The new proposals are not yet applicable to current NISQ architectures although they represent a clear advance because:

• The new encoding algorithm allows pricing derivative products with negative payoffs. In particular, as illustrated in Section 3.1, it works in cases where other proposals fail as it is the case for a payoff of the form V (x) = x−K.

• The new AE algorithm, the so-called Real Quantum Amplitude Estimation (RQAE), allows pricing financial products with negative values (see Figure 9), which is an absolute novelty in the area. Current AE algorithms in the literature are concerned with the efficient estimation of the probability of finding a particular state, but they are not designed to be sensitive to the phases present in the underlying amplitudes. In contrast, RQAE is specifically tailored to be sensible to the sign of the amplitude.

• RQAE achieves a similar performance when compared with other previous well-known AE algorithms. In fact, in reference (Manzano et al., 2022), tighter bounds on the convergence of RQAE than any of the existing methods in the literature are proved. In this work, the experimental results show that although the performance is not the best one, it is on par with the cutting edge methods.

However, there are some less positive results as:

• The new encoding algorithm gives a worse performance compared to the standard encoding algorithm. It depends on a factor (Npaths) that can overshadow or even kill the speedup depending on its specific setup. Nevertheless, NEASQC researchers who participate in the Use Case are actively working in new encoding methods to solve this issue.

Two identified challenges have to be addressed in the near future. On the one hand, how to improve these algorithms to execute on current Quantum Processing Units (QPU), where deep circuits such as those required by the AE routines are not feasible without error correction techniques. On the other hand, previous works such as (Montanaro, 2015; Rebentrost et al., 2018) implicitly assume that the simulation of the Stochastic Differential Equation (SDE) to solve for these financial calculations can be directly done by translating the classical circuits into quantum circuits. However, this direct translation would require in practice a number of qubits too far from the current possibilities of the NISQ era.

The main objective of this deliverable is the theoretical development of quantum machine learning machinery for reinforcement learning, which is near-term-device friendly, yet sufficiently general to be applicable to the task of inventory management. This deliverable documents this achievement.

With the advent of real-world quantum computing, the idea that parametrized quantum computations can be used as hypothesis families in a quantum-classical machine learning system is gaining increasing traction. Such hybrid quantum-classical systems, which use a classical loop over a parameterized quantum circuit, have already shown the potential to tackle real-world tasks in supervised and generative learning, and recent works have established their provable advantages in special artificial tasks. Yet, in the case of reinforcement learning, which is arguably most challenging and where learning boosts would be extremely valuable, no proposal has been successful in solving even standard benchmarking tasks, nor in showing a theoretical learning advantage over classical algorithms. In this work, we achieve both. We propose a hybrid quantum-classical reinforcement learning model using very few qubits, which we show can be effectively trained to solve several standard benchmarking environments. Moreover, we demonstrate, and formally prove, the ability of parametrized quantum circuits to solve certain learning tasks that are intractable to classical models, including current state-of-art deep neural networks, under the widely-believed classical hardness of the discrete logarithm problem.

Our approach is general, and has shown applicable to both discrete and continuous state domains, with discrete actions, and is thus sufficiently general for application to the problem of inventory management. Furthermore, it is built around parametrized circuits, and is thus within the accepted paradigm for near-term-friendly proposals.

This report is the second deliverable of Task 5.2 – QRL for the inventory management part of the NEASQC project. It describes how we successfully deployed a QRL agent on a real quantum computer to tackle a simplified version of the challenge of inventory management. We describe the setup that solved this problem and examines some interesting conclusions drawn from comparing the real device noise to simulators.

We begin by introducing the reader to quantum reinforcement learning as developed within the NEASQC project, and to the inventory management problem we apply our learning algorithm to in Section 2. Section 3 highlights the key insights we gained from our experiments, particularly the importance of noise while training on a simulator and the relative unimportance of the specific noise model. Section 4 goes into the specifics of our methods and results, going into detail, both about how we achieved this learning problem and the conclusions we draw from our experiments.

