The field of quantum computing is developing rapidly. As a result, a variety of quantum hardware, software development kits, and quantum algorithms have been developed in recent years. However, knowledge about these artifacts is either not available or spread among diferent sources. Thus, to analyze, compare, and evaluate knowledge on quantum computing an integrated knowledge base is required. In this paper, we introduce key concepts of an ontology for quantum algorithms and their implementations. The presented ontology serves as basis for a collaborative platform for researchers and practitioners to support collection and development of knowledge on the field of quantum computing.
exemplary programming code, which can form a valuable body of knowledge for
the development of quantum-inspired and -enhanced applications in the future.
This is important because, even being in the so-called Noisy Intermediate Scale
Quantum (NISQ) era [
However, for companies and scientists trying to leverage quantum computing
for business, development, and research, this means hard times ahead. This is
because the knowledge about quantum computing and, especially, how to build
applications that can make use of quantum resources to gain improvements over
classical algorithms is not systematically available. Explanations of quantum
algorithms, such as estimations of the speedup over classical algorithms,
theoretical considerations of required quantum resources, and actual implementations of
the algorithms are typically spread among diferent sources. As a consequence,
required knowledge has to be collected and obtained manually from a vast amount
of scientific publications, vendor-specific documentation pages, or public code
repositories. Yet, such information has to be analyzed holistically to understand
how to implement quantum algorithms and quantum applications for specific use
cases and scientific problems at hand. Moreover, the absence of an integrated
knowledge base hinders to establish a community bridging theoretical foundations
and research on new quantum algorithms with their usage, application, and
implementation for relevant and real scenarios. In this regard, an open ecosystem is
key for rapid technological progress in quantum computing via close cooperation
and steady interchange of ideas between research and industry [
Therefore, it is required to come up with a systematic approach to semantically
represent and curate knowledge about quantum computing algorithms along
with their implementations, as presented in this paper. We contribute with
a semantified meta-model that was engineered to provide the core knowledge
structure for semantic knowledge curation in the project PlanQK – platform and
ecosystem for quantum-enhanced AI [
This paper is structured as following: We introduce the PlanQK project in Sect. 2 and discuss the key objectives of the intended knowledge platform. We introduce the mentioned core meta-model as an ontology in Sect. 3. Finally, we conclude this paper in Sect. 4 by an outlook to future work, which will be conducted in PlanQK based on the presented ontology. Specialist Algorithm Developer
Data Provider
Researcher QPU Provider
Software Architect and Developer
Analysis and development platform for algorithms, data, and applications Crawler IntUesrefarce Expert Portal Customer Service Provider
System Integrator Consultant
Marketplace Customer Provider Portal Portal API
API
API
API Publication Content Store
QAlgo- QC-Pattern- Data- QApp
Repository Repository Repository Repository NISQ-Analyzer ArXiv/ GitHub / Bitbucket / GitLab / Docker Hub / Dataset Search / … Requests/ Purchases/ Offerings
Deployment &
Management
QC-, Cloud- and
OnPremise-Infrastructure
The vision of a collaborative platform for the exchange of knowledge in the field
of quantum computing has already been presented in previous work [
The key knowledge artifacts that are provided on the analysis and
development platform include Quantum Algorithms (QAlgos) and their Implementations
using diferent SDKs for the diferent quantum computing vendors, Quantum
Design Patterns (QC-Patterns) that provide best practices for quantum
algorithms, Datasets (Data) for specific machine learning and AI algorithm, and
Quantum Applications (QApps) that can be deployed and integrated with classical
applications. New knowledge, e. g., in form of publications, can be added using
the user interface or in an automated manner using the crawler. The knowledge
artifacts can then be extracted and linked, discussed and evaluated, and made
available to customers to identify suitable algorithms or implementations for their
specific use cases. Selected QApps can be automatically deployed and managed,
e. g., using established deployment technologies. The NISQ-Analyzer component
supports users by analyzing which implementation of a quantum algorithm and
which quantum computer are recommended for specific input data [
Publication referenced by
An important goal of the PlanQK platform is to build a quantum community and establish knowledge exchange between scientific and commercial users. The ontology presented in this work defines an unambiguous machine-interpretable semantic description of the platform knowledge artifacts and intend to used to support the user exchange through (i) proving the logical consistency of the curated data, (ii) serving as the foundation for the realization of various AIbased features, e.g., semantic faceted search, natural language question answering engine, or recommendation system for the selection of an appropriate quantum algorithm in a specific use case, and (iii) providing an opportunity to document the expert discussions held on the platform in a semantically usable way. 3
Towards a Unified Ontology for Quantum Algorithms
In developing the ontology, we followed existing ontology development
guidelines [
Fig. 2 depicts the connections between key concepts of the ontology, which we
specify as OWL4 classes. This design was inspired by the
Algorithm-Implementation-Execution Ontology Design Pattern (ODP) [
Quantum
Annealing Measurementbased Quantum Computation owl:Class owl:NamedIndividual owl:ObjectProperty rdfs:subclassOf rdf:type
Solution and Problem Type, and connect them with Algorithm through object properties “provides” and “solves”. Solution is defined as algorithmic steps to solve a computation problem, typically pseudocode or/and circuit. Solution can have connection to the class Function when it is an essential part of the solution, such as an appropriate objective function is a fundamental element of optimization algorithms or a quantum oracle is a crucial part of some quantum algorithms, e.g., Deutsch-Jozsa algorithm. Problem Type represents types of problems that are solvable by algorithms. Many real-world problems can be mathematically formalized in terms of other problems, e. g., a cluster problem can be expressed as an optimization problem. Complexity Class stores knowledge about the hardness of a problem. The class Input represents the input accepted by an algorithm, and Output specifies the output produced by an algorithm. The ontology is able to express two relation types between algorithms: An algorithm can improve an existing algorithm or be based on the idea of other algorithms.
