Predicting Good Quantum Circuit Compilation Options Nils QuetschlichLukas BurgholzeryRobert Willez

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Predicting Good Quantum

Circuit Compilation Options

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—Any potential application of quantum computing,

once encoded as a quantum circuit, needs to be compiled in

order to be executed on a quantum computer. Deciding which

qubit technology, which device, which compiler, and which corre-

sponding settings are best for the considered problem—according

to a measure of goodness—requires expert knowledge and is

overwhelming for end-users from different domains trying to use

quantum computing to their advantage. In this work, we treat

the problem as a statistical classiﬁcation task and explore the

utilization of supervised machine learning techniques to optimize

the compilation of quantum circuits. Based on that, we propose

a framework that, given a quantum circuit, predicts the best

combination of these options and, therefore, automatically makes

these decisions for end-users. Experimental evaluations show that,

considering a prototypical setting with 3000 quantum circuits,

the proposed framework yields promising results: for more than

three quarters of all unseen test circuits, the best combination

of compilation options is determined. Moreover, for more than

95% of the circuits, a combination of compilation options within

the top-three is determined—while the median compilation time

is reduced by more than one order of magnitude. Furthermore,

the resulting methodology not only provides end-users with a

prediction of the best compilation options, but also provides

means to extract explicit knowledge from the machine learn-

ing technique. This knowledge helps in two ways: it lays the

foundation for further applications of machine learning in this

domain and, also, allows one to quickly verify whether a machine

learning algorithm is reasonably trained. The corresponding

framework and the pre-trained classiﬁer are publicly available

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

of the Munich Quantum Toolkit (MQT).

I. INTRODUCTION

The capabilities of quantum computers are steadily

evolving—achieving more physical qubits, lower error rates,

and faster operations. Devices are increasingly made available

through manufacturers, such as IBM Quantum, or third-party

cloud providers, such as Amazon Web Services. Furthermore,

several Software Development Kits (SDKs) for programming

these devices have been developed, e.g., IBM’s Qiskit [1],

Quantinuum’s TKET [2], Google’s Cirq [3], Xanadu’s Penny-

lane [4], and Rigetti’s Forest [5]. As a result of this progress,

academia and industry have started to elaborate possible

applications for this new technology. In fact, the potential of

quantum computing is currently being explored for several

application domains such as chemistry (e.g., [6]), ﬁnance (e.g.,

[7]), optimization (e.g., [8]), and machine learning (e.g., [9]).

Even dedicated workﬂows describing the steps required to

solve a classical problem using quantum computing start to

emerge (e.g., [10]).

The process towards executing corresponding quantum al-

gorithms on quantum computers has a lot of similarities to

the process of executing classical algorithms or programs on

classical computers. In the classical world, a program must be

transformed so that it can be executed on a speciﬁc Central

Processing Unit (CPU) which provides its own Instruction

Set Architecture (ISA). This transformation process is called

compilation and is conducted by compilers—usually coming

with numerous settings and optimization parameters. Simi-

larly, once an application for quantum computing has been

encoded as a quantum circuit, it needs to be compiled to the

targeted device’s native gate-set while obeying all restrictions

imposed by the device, e.g., limitations on the interaction of

qubits.

For classical compilation, guidelines and best-practices have

been developed over the previous decades such that even

end-users without a background in computer science can

compile and execute their programs. In quantum compilation,

however, this is not yet the case and classical compilation

schemes cannot be adopted in a one-to-one fashion. The reason

for that lies within the constraints (such as the restricted

connectivity of quantum devices) to be satisﬁed by a com-

piled quantum circuit compared to classical software. Since

comparable guidelines and best-practices have not yet been

developed for quantum circuit compilation, expert knowledge

is required and especially end-users without a background in

quantum computing are easily overwhelmed with a ﬂood of

different qubit technologies, devices, compilers, and (quite fre-

quently, poorly documented) settings to choose from. Without

actionable advice, it is extremely difﬁcult for an end-user to

decide on a combination of all these options for a correspond-

ingly considered application.

In this work, we treat the problem as a statistical classiﬁ-

cation task and explore the utilization of supervised machine

learning techniques to optimize the compilation of quantum

circuits. We propose a framework that, given a quantum

circuit, predicts the best combination of these options and,

by that, automatically decides for end-users which qubit

technology, which speciﬁc device, which compiler, and which

corresponding settings to choose for realizing their applica-

tions. By this, a similar kind of comfort is provided to the

end-users of quantum computers as is taken for granted in the

classical world.

arXiv:2210.08027v3 [quant-ph] 19 May 2023

In order to demonstrate the effectiveness of the proposed

methodology, we trained a machine learning classiﬁer on 3000

training circuits (taken from the MQT Bench library [11])

considering two qubit technologies, ﬁve different devices,

two compilers, and six corresponding settings. The resulting

classiﬁer, which is publicly available along with the proposed

framework, is shown to yield the best possible combination of

compilation options in more than three quarters of all unseen

test circuits. For more than 95% of the circuits, a combination

of compilation options within the top-three is determined—

with the median compilation time being reduced by more

than one order of magnitude compared to manually compiling

for all possible combinations of compilation options and

choosing the best result. Moreover, rather than functioning as a

black-box, the underlying model additionally provides means

to extract explicit knowledge from the classiﬁer—potentially

guiding further works towards exploiting the full potential

of machine learning in this domain and, also, to quickly

verify whether a machine learning algorithm is reasonably

trained. The corresponding framework and the pre-trained

classiﬁer are publicly available on GitHub (https://github.

com/cda-tum/MQTPredictor) as part of the Munich Quantum

Toolkit (MQT).