This deliverable provides a graphical representation of Ising Hamiltonians, with the explicit goal of using this representation to analyse later the QAOA algorithm. This analysis entails computations with both the Hamiltonian and its exponential.

To reach this goal, a language should be provided where both a matrix and its exponential can be described using the same diagrammatic formalism.

This deliverable achieves this goal by first building a specific graphical language, called UHD, to represent Hermitian matrices, then provide an algorithm to compute from this representation a representation in the ZX-calculus of both this matrix and its exponential.

Translations from the Hamiltonian to its exponential are streamlined as much as possible by use of monoidal func-tors. This implies the exponential is constructed brick by brick by putting together representation of each part of the Hamiltonian.

An example of such a translation is provided.

Derivatives contracts are one of the fundamental pillars of modern financial markets and are routinely traded by both financial institutions and traders with a variety of objectives, such as financial risk hedging. For this reason, the fair valuation of financial derivatives, known as pricing, and the computation of various risk measures, such as the Value at Risk (VaR), have become two of the tasks that consume a great amount of computational resources in financial institutions.

Classically, the problems of derivatives pricing and the computation of VaR are mainly solved by means of Monte Carlo-simulation (MC) techniques or numerical algorithms for solving partial differential equations (PDE). The key advantage of MC technique is that it is easy to implement, very general and scales well with the dimension of the problem. Therefore, it has become the de facto standard by financial institutions to tackle both problems.

In this context, NExt ApplicationS of Quantum Computing (NEASQC) Use Case 5 (UC5) works on the development and evaluation of quantum algorithms for derivatives pricing and VaR problems. Inspired by the aforementioned classical algorithms, the quantum computing community has developed different strategies to speed up the classical techniques.

This report summarises the advances on derivatives pricing and the computation of VaR since the publication of the deliverable D5.3 review. The report is divided in three main sections. The first section corresponds to the main line of research on quantum computing for pricing and VaR, namely, Quantum Accelerated Monte Carlo (QAMC). This technique promises to be as flexible and general as its classical counterpart while requiring quadratically fewer computational steps. The second section corresponds to quantum algorithms for solving Partial Differential Equations (PDEs). In this case it is possible to find some methods that promise to obtain even exponential speedups. However, such speedups can only be attained for very specific cases which makes it less attractive for practitioners. The last section is devoted to different techniques which do not fall in the previous two categories. Thus, we include recent advances on quantum machine learning techniques applied to finance, financial modeling via quantum mechanics and quantum assets.

It is important to note that some of the proposed techniques require far more quantum computational resources than are currently available. This includes limitations in the number of qubits, in the depth of the circuits and in the levels of “noise”. Hence, the current deliverable pays special focus to quantum algorithms in Noisy Intermediate-Scale Quantum (NISQ) computers.

This deliverable is part of a series of three deliverables, provided jointly by EDF and Université de Lorraine:

– D5.3 Specification of a QAO algorithm for algorithm for the minimization of charging time

– D5.8 Specification and implementation of coloring-based QAOA algorithm for minimising charging station numbers

– D5.10 Software suite for benchmarking of quantum algorithms applied to the two typical smart-charging optimisation problems

As a midpart of the triptych, this deliverable will contain some overlap with the other two deliverables. In particular, deliverable D5.3 already supplied some details on coloring problems, that will be made more precise here.

The deliverable describes the specification of an algorithm to find the minimum number of colors required to color the vertices of a graph such that two connected vertices do not have the same color. This quantity is known as the chromatic number.

This problem arises naturally when considering scheduling problems for charging stations, that can easily be encoded into a graph coloring problem.

The main specificity of the algorithm is that the QAO (Quantum Approximate Optimization) algorithm is not used directly on the problem, but is part of a general Branch and Price method, where the QAO algorithm serves as a heuristics.

This report constitutes the Deliverable 5.9 for Task 5.4, namely the benchmarking of QAOA-based algorithms for mesh segmentation, of the Work Package 5 of the NEASQC Project.

