Hello Quantum World A rigorous but accessible rst-year university course in quantum information science Sophia E. Economouand Edwin Barnes

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Hello Quantum World!

A rigorous but accessible ﬁrst-year university course in quantum information science

Sophia E. Economou∗and Edwin Barnes

Department of Physics, Virginia Tech, Blacksburg, Virginia 24061, USA

Addressing workforce shortages within the Quantum Information Science and Engineering (QISE)

community requires attracting and retaining students from diverse backgrounds early on in their

undergraduate education. Here, we describe a course we developed called Hello Quantum World!

that introduces a broad range of fundamental quantum information and computation concepts in

a rigorous way but without requiring any knowledge of mathematics beyond high-school algebra

nor any prior knowledge of quantum mechanics. Some of the topics covered include superposition,

entanglement, quantum gates, teleportation, quantum algorithms, and quantum error correction.

The course is designed for ﬁrst-year undergraduate students, both those pursuing a degree in QISE

and those who are seeking to be ‘quantum-aware’.

I. INTRODUCTION

The enormous interest in quantum information science

and engineering (QISE) from academia, industry, and

governments worldwide has led to new K-12 initiatives

such as the National Q-12 Education Partnership and

Q2Work [1] and has prompted many universities to start

degree programs, including minors, masters, and even

majors in QISE. An associated challenge is structuring

these degrees and selecting the courses to provide a solid

training in QISE. Considering the diverse nature of the

ﬁeld, these degrees can come in many diﬀerent ﬂavors

and place emphasis on diﬀerent aspects of QISE [2].

Regardless of the speciﬁc direction they follow, the stu-

dents need to learn the key concepts on which they can

build. These include the idea of a qubit, of superposition,

of a quantum circuit, and of entanglement. Addition-

ally, ideally students should also learn some basics about

quantum algorithms, quantum cryptography, and quan-

tum error correction. Exposure and familiarity with this

material should occur early on, both to build the founda-

tions for the more advanced material, and also to convey

to the students why this ﬁeld is exciting and diﬀerent

from what they have seen before in their STEM classes.

At ﬁrst glance, early exposure in a substantive fash-

ion may appear as a very challenging task, considering

that this material traditionally follows semesters of ad-

vanced math and quantum mechanics courses. We have

found, however, that with only high-school level math,

mostly addition, multiplication, a very small amount of

algebra, and a basic understanding of probability, stu-

dents can learn in a rigorous and, we would argue, much

more intuitive way the fundamentals of quantum infor-

mation and computation. This is done through the use of

a pictorial representation of qubits, gates, and quantum

circuits, combined with access to IBM’s Quantum Com-

poser [3]. After years of creating and reﬁning such an ap-

proach for outreach, we designed and taught a semester-

long freshman course along the same lines called Hello

∗economou@vt.edu

Quantum World! (HQW!). We received very positive

feedback from the students, and we found it to be a fun

course to teach. We have since been contacted by nu-

merous colleagues from universities around the US and

abroad asking for advice and help in setting up a similar

course. This short paper is aimed at such colleagues and

other instructors who are interested in starting a similar

course at their institutions, be it at the college freshman

or even high-school level.

In addition to its crucial role for building the required

foundations, early exposure through an accessible for-

malism enables equal opportunity, piques interest, allows

the students a conceptual grasp of quantum informa-

tion/computation and even of the underlying linear al-

gebra structure (without explicit teaching of linear alge-

bra). Hopefully, such an approach also helps to increase

diversity: without the need for advanced math and pre-

requisite courses, the diﬀerence between more and less

prepared students is practically diminished. Indeed, from

our experience we found that the students who had come

from prestigious high schools performed on average sim-

ilarly to those coming from less privileged backgrounds.

We hope that in the future, a careful evaluation of our

course by professionals can assess the validity of this em-

pirical ﬁnding and identify ways to further improve on

this aspect.

HQW! is the centerpiece of a multidisciplinary QISE

minor degree that was recently established at Vir-

ginia Tech. The minor is available to students from

7 diﬀerent departments and undergraduate degree pro-

grams, including Chemistry, Computational Modeling

and Data Analytics, Computer Science, Electrical and

Computer Engineering, Materials Science, Mathematics,

and Physics. The minor includes four mandatory courses,

of which HQW! is one, while the other three are linear

algebra, quantum software/programming, and an upper-

level introductory course on quantum information theory.