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

we describe the process of determining a good combination

of compilation options and review the related work. Based

on that, Section III details the methodology to predict good

combinations of options. Section IV describes the resulting

framework and summarizes our experimental evaluations. Sec-

tion V discusses how explicit knowledge can be extracted from

the proposed methodology and how changes in the underlying

data can be incorporated before Section VI concludes this

work.

II. CONSIDERED PROBLEM:

DETERMINING GOOD COMPILATION OPTIONS

In this section, we review the spectrum of options to choose

from when realizing an application on an actual quantum

computer, discuss the resulting dilemma for end-users, and

the related work available on this topic so far.

A. Motivation

Due to its promising applications and the steady evolution

of the corresponding technologies, quantum computing is no

longer a niche topic. Researchers in application domains very

different from quantum computing seek to utilize this technol-

ogy as a tool to solve their domain-speciﬁc problems in a more

efﬁcient fashion. As a consequence, quantum computers are no

longer exclusively used by physicists or computer scientists,

but by an interdisciplinary range of end-users.

After a quantum algorithm for solving a particular problem

from an application domain has been developed in terms of

a quantum circuit, the end-user is confronted with a ﬂood of

possible options and design decisions:

•Which qubit technology, e.g., superconducting qubits or

ion traps, is best suited for the application at hand?

•Which particular device, e.g., from IBM or Rigetti, ﬁts

the quantum algorithm best?

•Which compiler, such as IBM’s Qiskit or Quantinuum’s

TKET, is most efﬁcient for compiling the algorithm to

the respective device?

•Which settings and optimizations offered by the compil-

ers, such as different levels of optimization, are adequate

for the problem considered?

Figuring out good combinations of options (according to

some evaluation metric) for a particular application is a highly

non-trivial task due to several factors:

•Different qubit technologies have their own advantages

and disadvantages, e.g., devices based on ion-traps have

an all-to-all connectivity but suffer from slow gate execu-

tion times, while devices based on superconducting qubits

have limited qubit connectivity but fast gate execution

times [12].

•Individual devices greatly vary in their characteristics

such as qubit count, error rates, coherence times, qubit

connectivity, and gate execution times.

•Various compilers have been proposed by industry and

academia, i.e., in [1]–[5], [13]–[15]—each of which is

particularly suited for certain classes of circuits and

architectures.

•Compiler settings and optimizations, quite frequently, are

hardly or insufﬁciently documented.

•On top of all that, the domain of quantum computing

is fast-paced and constantly changing—quickly and fre-

quently redeﬁning the state of the art.

This leaves end-users without expert knowledge faced with

more options than they can feasibly explore. Since quantum

computing is still in its infancy, this diversity of options is

only going to increase in the future. Thus, automated tools

for predicting good combinations of options are absolutely

necessary in order to provide the same kind of comfort that is

taken for granted in the classical world today. Otherwise, we

might end up in a situation where we have powerful quantum

computers and tools, but only a selected group of people know

how to use them.

B. Related Work

Decades of work on classical compilers have led to many

sophisticated compiler optimization techniques. Autotuning

(which describes the process of trying different compilation

parameters and comparing their result against some metric)

and machine learning (overviews are given in, e.g., [16],

[17]) have shown promising results and established themselves

as state-of-the-art techniques in this domain. Even combined

approaches of those two techniques are explored in [18], where

a machine learning model is used not to directly determine

optimal compiler settings but to identify promising areas of

the optimization space. Additionally, reinforcement learning

gained a lot of attention in recent years with promising results,

e.g., in [19]–[21]—all targeting the LLVM [22] compiler.

In quantum compilation, a domain that is still in its in-

fancy, the applied techniques are not that highly developed.

Nevertheless, ﬁrst works towards this direction have already

been proposed nearly a decade ago in the form of hardware

resource estimates to reliably execute various quantum algo-

rithms [23] to provide guidance to end-users. Until today,

resource estimation has still been an open research question.

Microsoft recently proposed the Azure Quantum Resource

Estimator [24] which is publicly available in their SDK.

Furthermore, a application-speciﬁc resource estimator in the

domain of derivative pricing has been developed [25] and can

be used to estimate the minimal quantum computing resources

needed to achieve a real-world quantum advantage in this do-

main. However, resource estimation often requires end-users to

manually provide a lot of information on particular hardware

aspects such as gate times and ﬁdelities.

