Towards an Automated Framework for Realizing Quantum Computing Solutions Nils QuetschlichLukas BurgholzeryRobert Willez

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Towards an Automated Framework for

Realizing Quantum Computing Solutions

Nils Quetschlich∗Lukas Burgholzer†Robert Wille∗‡

∗Chair for Design Automation, Technical University of Munich, Germany

†Institute for Integrated Circuits, Johannes Kepler University Linz, Austria

‡Software Competence Center Hagenberg GmbH (SCCH), Austria

nils.quetschlich@tum.de lukas.burgholzer@jku.at robert.wille@tum.de

https://www.cda.cit.tum.de/research/quantum

Abstract—Quantum computing is fast evolving as a technology

due to recent advances in hardware, software, as well as the

development of promising applications. To use this technology for

solving speciﬁc problems, a suitable quantum algorithm has to be

determined, the problem has to be encoded in a form suitable for

the chosen algorithm, it has to be executed, and the result has to

be decoded. To date, each of these tedious and error-prone steps is

conducted in a mostly manual fashion. This creates a high entry

barrier for using quantum computing—especially for users with

little to no expertise in that domain. In this work, we envision

a framework that aims to lower this entry barrier by allowing

users to employ quantum computing solutions in an automatic

fashion. To this end, interfaces as similar as possible to classical

solvers are provided, while the quantum steps of the workﬂow are

shielded from the user as much as possible by a fully automated

backend. To demonstrate the feasibility and usability of such

a framework, we provide proof-of-concept implementations for

two different classes of problems which are publicly available

on GitHub (https://github.com/cda-tum/MQTProblemSolver) as

part of the Munich Quantum Toolkit (MQT). By this, this work

provides the foundation for a low-threshold approach realizing

quantum computing solutions with no or only moderate expertise

in this technology.

I. INTRODUCTION

Quantum computing devices are rapidly evolving and ma-

turing with the increase of the number of available quantum

computers as well as their number of qubits, error rates de-

creasing, and operations becoming faster. In parallel, numerous

Software Development Kits (SDKs), such as Google’s Cirq [1],

IBM’s Qiskit [2], Quantinmuum’s TKET [3], and Rigetti’s

Forest [4], are being developed to make use of the available

quantum computing hardware. Even specialized SDKs for

certain purposes are available, e.g., Xanadu’s Pennylane [5] for

differentiable quantum computing. These developments spark

interest in quantum computing from academia and industry—

leading to potential applications in various domains such as

physics [6], chemistry [7], ﬁnance [8], and optimization [9].

So far, many works aiming to solve speciﬁc problems

by utilizing quantum computing follow a similar workﬂow

consisting of four steps:

1) Selecting a suitable quantum algorithm.

2) Encoding the speciﬁc problem into a quantum circuit.

3) Executing it on a quantum device.

4) Decoding the solution from the quantum result.

While this has led to several promising quantum computing

applications (triggering a substantial momentum for quantum

computing in general), realizing the respective solutions comes

with two major challenges: First, for all four steps, expertise

in quantum computing is required. Without that, neither a

quantum algorithm can be selected if the user is not aware

of its prerequisites, nor can the problem be encoded, or the

resulting quantum circuit be executed and the solution be

extracted. Naturally, most of the users from those application

domains are not trained experts in quantum computing which

poses a huge roadblock in the further utilization and adoption

of quantum computing. Second, especially during the encoding

and decoding, many tedious and error-prone tasks have to be

conducted—resulting in a huge manual effort to actually solve

problems using quantum computing. Both aspects combined

lead to a high entry barrier to employ quantum computing and

make its utilization very challenging.

In this work, we envision a framework that simpliﬁes the

realization of quantum computing solutions—particularly for

users from the various application domains. To this end, we

exploit the fact that the current workﬂow summarized above

actually offers tangible opportunities to shield the user as

much as possible from the intricacies of quantum computing.

This is accomplished by keeping the interfaces for both, the

problem input and the solution output formats, as similar as

possible to classical solvers and by providing guidance for the

quantum algorithm selection procedure. Using this as a basis,

the remaining steps (encoding, executing, and decoding) are

then covered in a fully automated fashion.

To demonstrate the feasibility and usability of such a

framework, a proof-of-concept implementation—which is

publicly available on GitHub (https://github.com/cda-tum/

MQTProblemSolver) as part of the Munich Quantum Toolkit

(MQT)—has been realized for two different problem classes:

Satisﬁability Problems (SAT problems) and Graph-based Op-

timization Problems. For both, corresponding case studies

conﬁrmed the beneﬁts from a user’s perspective. By this, this

work provides the foundation for a low-threshold approach

of realizing quantum computing solutions with no or only

moderate background in this technology.

arXiv:2210.14928v2 [quant-ph] 28 Feb 2023

The rest of this work is structured as follows: Section II

gives a short introduction to quantum computing. Based on

that, a detailed explanation of the mentioned workﬂow of

realizing quantum computing solutions for speciﬁc problems

is given in Section III. Afterwards, the tangible opportuni-

ties to automate and simplify this workﬂow are identiﬁed

in Section IV—motivating the envisioned framework. Based

on that, the proof-of-concept implementations are described

in Section V and evaluated from a user’s perspective in

Section VI. Section VII concludes this work.

