ABOUT THE PROJECT

The NEASQC (NExt ApplicationS of Quantum Computing) project brings together academic experts and industrial end-users to investigate and develop a new breed of Quantum-enabled applications that can take advantage of NISQ (Noise Intermediate-Scale Quantum) systems in the near future. NEASQC is use-case driven, addressing practical problems such as drug discovery, CO2 capture, smart energy management, natural language processing, breast cancer detection, probabilistic risk assessment for energy infrastructures or inventory management.

NEASQC has the ambition to initiate an active European Community around NISQ Quantum Computing by providing a common toolset that will attract new industrial users.

Missions and Objectives

NEASQC aims at demonstrating that, though the millions of qubits that will guarantee fully fault-tolerant quantum computing are still far away, there are practical use cases for the NISQ (Noise Intermediate-Scale Quantum) devices that will be available in the near future. NISQ computing can deliver significant advantages when running certain applications, thus bringing game-changing benefits to users, and particularly industrial users.

The NEASQC consortium has chosen a wide selection of NISQ-compatible industrial and Financial use-cases, and will develop new quantum software techniques to solve those use-cases with a practical quantum advantage. To achieve this, the project brings together an unprecedented multidisciplinary consortium of academic and industry experts in Quantum Computing, High Performance Computing, Artificial Intelligence, chemistry…

The ultimate ambition of NEASQC is to encourage European user communities to investigate NISQ quantum computing. For this purpose, the project consortium will define and make available a complete and common toolset that new industrial actors can use to start their own practical investigation and share their results.

NEASQC OBJECTIVES

1.

Develop 9 industrial and financial use cases
with a practical quantum advantage
for NISQ machines.

2.

Develop open source NISQ programming libraries for industrial use cases, with a view to facilitate quantum computing experimentation for new users.

3.

Build a strong user community
dedicated to industrial
NISQ applications.

4.

Develop software stacks and benchmarks
for the Quantum Technology Flagship
hardware platforms.

Consortium

NEASQC brings together highly skilled and motivated academic experts and industrial end users, who collaborate on very relevant and representative Quantum Computing applications, and will share their learnings with their communities. To maximise industry/academia collaboration, each use case is investigated by an integrated team of a least one industrial partner and one academic partner.

Early users

NEASQC is organising a series of interactive webinars to share detailed information about the libraries and techniques we investigated and developed for our different use cases. Those webinars will benefit to all organisations and users currently involved or investigating quantum computing and interested in one or more of our uses cases. They will give potential users priviledged access to NEASQC information and return of experience, as well as the opportunity to exchange directly with project members.

Check our webinar programme regularly, we will be announcing new webinars each month until the end of the project (end 2024).

Deliverables

  • Symbolic AI and graph algorithmics
  • Machine Learning and Optimisation
  • Chemistry
  • Programming Framework

D6.1 QNLP design and specification

Understanding the applicability of NISQ-era devices for a variety of problems is of the utmost importance to better develop and utilise these devices for real-world use-cases. In this document we motivate the use of quantum computing models for natural-language processing tasks, focussing on comparison with existing methods in the classical natural language processing (NLP) community. We define the current state of these NISQ devices, and define methods of interest that will allow us to exploit the resources to implement NLP tasks, by encoding and processing data in a hybrid classical-quantum workflow. For this, we outline the high-level architecture of the solution, and provide a modular design for ease of implementation and extension.

D6.2 Quantum Rule-Based Systems (QRBS) Models, Architecture and Formal Specification

This report is the first deliverable related to the use case QRBS. It incorporates information on the approach to the work carried out so far. The report includes a brief description of invasive ductal carcinoma of the breast (IDC), the methodology followed for the modeling of a rule-based system for the diagnosis and treatment of IDC, a preliminary analysis to evaluate the suitability of quantum computing in this domain, a proposal about the quantum approximation that we want to use, and that we will later have to evaluate, and the analysis about the formal requirements of the application that we intend to carry out. We also include a quantum proposal on the uncertainty associated with reasoning in medicine.

A brief summary of the IDC is necessary to place the use case in the context of the project. The description will range from the initial symptoms that allow the clinician to consider the possibility of IDC, the diagnostic process, the degree of severity of the IDC, and the possible associated treatments.

