A Conversation with Dr. Peter Lee on Teaching Quantum Information Science

Photo: Professor Peter Shor (left) and Dr. Peter Lee (right) at Quantum.Tech World 2026.

Dr. Peter Lee is a co-author of The Scaffolding Series and was shortlisted for the 2026 Quantum.Tech Power 10 in the Enterprise, Government & Academia category. We are excited to share more details about his approach to QIS education.

1. Pedagogical Philosophy & Scaffolding

Q: What is scaffolding?

The “second quantum revolution” requires more than an expansion of technical knowledge. It requires a thoughtful transition from classical intuition to quantum logic. Navigating this landscape demands a strategic methodology that prevents the conceptual fragmentation that often affects emerging interdisciplinary fields.

Our series employs the Scaffolding Approach, a pedagogical framework rooted in the theories of Lev Vygotsky and Jerome Bruner. By operating within the learner’s Zone of Proximal Development and using Bruner’s concept of spiral reinforcement, we provide the incremental support needed to transform fragmented exposure into disciplined mastery. This methodology helps ensure that the student’s progress—from foundational mathematical rungs to advanced algorithmic architectures—is cumulative, rigorous, and conceptually durable.

Q: Why does the series prioritize a rigorous path through linear algebra and probability before addressing quantum mechanics directly?

In quantum information science (QIS), mathematics is not a supplementary tool; it is the primary language of the paradigm shift. We intentionally avoid the common pitfall of starting with differential equations. Instead, we establish a clear path through complex linear algebra and probability because these are the foundational rungs required for a smooth transition.

In Mathematical Foundations of Quantum Computing, we introduce Dirac notation and Hermitian and unitary operators early. By establishing the complex vector space as the native environment for quantum states, learners can treat these concepts as active working tools. This mathematical grounding is essential for understanding how quantum transformations drive algorithms and how noise manifests in physical systems.

Q: How does the series manage the prerequisite problem for physicists, computer scientists, and engineers?

The prerequisite problem is one of the most significant barriers to scaling QIS education. The three titles in the series, together with the sequence of chapters within each volume, are carefully designed to build the necessary prerequisites in a coherent order. In addition, we use a system of level indicators to modulate the technical intensity of the material:

• Unmarked content: Foundational “Core Pathway” content appropriate for all readers.
• ✸: Conceptual overviews followed by more math-intensive segments for senior undergraduates or early graduate students.
• ✹: Advanced exploration, deep-dive case studies, and specialized research topics.

We address gaps between disciplines by providing targeted foundational reviews in trigonometry, complex numbers, and summation rules, tailored for quantum applications. This allows a computer scientist without a wave-mechanics background, or an engineer new to algorithmic complexity, to find a viable entry point without being sidelined by nonessential classical prerequisites.

Q: Why are exercises interspersed throughout the text rather than confined to the end of chapters?

Managing cognitive load is essential when teaching high-level abstractions. We use interspersed exercises as immediate conceptual checkpoints. This contrasts with the comprehensive end-of-chapter problem sets, which are designed for deeper, multi-concept integration. By asking learners to reinforce specific skills immediately—a process known as representational transfer—we help ensure that each layer of the scaffold is secure before the next is added. This fosters stronger analytical skills and helps prevent the illusion of competence that can arise from passive reading.

2. Curriculum Design, Adoptions, & Instruction

Q: Are these textbooks part of a curriculum framework?

Yes. The textbooks are designed as part of an outcomes-based curriculum framework rather than as standalone texts. The framework follows a backward-design approach: it begins by identifying the competencies required by the global quantum workforce and then works backward to develop learning outcomes, instructional materials, and assessments.

This approach supports fidelity of implementation, with every learning activity explicitly aligned with program-level goals. As a result, the curriculum remains coherent, transferable, and relevant across different institutional settings. The Scaffolding Series textbooks embody these curriculum-design principles.

Q: How does the series transition from core primitives to advanced frameworks such as QSVT?

The series builds toward quantum singular value transformation (QSVT) through a staged progression. Mathematical Foundations of Quantum Computing establishes the necessary mathematical tools. Quantum Computing and Information applies them to qubits, circuits, measurement, entanglement, noise, and error correction. Quantum Algorithms and Applications then develops algorithmic models and core primitives such as the quantum Fourier transform, quantum phase estimation, Shor’s algorithm, amplitude amplification, and amplitude estimation.

The progression then moves to block encodings, linear combinations of unitaries, quantum signal processing, and QSVT, followed by applications in simulation, optimization, quantum machine learning, and linear systems.

Q: How do institutions adopt these textbooks in their curricula?