II. QUANTUM COMPUTING

In order to keep this work self-contained, this section gives

a short introduction to quantum computing. Compared to

classical computing, where each bit can have a value of 0

or 1representing its state, a quantum bit or qubit may also be

in a superposition of those values, i.e., the quantum state |φi

of a qubit can be written as

|φi=α0|0i+α1|1i=α0α1T

with amplitudes α0,α1∈Csuch that |α0|2+|α1|2= 1. For n

qubits, their state is composed of 2namplitudes αi∈Cwith

ifrom 0to 2n−1. Again, the quantum state can be written

as a superposition of all its basis states, i.e.,

|φi=

2n−1

i=0

αi|ii=α0. . . α2n−1Twith X

i|αi|2= 1.

Analogously to classical computing and its logical gate

operations, computations on quantum computers are conducted

using quantum gates which alter the state of the qubit. The cor-

responding functionality of a quantum gate can be described

by a unitary matrix; its effect on a quantum state can be

determined by multiplying the matrix representation and the

currently considered state representation.

Three prominent gates acting on a single qubit are the

Hadamard (H), the Pauli-X (X), and the Pauli-Z (Z) gate

which are deﬁned by the matrices

H=1

√21 1

1−1, X =0 1

1 0,and Z=1 0

0−1.

A prominent representative acting on two qubits (typi-

cally referred to as control and target qubits) is the

controlled-not (CNOT) gate. If the control qubit is |1i, the

CNOT gate switches the amplitudes of the target qubit. In

principle, any operation can be controlled by arbitrarily many

qubits. A corresponding multi-controlled operation is only

applied, if all control qubits are |1i. An example for such

a multi-controlled operation is the multi-controlled-Z (MCZ)

gate. If all the control qubits are |1i, the MCZ gate applies a Z

gate to the target qubit. Those two operations with the second

respectively the nth qubit being the target qubit are deﬁned

by the matrices

CNOT =





1000

0100

0001

0010







and MCZ =







1 0 . . . 0

0.......

....1 0

0. . . 0−1







|0i

Fig. 1. Exemplary quantum circuit starting in state |00i.

The state of a quantum system cannot be directly observed.

Instead, a measurement collapses the state to one of the

(classical) basis states |ii—each with probability |αi|2—which

can then be read out.

Quantum algorithms are typically described in the form of

aquantum circuit, i.e., a sequence of gates that are applied to

the qubits of a quantum system.

Example 1. Fig. 1 shows an exemplary quantum circuit with

two qubits that ﬁrst applies a Hadamard gate, followed by a

CNOT gate. In the end, the qubits are measured.

III. REALIZING QUANTUM COMPUTING SOLUTIONS

This section gives an overview of the main steps to be

conducted when aiming to solve a speciﬁc problem using

quantum computing. Based on that, the remainder of this work

will then deal with how to automate this workﬂow or, at least,

aid the user during this process. In order to properly illustrate

those steps as well as the proposed solution, a running example

is used, which is introduced in the following.

Example 2. Kakuro, a cross-sum riddle, is an example of a

SAT problem and is composed of a grid structure with Mrows

and Ncolumns, where each row and column shall add up to

a given sum. Additionally, numbers within each row and each

column must be distinct. A simple Kakuro riddle instantiation

with a grid structure of 2×2is shown in Fig. 2a, where the

goal is to determine a,b,c, and dsuch that the respective

sums add up to 1. Thus, all those variables are to be assigned

either 0or 1. A solution to this problem is characterized by

satisfying the constraints a6=b,b6=d, and c6=d.

A. Quantum Algorithm Selection

The ﬁrst step towards solving a problem using quantum

computing is to choose a proper quantum algorithm which is

suitable for the considered problem. Without going into the

details of quantum algorithms (for this, we refer to the given

references), some prominent representatives are

•Grover’s Algorithm [10], which is suited for unstructured

search (problems),

•Quantum Phase Estimation (QPE, [11]), which provides

the foundation of Shor’s Algorithm [12] used for integer

factorization, or

•Variational Quantum Algorithms (VQAs, [13]), e.g., Vari-

ational Quantum Eigensolver (VQE) and Quantum Ap-

proximate Optimization Algorithm (QAOA), which allows

for hybrid classical-quantum computing while also being

suited for combinatorial optimization problems, such as

the Max-Cut Problem.

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TowardsanAutomatedFrameworkforRealizingQuantumComputingSolutionsNilsQuetschlichLukasBurgholzeryRobertWillezChairforDesignAutomation,TechnicalUniversityofMunich,GermanyyInstituteforIntegratedCircuits,JohannesKeplerUniversityLinz,AustriazSoftwareCompetenceCenterHagenbergGmbH(SCCH),Austrianils.quets...

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Towards an Automated Framework for Realizing Quantum Computing Solutions Nils QuetschlichLukas BurgholzeryRobert Willez

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