In addition, students in their ﬁnal year must take either

an advanced course on quantum information from the

CS department or a Physics course called Quantum Op-

tics and Qubit Processors, which introduces the central

concepts and leading qubit platforms on which existing

arXiv:2210.02868v2 [physics.ed-ph] 6 Nov 2022

+ +

(a)

(b)

(c)

FIG. 1. (a) The single-qubit state |+iand (b) the two-qubit Bell state (|00i+|11i)/√2 represented as mists. (c) The single-qubit

NOT gate represented as a box that ﬂips the value of the (qu)bit input at the top.

and future quantum processors are based. Beyond these

ﬁve courses, students are required to take another two

QISE-related courses chosen from a long list of options;

students can typically satisfy this requirement by select-

ing courses from their home department that also count

toward their major. A more detailed description of the

minor, along with descriptions of other QISE degree pro-

grams, can be found in Ref. [2]. Because HQW! is a

mandatory course for the minor, we have purposely de-

signed it to be both broadly accessible and rigorous so

that it provides a ﬁrm foundation in QISE concepts in

preparation for more advanced courses to come.

II. SHORT DESCRIPTION OF THE COURSE

The HQW! course is based on a pictorial approach, in

which qubits are represented by shapes and logic gates

by boxes. The basis states |0iand |1iare represented by

colors, white and black respectively. Superpositions are

denoted by clouds (or ‘mists’), with diﬀerent conﬁgura-

tions are separated by bars. In the ﬁrst part of the course,

we limit ourselves to states with real, integer coeﬃcients

(positive or negative). Diﬀerent qubits are represented by

diﬀerent shapes. For concrete examples, see Fig. 1, which

shows the single-qubit state |+i=|0i+|1i

√2, the two-qubit

Bell state |00i+|11i

√2, and a single-qubit NOT (i.e., Pauli

X) gate, with state |0ibeing transformed to |1iand vice

versa.

We note here some diﬀerences compared to an earlier

paper, where we had described our outreach program [5].

While the basic features are the same (pictorial repre-

sentation combined with use of the IBM Quantum Com-

poser), we have made key updates. The main change

from our earlier approach, which was following the for-

malism introduced in Terry Rudolph’s popular science

book Q is for Quantum [4], is that diﬀerent shapes are

used to represent diﬀerent qubits. This makes a huge

diﬀerence in students’ understanding and avoids a com-

mon source of confusion: by using the same shape for

all qubits, it may be diﬃcult for students to distinguish

between, e.g., a superposition state of one qubit and a

two-qubit state. The use of distinct shapes makes it easy

to immediately see how many qubits are involved in a

given state, as it coincides with the number of distinct

shapes. Moreover, the use of diﬀerent shapes enforces the

idea of a physical system versus its state. For example,

consider the SWAP gate. When a single shape is used,

it is not transparent that the qubits are not swapped

but their state is instead. By using distinct shapes, this

becomes clear, as shown in Fig. 2. The ﬁgure also illus-

trates how the W state looks in the two notations. In

addition to using diﬀerent shapes for diﬀerent qubits, in

the new notation, we also separate terms in a mist us-

ing bars rather than commas. This makes the notation a

little more natural when we rotate mists to orient them

vertically in order to facilitate the mapping to standard

circuit notation, which the students do when they work

with the IBM Quantum Composer (see below).

The course begins with the introduction of the shapes

as (classical) bits along with boxes representing classi-

cal gates (i.e, gates that take computational basis states

to computational basis states), including NOT, CNOT,

and SWAP. Quantum circuits are constructed using these

gates, and students practice with classical logic. Next,

quantum superpositions are introduced through the use

of the cloud (or mist) representation, and the Hadamard

gate is introduced as the only intrinsically quantum gate

used throughout the course. Students are taught how su-

perpositions are passed through gates, and they practice

with quantum circuits. Measurement is discussed (prob-

abilistic nature and how to calculate probabilities). The

correspondence between the pictorial approach and the

circuit representation used in the IBM Quantum Com-

poser [3] is shown, and students start practicing with

the drag-and-drop interface, creating their own quantum

circuits and checking against their pen-and-paper calcu-

lations with the pictorial approach. With these tools

at hand, the following concepts are taught: quantum

key distribution, quantum algorithms (Deutsch, Grover),

entanglement (entangled vs separable states), quantum

teleportation, and quantum error correction. Finally, af-

ter the students spend most of the semester practicing

these concepts, the transition to linear algebra is pre-

sented by showing how omitting the shapes and keeping

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HelloQuantumWorld!Arigorousbutaccessiblerst-yearuniversitycourseinquantuminformationscienceSophiaE.EconomouandEdwinBarnesDepartmentofPhysics,VirginiaTech,Blacksburg,Virginia24061,USAAddressingworkforceshortageswithintheQuantumInformationScienceandEngineering(QISE)communityrequiresattractingandreta...

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Hello Quantum World A rigorous but accessible rst-year university course in quantum information science Sophia E. Economouand Edwin Barnes

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