In this report we demonstrate and benchmark a quantum algorithm that solves Quadratic Unconstrained Binary Optimization (QUBO) problems using a logarithmic encoding. In other words, an algorithm that solves a combinatorial optimization problem of size n using log2(n) qubits, as opposed to linear scaling algorithms like the Quantum Approximate Optimization Algorithm (QAOA). The algorithm used was initially proposed as a Maximum Cut algorithm (Rancic, 2023). It was eventually generalized for a larger pool of problems (Chatterjee et al., 2023).

A triangular mesh consists of a collection of triangles that together form a surface or solid representation of a 2D or 3D object. Each triangle is defined by its three vertices, and the entire mesh is formed by connecting these vertices. Each node of the mesh has an associated color or property. In this deliverable we will use only 2D triangular meshes. In order to solve the problem of mesh segmentation using our algorithm, we first need to convert it into a graph optimization problem consisting of an objective function and constraints if necessary.

To do this we create a graph from the mesh. The nodes of the graph are the nodes of the mesh and the edges of the graph are the sides of the triangle. The edges are then weighted with a weight equal to the difference in color between the nodes. Hence we have an edge-weighted graph.

Once we have a graph, we need to define an objective function that will help us get the different segments of the mesh. Here we will use the maximization of modularity (Newman, 2006) for meshing. Modularity is a measure of how well a network is split into different groups or clusters. It helps us see if these groups have more connections within themselves than we’d expect just by random chance.

We define the modularity objective function in form of a QUBO problem and then use our algorithm to get the solution.

Despite the algorithm being able generate multiple segments as required, the performance is still quite inferior compared to the classical algorithm. However this serves as a good initial attempt to solve the mesh segmentation problem using our quantum algorithm.

This report presents the advancements in quantum computing techniques for quantitative finance within Use Case 5 (UC5) of the NEASQC project. The research is a collaborative effort among the University of A Coruna (UDC), the Galician Supercomputing Center (CESGA), and the Hong Kong and Shanghai Banking Corporation (HSBC). Each organization brings unique expertise to the project: UDC focuses on theoretical foundations, CESGA on technological implementation, and HSBC on identifying industry-relevant problems.
The research addresses two main areas critical to HSBC: Quantum Accelerated Monte Carlo (QAMC) for option pricing and Quantum Machine Learning (QML) for risk assessment using metrics such as Value at Risk (VaR). These areas are essential for enhancing the efficiency and accuracy of financial modeling and risk management. More specifically, QAMC aims to expedite the option pricing process, while QML provides advanced techniques for risk assessment, offering deeper insights and more robust predictions.
Despite significant progress, the integration of these quantum techniques into industrial applications remains challenging due to current hardware limitations and the early stage of quantum computing technology. The project highlights the need for further development of quantum hardware and algorithms to bridge the technological gap between classiccal and quantum methods.
Notable advancements include new techniques for QAMC and QML, which are particularly relevant for financial institutions. The project has also produced five research papers and developed a comprehensive software library, QQuantLib, to facilitate further research and experimentation.
In conclusion, while significant progress has been made in developing quantum algorithms for pricing and VaR estismation, these algorithms are not yet enough competitive with classical algorithms on current Noisy Intermediate-Scale Quantum (NISQ) architectures. The primary challenges for moving forward are related to the execution of QAMC and QML algorithms, which require both deeper circuits (more layers of gates) and wider circuits (more qubits) than are currently feasible on available quantum hardware.

This report constitutes the delivery no 5.10 of the NEASQ project. It details te
implementation of a software suite for benchmarking quantum algorithms applied
to two typical smart-charging optimization problems. This deliverable builds upon
the methods developed during the Phd of Margarita Veshchezerova [6] and already
described in the reports of deliverable no 5.3 : ”Specification and implementation
of QAOA algorithm for the minimizing of electric vehicles charging time” and inte￾grates them into a comprehensive open-source library which can be use as an initial
step for future studies.

This report constitutes the Deliverable 5.11 of Task 5.4 of the NEASQC Project.