The methodological description of the knowledge engineering used is necessary to understand the architecture of a classical rule-based system, and to be able to formalize the problem in terms of declarative knowledge, procedural knowledge and inferential circuits.

Next, a qualitative analysis of the problem in terms of quantum logical operators is presented to illustrate the possibility of converting a conventional rule-based system into a quantum rule-based system.

Finally, the formal requirements of the quantum rule-based system will be mentioned. Also, we will pay special attention to the imprecision of the information and the uncertainty associated with clinical practice.

D6.3 QNLP Pre-Alpha prototype

The NEASQC project aims at demonstrating and advancing the capabilities of NISQ-era devices through the development of practically-relevant use-cases. Under the category of Symbolic AI and Graph Algorith-mic algorithms, one of the use-cases that is being developed is for Quantum-enabled Natural Language Processing (QNLP). The objective of the QNLP use-case in NEASQC is for the investigation, development and comparison of existing methods in classical NLP with a QNLP approach for encoding and processing sentences in a hybrid classical-quantum workflow.

For this, deliverable D6.1 “QNLP design and specification” was presented in M6 with an overview of the background and existing approaches for classical NLP and quantum NLP along with a detailed illustration of the proposed QNLP software architecture solution and methods for testing and benchmarking the QNLP implementation.

Deliverable D6.3 “QNLP pre-alpha prototype” is the first version of the QNLP software (pre-alpha prototype) which is primarily aimed at assessment within the NEASQC project. D6.3 implements a first version of the modules for generating training datasets (composed of sentences of specific grammatical structures), quantum circuits for training using single sentences and whole datasets, and classical NLP approaches for evaluation. This report accompanying D6.3 provides an overview of the currently implemented modules along with access and usage details of the QNLP pre-alpha prototype.

D6.5 Quantum Rule-Based System (QRBS) Requirement Analysis

This report is the second deliverable of Task 6.2-Quantum Rule-Based Systems (QRBS) for breast cancer detection of the NEASQC project. The document presents the work carried out so far, and is complementary to the other deliverables of this task.

The report begins with an introduction into the requirement analysis process, explaining the necessary concepts to understand the development of the work. Along with said concepts,the applied procedure for the analysis of requirements used in this work is also presented, to put the reader in context and to justify the following sections.

Once the necessary concepts have been presented, the report illustrates the different phases of the work carried out, starting with the needs and features (vision). This phase serves to detect several factors that are crucial to the requirement analysis, such as the actors related to the system or the needs that the system must cover.

The document continues with next step of the process, related to the use cases, which are decompositions of the previous needs according to their functionality and logical structuring. Each use case is studied, explained and detailed in depth. This decomposition allows for a more robust and traceable development across the next phases of the work.

Finally, following the previous decomposition, test cases are defined. This test cases conform a test plan that will help on later stages of the development,when it arises the need to check whether the system meets the requirements specified.

D6.6: Divide and quantum open source software

Fault trees are a type of model which captures how small failures in probabilistic systems can propagate and ultimately lead to a critical system failure. An important component of fault tree analysis is finding small subsets of events which can cause a critical failure (often called “cut sets”). Finding these small cut sets is important because they often correspond to the most likely way a system will fail.

In this deliverable we provide an open source implementation of a procedure which computes minimal cut sets from fault trees by translating the problem to a satisfiability (SAT) problem. This SAT formula can then either be solved with a classical SAT solver, or with a quantum algorithm: specifically Grover’s algorithm for amplitude amplification. The solutions found by both methods are the same, but the quantum algorithm allows for a quadradic speedup in time complexity. Additionally, for quantum computers which have too few qubits to handle the entire problem instance, a divide and conquer approach can theoretically be used to split the problem up and obtain smaller quantum speedups (Rennela, Brand, Laarman, & Dunjko, 2021).

The main component of this deliverable is the open source library itself, which can be found online here: https://github.com/NEASQC/ft-2-quantum-sat. In section 2 of this document we give an overview of problem of finding cut sets, and how the library solves this problem.