A researcher designs an algorithm with a computational model in mind. We
distinguish between Classical and Quantum Computational Model and classify
algorithms in Quantum, Classical and Hybrid Algorithms depending on the model
for which an algorithm was designed. Quantum Algorithm is an algorithm that is
designed only for a quantum computational model. Examples of the Quantum
Computational Model are “gate model”, “measurement-based quantum
computation”, “quantum annealing”. Classical Algorithm is equivalent to an algorithm that
is constructed only for a classical computational model. Hybrid Algorithm is an
algorithm that utilizes some quantum and some classical computational models.
In addition to the above presented classification of algorithms, the ontology also
forms the taxonomy of algorithms based on the underlying problem type (machine
learning, optimization, search algorithms etc.). The classes for specific algorithm
types can act in the future as connection points for linking semantically similar
knowledge bases, e. g., machine learning algorithms can be linked with such
knowledge bases as MEX [
realizes
Classical Computational
Resource
By exploiting quantum-mechanical efects, such as superposition,
entanglement, and quantum tunneling, quantum models perform computation more
eficiently than classical ones [
For the class Algorithm we define the following data properties (not shown
in Fig. 3):“skos:prefLabel“ and “skos:altLabel“ (algorithm name and its
abbreviation, this properties are reused from SKOS Schema [
A Computational Model is realized by a Computational Resource, which collects instances utilized for the execution of an implementation. Fig. 4 illustrates relations between Computational Model and Computational Resource. We distinguish between Classical and Quantum Computational Resource that realize only Classical and only Quantum Computational Model, respectively. Quantum computational resources are categorized in Quantum Processing Unit (QPU) and Quantum Simulator. Since quantum simulators run on a classical hardware, Quantum Simulator is connected with Classical Computational Resource through the property “compatible with”. Quantum computational resources have specific characteristics defined by the class Quantum Resource Characteristic, which has subclasses Gate Set, Fidelity, Quantum Access Random Memory (qRAM), Number of Qubits, and Qubit Connectivity. Also quantum and hybrid algorithms can specify hardware characteristics that are required for their realization, as shown in Fig. 4. For example, an algorithm can require a specific set of gates realizable only by some computational resources or show a theoretical speedup but assumes the availability of a qRAM such as Grover‘s algorithm for database search, or HHL for solving linear systems of equations. This information allows Computer Language
written in Programming
Language
Instruction
Language
Classical Quantum Programming embedded Programming
Language in Language developers (i) to evaluate the practical usage of an algorithm, and (ii) to select an appropriate quantum computational resource for executing an algorithm. 3.2
Fig. 5 presents classes connected with the class Implementation. An
implementation is written in a Computer Language and can depend on a Software Tool.
The class Computer Language formalizes languages that can be used to write a
machine or programming code. Similar to Lando et al. [
The class Quantum Provider collects vendors that provide access to quantum
computational resources. Most quantum providers supply software tools for
developing and executing implementations on their quantum computational
resources [
Apart from the algorithm realization itself, an implementation can include error correction, pre- and postprocessing. Error Correction Technique collects methods for limiting errors that occur during information processing. Data Preprocessing Technique specifies operations that are applied on the input data before the actual algorithm steps will be executed. The class Data Postprocessing Technique includes methods that are applied on the algorithm output. A common postprocessing technique for quantum and hybrid algorithms is the Read-out Error Correction that is specified in the ontology as a subclass of both Error Correction Technique and Data Postprocessing Technique.
Ontology source can be found in our repository5. The first prototypical implementation of the platform services has shown that the ontology is consistent and can be used for the realization of semantic features. 4
Conclusion and Future Work In this work we present the first key entities towards a unified ontology for semantically curating knowledge about quantum algorithms and their implementations. The ontology provides a basis for the AI-powered semantic features on the PlanQK platform, such as semantic search and semantic services. The next steps will be to extend the ontology to not yet covered knowledge artifacts, such as quantum applications and data, and to refine the existing artifacts. In addition, provenance data about implementation execution and performance will be included, which is important to identify suitable algorithms for a given problem. Furthermore, a standard-based API for supporting the semantic access to the curated knowledge artifacts and semantic services will be developed. Acknowledgments This work was partially funded by the BMWi project PlanQK (01MK20005N / 01MK20005F).