Encoding and Provisioning Data in diferent Data Models for Quantum Computing

Abstract

Quantum computers promise polynomial or exponential speed-up in solving certain problems in comparison to classical computers. In practical use, however, there are currently a number of fundamental technical challenges. One of them concerns the loading of data into quantum computers and the corresponding encoding, since they cannot access database systems directly. In this paper, a hybrid data management architecture in which databases can serve as data sources for quantum algorithms is presented. Furthermore, a first encoding approach for data organized in tree structures is given.

Keywords

• eol>Data management for quantum computing
• hybrid quantum computing
• data encoding
• data loading

1. Brief Introduction from a

Database Perspective

2. Related Work

as an example for this. In addition, event-driven worklfows are to be supported and economical data exchange It can be generally stated that research on the use of quan- between database systems and quantum computers is tum computers around database systems and data-driven to be explored (cf. Subsection 3.1). Works describing applications is rather rare. As outlined in Section 1, work communication between database systems and quantum on this may well be visionary. However, in order to con- computers considering these aspects are not known so cretely use data in a quantum computer, that data must far. Initial design of this architecture is described in Subbe loaded by encoding it into the state of the qubits [ 4 ]. section 3.1. However, it is a work in progress and will be In paper [ 6 ] it is generally mentioned that loading data continuously developed. into a quantum computer is a hard problem. The fact that Comments on Q2: For developed encoding methods a databases can provide data for quantum computing is runtime and space complexity analysis is performed. The almost not discussed in the literature. The same applies ifrst analyzes the runtime of the encoding methods, the to possible data exchange procedures between database second the demand for qubits. This task is described as systems and quantum computers. The paper [15] deals challenging [ 5 ]. In this way, methods can be compared with the orchestration of hybrid quantum applications with each other. In Subsection 3.2, an encoding approach in the cloud using BPMN-Workflows and uses a database for a tree structure is conceptually developed, which, as input for a specific use case. In [ 5 ], there is mention of however, has not yet been experimentally verified. the need to transform data from databases for quantum computing. 3.1. Data Exchange Framework–A Hybrid

The next important topic concerns encoding. Encoding represents the transformed classical data by means Data Management Architecture of qubits [ 5 ]. Only then can the data be processed on In this Section, we introduce the Hybrid Data Managea quantum computer. In [ 4, 16, 17 ], various encoding ment Architecture, which acts as a data exchange frameprocedures are explained, which are understood as pat- work. A first conceptual idea of the architecture was terns. These patterns are self-contained, reusable build- published in [18]. Figure 1 shows the schematic structure ing blocks that are to be reused in the construction of of the architecture. It can be roughly divided into two quantum algorithms. The fit of these patterns to real- parts: On the left, a classical system with Applications, world data-driven use cases is not discussed. The use Coordinator, and Databases, and on the right, Quantum case data itself can be organized in diferent data mod- Circuits that process data using quantum hardware or els or structures. For example, they can be available in simulators. Quantum hardware may well be provided as relations, in documents (as semi-structured data), or as la- a service in the cloud. beled/unlabeled trees/graphs. The papers do not address how these logical structures can be encoded. Quantum Hardware

3. Research Direction

Based on the challenges of Section 1 and the related work in Section 2, the following research questions arise for the PhD thesis:

Q1: How is a framework for exchanging data between

database systems and quantum computers?

Q2: How can data in diferent data models and struc

tures be encoded using qubits?

Comments on Q1: Previous work [15] uses a BPMN workflow engine for enterprises to orchestrate a variety of tasks. In addition, various other tools and programming languages are used, which form a complex mesh in the end. The framework of this thesis is intended to reduce complexity. A uniform programming language and alternative workflow options are to be evaluated for this purpose. The service layer pattern1 can be considered 1 2

Application Coordinator 3

Create 

Circuit Data Management  4 5

State Preparation (Loading Data by  Q

Encoding) au

n |ψ⟩ tum  

C Algorithm (Unitary  ir

c Transformations) itu

M Databases with different data  models (document store,  graph store, relational)

Firstly we consider the classical system using the example of a workflow. For example, an Application should 1Architecture Patterns with Python. https://www.cosmicpython. solve an optimization problem or classify data, to name com/book/chapter_04_service_layer.html just two examples. The Coordinator is responsible for 3.2. Encoding Approach using the data exchange and communication between the compo- Example of Labeled Unranked Trees nents of the classical system and the quantum computer.