D6.7 QNLP Alpha Prototype

Being a software deliverable, D6.7 “QNLP alpha prototype”, is an intermediate version composed of the approaches that are being explored and evaluated for the targeted QNLP tasks – parallel data extraction and intent detection.

The deliverable D6.3 “QNLP pre-alpha prototype” (Villalpando et al., 2021a) developed an early implementation of the DisCoCat-based model using parameterised quantum circuits to encode a pre-defined dataset of sentences, and trained the parameterised circuits which were evaluated using a test dataset for true/false conditions. Further description of the DisCoCat model is available at (Coecke et al., 2010).

This deliverable D6.7 is a software prototype that adds an additional approach based on Dressed Quantum Circuits (Mari et al., 2020) in which pre-trained classical models are used as pre-processing layers in a transfer learning fashion. Neural Networks are implemented to transform pre-trained word vectors into usable lower dimensional vectors acting as the parameters for the rotations of variational quantum circuits.

The software implementation of this approach is available for internal evaluation at the NEASQC QNLP GitHub repository under a dedicated releases branch tagged v0.2-alpha-d0.9.

An outline about the Dressed Quantum Circuits approach is summarised at the README.md file of the alpha prototype, and the dedicated Jupyter notebook.

An outline of instructions for downloading and running the associated Jupyter notebooks for the pre-alpha and alpha prototypes are provided in README.md file of the NEASQC QNLP GitHub repository, and listed in Section 3.

It is to be noted that both the pre-alpha and alpha prototypes of the QNLP software are works in progress and intended for internal evaluation and testing of the theoretical/algorithmic approaches.

D6.8 State of the art of SAT and PSA solvers in the light of quantum
computing

The main objective of this report is to understand the main factors that may help to solve fault tree analysis problems using quantum algorithms. It turns out that fault tree analysis can be considered an extended variant of Boolean Satisfiability Problem (SAT) which has attracted for decades a lot of research efforts from people and communities with a strong background on computer science and, particularly, in computational complexity related disciplines.

Many solvers exist for SAT and an annual competition is organized every year to push forward the performances of the algorithms to solve SAT instances.

In this report, an overview of last SAT competition winners is provided. Main review objectives were getting an idea of the different strategies and heuristics for solving SAT problems, understanding where the complexity of these algorithms is located and how non chronological search algorithms succeed to solve complex and big instances. The ultimate goal is to see to what extent these strategies can be embedded to enhance the design of hybrid quantum algorithms. Indeed, up to now the quantum algorithm that were already designed to solve either SAT or Probabilistic Safety Assessment (PSA) are limited by the hardware limitation regarding the number of available qubits and the decoherence time.

After a brief presentation of the main SAT-solvers, a synthesis of the experiments and results of the last SAT-competitions is presented, with an indication of the minimal and maximal sizes of the different instances that were solved. This confirms that these instances, can be generally at least as big as the industrial instances one can find in the reliability problems (or fault tree analysis) for complex industrial systems. Regarding the instances’s complexity, we should note that the nature of the industrial instances has many particularities that one take can consider for simplification. Indeed, aside from redundancies (which may be the most complexity related aspect), there are many symmetries and modules that could be simplified for better performances.

Different quantum algorithms are presented to deal with SAT, they fall in different classes of quantum algorithms:

• Quantum walks,

• Harrow-Hassidim-Lloyd (HHL) based algorithms,

• Adiabatic algorithms,

• Chaotic dynamics,

• Ground state quantum computer algorithms,

• Parallel quantum algorithm,

• Cooperative search algorithm,

• Divide and Quantum.

For the PSA problem, in addition to many of the SAT algorithms that can be also used, we present other more specific algorithms

• Direct implementation with reversible game pebbling or ZX directed optimization,

• a vertex separator quantum algorithm,

• quantum unconstrained binary optimization

• a counting/grover algorithm

We present some tests on different small instances of fault trees and show that scaling remains an important question and therefore requires a focus on efficient hybrid approaches that combine performant classical solvers with a relevant use of quantum superposition when it matters.

D6.9 QRBS software specifications

This report is the third deliverable of Task 6.2 – Quantum Rule-Based Systems (QRBS) for breast cancer detection of the NEASQC project. The document presents the work carried out so far, and is complementary to the other deliverables of this task.