In Deliverable 5.9, we demonstrated the LogQ encoding (Chatterjee, Bourreau, & Rancic, 2024) for Quadratic Uncon￾strained Binary Optimization (QUBO) problems. We used LogQ to tackle the mesh segmentation problem and also
provided benchmarks against the classical KMeans clustering algorithm. In this deliverable, we present the software
package to solve mesh segmentation using LogQ.
This report presents an overview of the files provided in the package and a short documentation on how to use them.
There are two folders in the package: Log-Encoding and Mesh-Segmentation.
The folder Log-Encoding contains all the files required to run any QUBO problem using the LogQ encoding. On the
other hand the Mesh-Segmentation folder contains a Jupyter notebook which solves the mesh segmentation problem.
It imports files from the Log-Encoding.
Note that this deliverable does not contain any description of the problems themselves. This document is to be read in
conjunction with the paper (Chatterjee, Bourreau, & Ranciˇ c,´ 2024) and the Deliverable 5.9 (Chatterjee, Bourreau, &
Calandra, 2024).

Here we present the quantum computing computational package for quantum chemistry. It contains the implementation of the variational Hamiltonian ansatz state preparation for chemical systems. Equipped with the variational algorithms for imaginary- and real-time evolution, the package can optimize and propagate in time wave functions for chemical systems. As the Pre-Born-Oppenheimer molecular structure is implemented, one can describe nuclear quantum effects. We show the use cases for the developed methods on small chemical systems such as lithium hydride and hydrogen molecules. Specifically, the real- and imaginary-time evolutions have been proven to work correctly and efficiently. The Pre-Born-Oppenheimer scheme delivers results in agreement with the reference. Furthermore, it is shown that the variational Hamiltonian ansatz may approximate wave functions more efficiently than traditional variational ansatzes.

The code presented in this document allows for the calculation of the ground state energy of benzene under spatial de-formations by using a state-of-the-art quantum computing methodology – the variational quantum eigensolver (VQE). Two types of quantum computing ansatze are implemented (the hardware efficient one and the qUCC). The code supports noisy simulations and three types of spatial deformations of the benzene molecule. The code is available on Github : https://github.com/NEASQC/D4.2.

Here, we present an overview of the quantum computing computational package for quantum chemistry. It is comprised of the following two repositories:

• Automatic fragmentation tool (Chagas & Sànchez, 2022)

• Variational algorithms suite (Kovyrshin & Silvi, 2021)

The first repository contains molecule analysis and fragmentation tools based on graph theory. The second con-tains variational Hamiltonian ansatze adapted to chemical systems is used for state preparation. Equipped with the variational algorithms for imaginary- and real-time evolution, the package can optimize and propagate in time wave functions for chemical systems. As the Pre-Born-Oppenheimer molecular structure is implemented, one can describe nuclear quantum effects.

In this report, we first give an introduction of the features of the each repository. Aferwards we explain briefly the theory behind the methods. Later, we show use cases for the developed methods on small chemical systems such as lithium hydride and hydrogen molecules. Specifically, the real- and imaginary-time evolutions have been proven to work correctly and efficiently. The Pre-Born-Oppenheimer scheme delivers results in agreement with the reference. Furthermore, it is shown that the variational Hamiltonian ansatz may approximate wave functions more efficiently than traditional variational ansatzes.

For more information about the code and for a documentation we refer the reader to the respective repositories (Chagas & Sànchez, 2022; Kovyrshin & Silvi, 2021).

This document gives an overview of the software delivery D4.5 “RO Beta and QCCC Beta”, where RO stands for readout optimization and QCCC stands for quantum computing for carbon capturing. It consists of three main contributions:

Two methods for improving the measurement results of a quantum computation, one based on enhanced sampling using Bayesian statistics and one based on projecting the result to fulfill so-called n-representability constraints which may be violated in a noisy quantum computation. Furthermore, a VQE ansatz investigating the formation of bound states between CO2 and benzene in the context of utilizing benzene structures to perform CO2 recapturing.