A different, but related, approach is to evaluate whether

existing architectures and compilers are capable of executing

a given quantum circuit. One example is the NISQ Analyzer

proposed in [26] which allows one to determine architectures

that are expected to be capable of reliably executing a given

circuit based on their number of qubits and a measure of

their maximum supported circuit depth. Although this solution

requires less manual input, it still provides no advice on which

compiler (settings) to use and also on which of the determined

architectures to pick.

In the recent past, many tools for comparing the

performance of different quantum circuit compilers for

different devices and/or compilation options have been

proposed [27]–[30]. However, in all these approaches, each

input circuit is simply compiled for every possible combination

of compilation options and the best circuit according to

some metric is reported, i.e., the best option is determined

in a brute-force fashion. While this provides the basis for

interesting case studies, such an approach cannot be feasibly

employed in practical situations due to the sheer amount of

time it takes to try out all options on every invocation with a

particular circuit—a situation which is only going to get worse

with the ongoing increase in options.

In addition to the above approaches, machine learning meth-

ods have been proposed to tackle certain quantum compilation

challenges by learning from data. In [31], the inﬂuence of

several circuit characteristics on the quality of the circuit

execution results is studied using Multi-Criteria Decision

Analysis methods and machine learning approaches to opti-

mize such. Similarly, the approach proposed in [32] tries to

learn an estimate of circuit ﬁdelity for speciﬁc devices using

the graph structure of quantum circuits. Complementarily, a

reinforcement learning-based approach that models quantum

compilation as a Markov Decision Process with the goal

of learning optimal compilation sequences has recently been

proposed in [33].

Overall, there are many interesting activities happening in

this area. Nevertheless, to the best of the authors’ knowledge,

there is no automatic solution to determine the best com-

bination of quantum compilation options without explicitly

executing and examining all of them—which might be feasible

for conducting a case study on a handful of devices and

compilers but is certainly not scalable enough to support

end-users in realizing their real-world applications. In this

work, we apply similar techniques as in classical compiler

optimization targeting this problem.

III. PROPOSED SOLUTION:

PREDICTING GOOD COMPILATION OPTIONS

As discussed in the previous section, naively executing and

evaluating all possible combinations of compilation options on

demand quickly becomes infeasible due to the large number

of possible options. Even if an end-user was able to utilize all

those different SDKs to compile the speciﬁc quantum circuit

for all computers, it would have been a very time-consuming

and costly endeavor. Thus, in this work, we propose a method-

ology that allows one to predict good combinations of options

without the need for explicit compilation. To this end, the

problem is interpreted as a statistical classiﬁcation task which

constitutes a prime task for supervised machine learning algo-

rithms. In the following, each individual aspect of the proposed

methodology is described and illustrated exemplary. Based on

that, Section IV then covers how this results in a corresponding

framework for the prediction of good combinations of options

and evaluates the beneﬁts for end-users.

A. Compilation Options and Compilation Pipeline

Given certain qubit technologies with a set of respective

devices and certain compilers with various settings, the search

space of all compilation options is spanned by all the possible

combinations of technologies, devices, compilers, and settings.

Therefore, a compilation pipeline needs to be set up to realize

each combination of compilation options as a basis for the

proposed methodology. This poses a signiﬁcant challenge as a

result of the vastly different interfaces and usability levels of

existing SDKs. Overall, this results in a decision tree structure,

where each path from the root node to a leaf node represents

one possible combination of compilation options.

Example 1. For illustration purposes assume that in the

following, the end-user has to decide between four devices

based on superconducting qubits (with 8,27,80, and 127

qubits, respectively) and a single ion trap-based one (with

11 qubits). Additionally, assume that IBM’s Qiskit [1] and

Quantinuum’s TKET [2] are available as state-of-the-art rep-

resentatives for compilers. Last but not least, assume that in

the case of Qiskit four different optimization levels (called

O0to O3) are considered, while in the case of TKET two

different qubit placement algorithms (called Line Placement

and Graph Placement) can be used for the compilation.

Both considered compilers are capable of compiling a

quantum circuit for all the considered devices. Therefore,

the corresponding search space for compilation options is

structured as illustrated in Fig. 1—comprising a total of 30

different combinations of compilation options.

B. Evaluation Metric

Based on the constructed search space, the deﬁnition of

an evaluation metric—determining whether a combination of

compilation options is good for a certain quantum circuit—is

an essential part of the proposed framework. All further steps

aim to optimize the prediction quality of the resulting model

according to this evaluation metric.

In principle, this evaluation metric can be designed to be

arbitrarily complex, e.g., factoring in actual costs of executing

quantum circuits on the respective platform or availability

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PredictingGoodQuantumCircuitCompilationOptionsNilsQuetschlichLukasBurgholzeryRobertWillezChairforDesignAutomation,TechnicalUniversityofMunich,GermanyyInstituteforIntegratedCircuits,JohannesKeplerUniversityLinz,AustriazSoftwareCompetenceCenterHagenbergGmbH(SCCH),Austrianils.quetschlich@tum.delukas...

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