The report begins with an introduction into the software specification process, presenting the necessary definitions for the reader to comprehend the work carried out. Following those concepts come the several specifications obtained, including both static and dynamic design, as well as the implementations specifications for this use case.

Following that, focus is on the testing phase, in order to prove that the specification obtained is coherent regards both itself and the previous work.

To close the report, the conclusions obtained during the development of the work carried out are presented to enhance the following work.

D6.11 Preliminary QRBS software and IDC application specification

This report is the fourth deliverable of Task 6.2 – Quantum Rule-Based Systems (QRBS) for breast cancer detection of the NEASQC project. The document presents the work carried out so far, and is complementary to the other deliverables of this task.

D6.11 (M32) will include a preliminary version of the RBS and QRBS software along with the specification of the IDC application that will be developed.

The report begins with an introduction of the preliminary version of the QRBS software, presenting how the project is structured, providing some use examples of common operations users will make with the library, and a brief com-mentary on the library’s documentation which is presented in an appendix.

Following that, we present the specification for the Invasive Ductal Carcinoma (IDC) application, based on previous work on quantum computing techniques and applying them to the clinical problem specifically.

We continue by extending the work on previous deliverables regarding traceability and testing of the QRBS software, which is a critical part on making sure that the developed library provides valid and verified functionalities.

To close the report, the conclusions obtained during the development of the work carried out are presented and some ideas for future work to be included in upcoming deliverables are shown.

D6.18 QPSA Quantum Walks and Markov Algorithms

In this work, we present a quantum walks based approach for Probabilistic Safety Assessment problems in the dynamic Markovian framework.

After presenting well known quantum walk algorithms for detecting or finding marked elements in a graph or for finding paths in specific graphs, we propose two algorithms to address the more general problem of finding paths from some point to marked elements. The first algorithm is based on move and store strategy to built failure sequences from an initial state to the marked states. It uses a full register assembling qubits representing components of the system under study and other control and ancilla qubits (between n and 2n) to identify all the sequences. The second algorithm is based on a hybrid approach to consider di˙erent cascading circuits for solving relatively large instances.

We present some tests on a Qiskit simulation library that were performed to compare our algorithms against classical random walks. These tests showed that classical approach has advances in the first iteration but the hybrid approach scales better in the sense that it identifies a large number of paths and converges towards all the possible paths to these marked vertices.

D6.10: WP6 QNLP Report

The NEASQC project aims at showcasing and advancing the capabilities of noisy intermediate-scale quantum (NISQ) era algorithms through the development of practically relevant use-cases. Under the symbolic AI and graph algorithms work package WP6, the use-case WP6.1 that we present here focuses on hybrid quantum natural language processing (QNLP). The objective of this use-case is to investigate and develop hybrid classical-quantum approaches to natural language processing (NLP) and compare their performance with classical counterparts. In this deliverable D6.10 we present a series of variations of former algorithms and their application to the task of binary sentiment analysis.

At its core, a large part of D6.10 is centered around the task of sentence classification which, together with clustering, is pivotal to a wide range of applications including sentiment analysis (Wankhade et al., 2022), intent detection (Weld et al., 2022) and language identification (Burchell et al., 2023). The ability to classify and cluster sentences effectively is not only vital for streamlining information retrieval and content organisation, but is also a key application in fields such as healthcare (Demner-Fushman et al., 2009), finance (Kalra & Prasad, 2019), government policy (Jin & Mihalcea, 2022) or in certain versions of recommendation systems (Al-Ghuribi & Noah, 2021; Rich, 1979).

The project aims to investigate possibilities and limitations of hybrid quantum-classical methods for such tasks. Due to current hardware limitations, it seems unlikely that quantum methods could present major computational or accuracy benefits over their existing high-performing classical counterparts. This project aims at investigating the possibility of using hybrid classical-quantum NLP approaches on near-term hardware. Thus, we have worked with low numbers of qubits in line with the capabilities of such devices, and we plan to introduce noise into our models in future.