Consequently, in Chap. 2 we discuss the method for enhanced sampling and show some key results. The software implementation we developed is based on what can be found in literature, and we will make the code available in the NEASQC GitHub. Currently, it can be found here:
https://github.com/gsilviHQS/Variationals algorithms/tree/enhanced sampling/enhanced sampling

Next, in Chap. 3 we present briefly the projection method based on n-representability constraints and show selected results. A detailed analysis can be found in our publication on the subject [3]. The software will be made available in the NEASQC GitHub [2] after the review phase. Currently, it can be found here:
https://github.com/gsilviHQS/Variationals algorithms/tree/enhanced sampling/n-rep projection

Finally, in Chap. 4 we give a short discussion of the findings regarding using quantum computing to analyze the formation of a benzene-CO2 dimer. Again, the code will be made available online in the NEASQC GitHub. It is a continuation of an earlier deliverable, where some of the Python script’s dependencies originate from and can also be found. Currently, the program for the benzene-CO2 dimer calculation is published here:
https://github.com/gsilviHQS/Variationals algorithms/tree/enhanced sampling/benzene CO2

The NEASQC project aims at demonstrating and advancing the capabilities of NISQ-era devices through the development of practically-relevant use-cases.

In WP4 to develop chemistry use-cases, Task 4.1 is to develop a tool to fragment the structure of a given molecular system into subsystems that retain the chemical meaning. To address this, the Automatic Subspace Generation (ASG) is a new tool designed to fragment the structure of the system into smaller subsystems. The motivation is that the smaller subsystems could fit into a quantum computer compared to the larger molecular system to perform energy calculations, and can be explored by the users of the AGS tool.

This deliverable D4.6 titled “Automatic Subspace Generation (ASG) 1.0” is a short report accompanying the ASG open source software called Krachem that has been produced and is available in the NEASQC GitHub repository under the project qfrag (Chagas et al., 2023). The deliverable outlines the key functions of Krachem along with pointers to the repository of its implementation and a quick start user guide.

This document gives an overview of the software delivery D4.7 “Readout Optimization (RO) V1.0”, comprised of the three readout optimization methods for quantum computing measurements that were researched and implemented by HQS Quantum Simulations within the NEASQC project. The software implementations can be found on the NEASQC GitHub [1].
The three measurement optimization methods studied include one utilizing shadow measurement in the context of spectroscopy, one based on enhanced sampling using Bayesian statistics, and one based on projecting the result to fulfill so-called n-representability constraints which may be violated in a noisy quantum computation. The later two were already reported in the earlier NEASQC delivery D4.5 [2], but are included within this document as well for the sake of completeness and reader convenience. The document is structured as follows:
In Chap. 2, we introduce the technique for utilizing the measurement of classical shadows in the context of spectroscopy, a promising use case for near future quantum computing. We also show numerical results. The method was implemented based on a recent paper [3], and implemented on our NEASQC GitHub repository [1], where the associated code can be found here:
https://github.com/NEASQC/Variationals_algorithms/tree/main/classic_shadows
Next, in Chap. 3 we discuss the method for enhanced sampling and show some key results, which was already reported in a previous NEASQC deliverable [2]. The software implementation we developed is based on what can be found in literature [4], and we will make the code available in the NEASQC GitHub [1]. Currently, it can be found here:
https://github.com/NEASQC/Variationals_algorithms/tree/main/enhanced_sampling

The software described in this document allows for the calculation of the ground state energy of a graphene+CO2 sys￾tem by using the variational quantum eigensolver (VQE). Such as in the D4.2-QCCC alpha report (Sennane & Rancic, 2022a), two types of quantum computing ansatze are implemented (the hardware efficient one and the qUCCSD), al￾though this report particularly focuses on VQE+qUCCSD. The code supports noisy simulations, modification of size and deformation of the graphene sheet as well as modifying the orientation of CO2 molecule. The code is available on Github : https://github.com/NEASQC/D4.8.