The following table summarizes recommended adoption models, incorporating feedback from pilot programs and reviewers at leading institutions.

Q: How do you balance analytical mathematics with hands-on coding?

We integrate mathematical formalism with computational practice by incorporating Qiskit simulation code, with contributions by John Hurst and others. This component remains in progress. It allows students to move fluidly from “paper math”—deriving operators and state vectors—to practical programming on cloud-based quantum hardware.

Q: What are the most critical mistakes in building QIS programs, and how does your framework mitigate them?

Our research and pilot data identify three primary challenges:

1. Institutional fragmentation: Courses are often scattered across departments. Our vertically integrated pathway provides a unified disciplinary home.
2. Interdisciplinary barriers and prerequisite gaps: As Michael George of San Diego City College has noted, many students encounter difficulty because high schools no longer emphasize linear algebra. We address this by providing a math-first volume that replaces general-purpose preparation with QIS-specific foundations.
3. Cognitive and pedagogical challenges: Misconceptions about superposition and measurement are pervasive. Our scaffolding approach and active-learning exercises address these through continual spiral revisiting of the core postulates.

Q: Why prioritize principles over ephemeral software platforms?

Software tools such as Qiskit and Cirq are essential, but they evolve rapidly. We categorize the field’s trajectory into four broad phases:

1. Early noisy intermediate-scale quantum (NISQ) hardware demonstrations;
2. practical utility;
3. the MegaQuOp and GigaQuOp regimes; and
4. large-scale fault-tolerant quantum computing (FTQC).

By focusing on the durable principles required for these regimes, we help ensure that a student’s education remains valuable as the industry moves toward large-scale quantum systems.

Q: How do you see the intersection of quantum computing, AI, and HPC?

We see these fields converging through hybrid computational workflows rather than as separate technologies. High-performance computing provides the classical simulation, optimization, data processing, and workflow orchestration needed to develop and use quantum systems. AI can assist with tasks such as device calibration, error mitigation, circuit compilation, materials discovery, and the analysis of experimental data.

Quantum processors may eventually contribute specialized capabilities for selected problems in simulation, optimization, and scientific computing, but they will operate alongside CPUs, GPUs, and AI systems rather than replace them. The educational goal is therefore to prepare students to work across this larger classical–quantum ecosystem while distinguishing promising research directions from capabilities that are already practical.

Q: Are QML and quantum linear solvers ready for the classroom?

They are ready for the classroom as important topics for critical study, but not as established general-purpose solutions. Quantum machine learning and quantum linear solvers introduce useful ideas about data encoding, state preparation, condition numbers, readout costs, and the assumptions behind claimed speedups.

Students should learn both their conceptual promise and their practical limitations, including data-loading overhead, noise, and the need to compare carefully with strong classical methods. In this way, these topics help students develop sound judgment about where quantum methods may eventually be useful.

3. Author Perspectives & Personal Narratives

Q: Who are your collaborators?

The Polaris QCI Series is the product of interdisciplinary collaboration. Dr. Peter Y. Lee brings expertise from electrical engineering at Princeton and Bell Labs. Dr. James Yu of Fei Tian College specializes in mathematical modeling and biophysical simulation. Dr. Ran Cheng of the University of California, Riverside, is an expert in spintronics and magnetism and a National Science Foundation CAREER award recipient. Dr. Huiwen Ji of the University of Utah brings a background in solid-state chemistry and quantum materials and is also a National Science Foundation CAREER award recipient.

This diversity helps the series bridge physics, chemistry, mathematics, and computation.

Q: How did your background in patents influence your textbook writing?

During my earlier career, I wrote research papers, where there can sometimes be a tendency to make relatively simple ideas appear more complicated than they are. At Bell Labs, I wrote many patents, where the goal was often to disclose only what was necessary to protect an invention.

Later, in higher education administration and formal instructor training, I came to understand that teaching—and textbook writing—is an art in its own right. Its purpose is to make complicated ideas clear, give students both the big picture and the full picture, and provide a practical path toward mastery. My motivation for authoring the Scaffolding Series has been deeply shaped by that experience.

Q: How did your role as an educational administrator influence the series’ design?

Being an administrator requires one to think about the educational ecosystem. This perspective drove our backward-design approach, ensuring that the series functions as a framework for an entire academic program rather than simply as a collection of books.

Balancing administrative responsibilities with textbook rigor requires disciplined engineering thinking about time. I approached the books much as I approach an engineering problem: everything must be accounted for, every section must serve a specific objective, and there is no room for filler. Clarity and efficiency were my guiding principles.