This report begins by laying out the theoretical foundations that underpin our work in Sec. 3, followed by a description of our models and the datasets used in Sec. 4. The results and details of our experiments are then displayed in Sec. 5 and subsequently analysed and discussed in Sec. 6. The report then ends with a discussion of the limitations of our models and future work in Sec. 7, followed by a bibliography and an appendix (Sec. 8) with further information on the theoretical aspects and user instructions for running the discussed models.

D6.14: Final QRBS software and IDC application

This report is the fifth deliverable of Task 6.2 – Quantum Rule-Based Systems (QRBS) for breast cancer detection of the NEASQC project. The document presents the work carried our so far, and is complementary to the other deliverables of this task ( Moret-Bonillo, Mosqueira-Rey, & Magaz-Romero, 2021; Moret-Bonillo, Mosqueira-Rey, Magaz-Romero & Gomez-Tato, 2021; Moret-Bonillo et al, 2022, 2023).

D6.14 (M40) includes the final version of the RBS and QRBS software along witht he IDC application that has been developed.

The report begins with an introduction of the final version of the QRBS software, presenting the different functionalities it provides, as well as the revisions that have taken place regarding the previous work, the different models developed to implement QRBS, and a commentary on the library’s documentation current state, which is extended in the appendix.

Following that, we present the implementation of the Invasive Ductal Carcinoma (IDC) application, based on previous work on quantum computing techniques and applying them to the clinical problem specifically.

We continue by extending the work on previous deliverables regarding traceability and testing of both the QRBS software and the IDC application, which is a critical part on making sure that the developed software projects provide valid and verified functionalities.

Closing the report, we present the conclusions obtained during the elaboration of this work, along with ideas for future work.

D6.12 NEASQC Approximations-like QPSA Algorithms state of the art

In this NEASQC deliverable, we present an overview of state-of-the-art approximation-like quantum algorithms for solving probabilistic safety assessment problems. Classical approximation algorithms, widely used for real-life complex systems, aim to reduce the search space by pruning branches where cutsets or prime implicants have very low or negligible probabilities. These algorithms also employ various approximations for computing sums of probabilities.

In this document, we outline the state-of-the-art in approximation quantum algorithms that could be applied to probabilistic safety problems.

We have identified numerous approximation algorithms from different classes and quantum routines. Notably, hybrid classical/quantum algorithms—including interpolation, parallelization, cooperative search, a search algorithm via st-network connectivity, quantum walks, and approximate counting—appear promising. They should enhance the resolution of such problems using limited performance quantum hardware. Recent advances in quantum communication have also paved the way for distributed algorithms, which may be particularly relevant in this context.

In this document, two distributed algorithms are identified: the first provides a general framework for distributing algorithms across a network of quantum nodes or machines, while the second specifically utilizes a Long algorithm.

D5.1 Review of state-of-the-art for Pricing and Computation of VaR

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.

D5.4 Evaluation of quantum algorithms for pricing and computation of VaR

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.

D5.2 Specification of QRL algorithm for inventory management

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.

D5.5 Implementation of QRL algorithm on real architecture

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.

D5.6 Diagrammatical languages to represent Hamiltonians and how to compute the exponential of Hamiltonians

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.

D5.7: Update of review of state-of-the-art for Pricing and Computation of VaR

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.

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

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.

D5.9: Benchmarking of QAOA-based algorithms for mesh segmentation, against
K-Means, normalized and randomized cuts, and core extraction methods

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.

D4.1: VA Beta and BBO Beta

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.

D4.2 QCCC alpha

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.

D4.4 Chemistry – Completion of First software suite (open source software)

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).

D4.5 RO Beta and QCCC Beta

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

D4.6 Automatic Subspace Generation (ASG)

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.

D3.3 Initial release of the open-source libraries

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.

D3.4 myQLM special build

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.

D3.5 The NEASQC Benchmark Suite (TNBS)

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.

Project factsheet

Project factsheet

Project NameNExt ApplicationS of Quantum Computing
AcronymNEASQC
Project TypeResearch and Innovation Action (RIA)
Time span01/09/2020-30/11/2024
CallH2020-FETFLAG-2020-01
Grant Agreement951821
CoordinatorAtos (Bull SAS)
EU Contribution€ 4 671 332,50

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