With the help of the Coordinator, the following proce- In this section, we sketch an idea of how labeled unranked dure results: (1) An Application submits a request to the trees could be encoded. Figure 2 shows a tree that is to Coordinator. The Coordinator initially verifies whether be encoded. The source tree is converted into a relational a problem should be solved by means of a quantum al- form. The column y of the table represents the neighborgorithm on a quantum computer in order to process the ing nodes, the column x represents the corresponding request. The Coordinator notifies the Application of the level. For the purposes of illustration, we represent the decision. We assume in the following that a quantum entries of the table in a coordinate system. There, the computer will be used. Otherwise, the data is retrieved connections between the stages and neighboring nodes from the Databases and made directly available to the per level can be seen directly. Based on this, tree-pattern queries can be performed. David [19] describes other Application. The problem will be solved classically. (b2)eletimde-UconnsurmainngkperodbleTmrseoen s(u1ch)trees. Suitable quan

Encoding La The required data is extracted from the Databases and pre-processed if necessary. (3) To solve a problem, a tum algorithms can achieve a quadratic speedup. corresponding Quantum Circuit (see below) is generated. (4) The generated circuit is transmitted to a quantum y x label computer and execution is initiated. (5) The Coordinator 0 0 1 (≙ a) fetches the achieved result of the algorithm and provides 0 -1 2 (≙ b) it to the Application. The Application itself is then in 1 -1 3 (≙ c) charge of post-processing. 1 -2 1 (≙ a)

Next, we look at the structure of a Quantum Circuit. A 2 -2 5 (≙ e)

Quantum Circuit can be roughly divided into the areas of

State Preparation and Algorithm [ 4 ]. The State Preparation 3 -2 6 (≙ f) block is responsible for encoding, which means that data 2 Left tree in tabular view and, if necessary, parameters are loaded and encoded in a a quantum state. This quantum state forms the starting point for the actual algorithm in the Algorithm block, b c which can manipulate the initial state. The execution of an Algorithm ends with the measurement of the final quantum state, which represents the result. 1 Labeled Unranked Tree a e f

Finally, we would like to discuss some aspects of the realization of the data exchange in Figure 1.

Event-driven workflows : Certain use cases assume 3 Left tree in coordinate system that the relevant data is exchanged on demand. In this Figure 2: Various representations of a labeled unranked trees. case, the Coordinator creFaotliees5and transm1i0t.0s5.t2h02e3 circuit 1) Source tree 2) The same tree in tabular representation 3) on request. In other use cases, changes may occur to the Translation of the table into a coordinate system. data in the Databases and new data may be added. In such a case, the circuit should also be updated immediately.

In this scenario, a quantum algorithm operates on data Using the coordinate system, we explain the concept that is always up-to-date. Both variants are understood behind encoding the tree in a quantum state (Figure 3). For encoding, each level is first encoded using the basic taisveevaepnptrso.aFchores(oarreinbsetienagdteosft)etdhienCthoiosrdcionnatteoxrt,, aslutcehrnaas- encoding method [ 17, 5 ] (A). For this, each level must be publish/subscribe messaging. represented as a bit string . This contains all the information of a level (like labels and node links). The basic arcDhaitteacteucroe nisocmruyc:iaClotonsqiudaenritnugmdcaotamrpeusttirnicgt.ioMnosreindtahtea encoding method encodes each level into a quantum state requires more qubits and longer runtimes of state prepa- |⟩. To take advantage of a quantum computer, these states are used to generate a so-called superposition [ 5 ] (B), which encodes the tree in one state. A superposition state is the starting point of a quantum search algorithm.

The encoding approach can be regarded as general.

First, logically related information is encoded via the base encoding before a superposition is generated. Intermediate formats (like a table in Figure 2) can be used to compose related information. ration routines. We propose to store data constraints in profiles to define only a reasonable minimum amount of data to be processed on a quantum computer. For a use case, diferent profiles can be used to manage, for example, diferent data value ranges or diferent node sets (to partition graphs from graph databases). In the

NISQ era, this is of particular interest since hardware limitations allow only quantum circuits of certain size.

Fakul Encoding Labeled Unranked Tree (2) b a f |bl=1⟩ |bl=3⟩

N levels =1 1 B |bl⟩ 6 10.05.2023 each level. B) The total tree encoded in superposition.

4. Conclusion

In this paper, the research direction of the PhD thesis

was presented. It covers two topics. Firstly, a hybrid data management architecture that makes classical data available to quantum computers using a suitable encoding.

Secondly, the development of eficient encoding methods

for classical data in diferent data models. The concept of data management architecture was briefly presented.

Also, a first encoding approach for tree structures was provided.

Acknowledgments

This work has been funded by Deutsche Forschungsgemeinschaft (German Research Foundation) - 385808805.

based quantum algorithms in the NISQ era, Quantum Science and Technology 5 (2020) 044007. in: 2021 IEEE International Electron Devices Meeting (IEDM), 2021.

Platform (SHM3P) Databases, in: Proceedings of

the International Semantic Intelligence Conference 2021 (ISIC 2021), volume 2786 of CEUR Workshop

Proceedings, CEUR-WS.org, 2021, pp. 16–26.

2018.

Processing Time in NoSQL Databases Based on

Grover’s Algorithm, in: Proceedings of the 3rd In

ternational Conference on Smart City Applications,

SCA ’18, Association for Computing Machinery,

Hybrid Quantum Applications Need Two Orches

trations in Superposition: A Software Architecture

Perspective, in: 2021 IEEE International Conference

on Web Services (ICWS), 2021, pp. 1–13. ence on Software Architecture Companion (ICSAencoding patterns for quantum computing, in: Proceedings of the 27th Conference on Pattern Languages of Programs, PLoP ’20, The Hillside Group, for industrial Data-driven Services, in: Proceedings of the 2022 IEEE International Conference on

Quantum Software (QSW), IEEE, 2022.

2022. 289.

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