This document is a continuation of deliverable D4.3 of the NEASQC project and is concerned with benchmarking the
applications for quantum computing researched and implemented within the quantum chemistry work package of the
project.
In D4.3 we reported assessments contributed from three of the partners within the work package:
AstraZeneca presented a benchmarking study for chemical reactivity with our previously implemented Pre-Born-Oppenheimer quantum computing computational package [1], where the showcase was the reaction of water hydro￾genation.
HQS Quantum Simulations demonstrated a performance analysis of their implemented variational algorithms [1], comparing a Variational Quantum Eigensolver (VQE) implementing UCCSD, an Adaptive Variational Quantum Eigensolver (AdaptVQE) using UCCSD, a variational Hamiltonian ansatz (VHA), and a variational imaginary time evolution (VITE) with two-local ansatz [2–5].
TotalEnergies estimated the feasibility to execute families of Hardware Efficient (HE) quantum computing ansatzes and quantum Unitary Coupled Cluster (qUCC) ansatzes on (noisy) near-term quantum computers, applied to a calcu￾lation of the ground state energy of strained benzene [6, 7].
In this report, that constitutes deliverable D4.9 of the NEASQC project, we extend on these contributions:
In Chap. 2, AstraZeneca extended their investigations to the interaction of CO2 with a hydrogen radical using the Nuclear-Electronic Orbital (NEO) Quantum Computing Framework [8, 9], with a specific focus on simulating the reduction of CO2
.
In Chap. 3, HQS Quantum Simulations focuses here on the evaluation of methods to improve quantum measure￾ments, one utilizing shadow measurement in the context of spectroscopy [10], one based on enhanced sampling using Bayesian statistics [11], and one based on projecting the result to fulfill so-called n-representability constraints which may be violated in a noisy quantum computation [12]. This is reported on in more detail in deliverable D4.7, with software implementations available on the NEASQC GitHub [1].
In Chap. 4, TotalEnergies continued their studies regarding benzene to a calculation of a system of graphene and a CO2 molecule using a VQE approach, which could be used in the context of understanding recapture processes of carbon dioxide. Similar to above, this study is reported on in more detail in deliverable D4.8, with related software found on the NEASQC GitHub [13].
Finally, in Chap. 5, ICHEC gives an overview of the software tool KraChem which was developed within the NEASQC project. The tool is designed to automatically fragment molecular systems into smaller subsystems, allow￾ing breaking down large problems into subproblems, making them digestible for NISQ computations. This automatic subspace generation was reported on earlier in detail in deliverable D4.6, and is available on the NEASQC GitHub as well [14].

This report summarizes deliverable 3.3: initial release of open-source libraries. Its goal is to provide an insight on the rationale behind the release of the open source libraries developed in the project and provide details on the various steps taken to help and coordinate these releases. Before diving into the technical details, let us introduce the methodology as specified in the initial proposal.

1. The libraries will focus on circuit-based programming

2. The programming language will be myQLM python (pyAQASM)

3. Bull will act as the integrator of the libraries, as in Bull will notify developers when new bugs are introduced due to changes in the core quantum programming library

4. Following the best practice in software engineering, continuous integration (CI) will be used. The CI platform is in place and operated by Bull.

5. Every 4months, the WP leaders and Bull will synchronize on the UC developments and will identify candidates for additional libraries, in full agreement with the partners who developed the code.

6.During the project, the libraries (source codes and compiled) will be made public outside only once they have reached a correct level of integration quality. By default, no external contribution will be possible until the end of the project, in order to avoid disorganizing the use case developments. External change requests may be allowed, but without any warranty

7.The library sourcecode is required to be documented and accompanied by application examples, according to the standard coding best practices

Points 6 and 7 are here to ensure best practice and user experience. Points 1 to 5 were decided during proposal redaction and ensure a uniformity of the released libraries: they are all supposed to rely on the same core package, thus allowing for interoperability between them.

This report is the logical follow up of report D3.1: myQLM Specifications to support Hardware platforms. In D3.1, we detailed the software architecture behind myQLM and listed the various quantum circuit compilation and transpilation tools that can be used to efficiently target specific hardware platforms. This new report provides a detailed presentation of a black-box compiler that combines quantum circuit optimization, compilation, and transpilation, all behind a user-friendly interface. After this presentation, we give results of execution and simulation of compiled quantum circuits and compare the resulting algorithmic performances against quantum circuits compiled with other frameworks.

This document describes The NEASQC Benchmark Suite (TNBS). The objective of the document is to define the benchmarks that compose it, and the methodology for executing them and reporting their results. It includes also a short description of the TNBS website and the associated repository of submitted benchmark results.

TNBS has been designed to take into account four main objectives:

• Objective 1: the test cases which compose the suite must help computer architects, programmers and researchers to design future quantum computers, taking into account the variability in the performance introduced by the different components of the stack.

• Objective 2: the test cases must help to understand the evolution of quantum computers (more qubits, better topologies) or to improve the current one (reduction of noise, better compilers, etc.).

• Objective 3: the test cases must allow to compare the performance of different platforms. Currently, there are many different proposals (as transmons, ions, neutral atoms, etc.) which use different one- and two-qubit gates. The benchmarks must allow users and researchers to compare the performance of different platforms, and find their bottlenecks. For users, they should allow them to find the best platforms for their application.

• Objective 4: the test cases should consider other metrics which may be important to understand the quantum computing advantage (such as energy consumption, throughput or better scalability).

To achieve these objectives, TNBS has found representative kernels among the NEASQC uses cases to define a set of well-defined tests. Currently, TNBS is composed of four cases, each of them with:

1. A full and detailed documentation of the suite and of each microbenchmark. This documentation will include the definition of the microbenchmarks, the rules for executing them, the methods for reporting the results, and the methods for evaluating the final results.

2. An Eviden myQLM reference implementation, that allows the analysis of their complete results.

This document includes sections for describing the general rules for executing the benchmarks, the methods for gener-ating the results, the process to submit them, the list of benchmarks that compose the Suite, and a brief summary of the capabilities of the repository. As appendices, the JSON schema for reporting the results, the template for defining new cases, and the four documents that describe the current benchmarks are included. All the cases included a reference version based on Eviden myQLM framework.

In the future, the TNBS will increase the number of cases, from NEASQC use cases or from external proposals. So, this document will be a live document, with continuous improvements.

This report presents the results of The NEASQC Benchmark Suite (TNBS) testing phase and the noisy emulation of some of the benchmark cases included in the TNBS. The main objective of this study is to evaluate the performance of Quantum Computing (QC) platforms using benchmark cases defined from the NEASQC project use-cases.
The report is divided into two main phases:
Phase I: Benchmark Validation. In this phase, the benchmark cases based on the NEASQC project documentation were replicated, and their performance was validated. The main benchmark cases evaluated included:Probability Loading Algorithms: Assessing algorithms’ capability to map classical probability distributions onto quantum states for use in various quantum applications.
Amplitude Estimation Algorithms: Focused on estimating integrals using quantum circuits.
Phase Estimation Algorithms: It enables the determination of the phases of a quantum state, allowing for the calculation of eigenvalues of a specific unitary operator applied to that state.
Parent Hamiltonian Benchmark: This evaluated the system’s energy to find the ground state using variational algorithms.
Phase II: Noise Implementation and Analysis. In this phase, noise was introduced into the emulation of the benchmark execution, and its impact was studied using different models, such as Amplitude Damping, Pure Dephasing, Idle noise, Depolarizing Channel, and Depolarising Channel + Idle noise. The experiments used parameters from superconducting qubit technologies from IBM and trapped-ion qubits from Quantinuum. The report analyzed how noise affects the performance and the reliability of quantum algorithms, focusing on error metrics such as KS, KL, Energy and execution times.
The results of these phases demonstrated that TNBS can be effectively used to compare different quantum computers with varying architectures. Additionally, the knowledge gained about the impact of noise on this set of benchmarks will contribute to a better understanding of the robustness of quantum systems under real conditions, which is crucial for the advancement of quantum technologies.
This report concludes that TNBS provides valuable tools for evaluating the performance of QPUs, laying the foundation for future quantum applications and hardware optimizations.