Introductory Course on Quantum Computing

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Enrollment in this course is by invitation only

Section 1.1: Quantum computers are expected to harness the exotic properties of quantum mechanics to perform calculations that are beyond the reach of present day classical computers. From drug discovery to optimizing supply chains to cryptography, quantum computing is likely to be the key disruptive technology of our generation, and would fundamentally alter the way we process data. This online certification course, delivered by frontline researchers in the field, offers a broad introduction to this rapidly evolving area. Irrespective of whether you are a curious beginner or a seasoned technology enthusiast, this course is designed to ignite your passion and expand your horizons.

Section 1.2: Why quantum computing?

This lecture introduces quantum computing as a combination of quantum physics and information processing, explaining how phenomena like superposition and entanglement can be used for computation. It emphasizes that the course will focus on conceptual understanding and practical algorithms rather than heavy mathematical proofs. The need for quantum computing is motivated by the physical limits of classical computing (like transistor scaling) and the energy costs of irreversible computations. It also highlights how quantum computing may help solve certain “hard” problems more efficiently than classical methods. Overall, the lecture sets the foundation and motivation for exploring quantum computing in the course.

Section 1.3: Introduction to Quantum Physics via two-level system

This lecture introduces the fundamental postulates of quantum mechanics using a two-level system (qubit) as an example. It explains how quantum states are represented as vectors and can exist in superposition, unlike classical bits. The lecture also covers operators as representations of observables, measurement outcomes with associated probabilities, and the concept of wavefunction collapse. Finally, it discusses how quantum states evolve over time using unitary operators and the Schrödinger equation. Overall, it builds the foundational rules needed to understand and manipulate quantum systems for computation.

Section 2.1: Rules of Quantum World in Practice

This lecture makes the abstract postulates of quantum mechanics more concrete by applying them to a simple system—a particle in an infinite potential well. It introduces the Schrödinger equation (time-dependent and time-independent) as the quantum equivalent of classical equations of motion. The session explains how quantum systems have discrete energy states and how particles can exist in superpositions of these states. It also shows how wavefunctions describe probabilities and how energy levels can be derived. Finally, the uncertainty principle is highlighted as a fundamental concept that explains key quantum behaviors.

Section 2.2: What it takes to make a Quantum Computer

This lecture introduces the DiVincenzo criteria, proposed by David DiVincenzo, which outline the essential requirements for building a quantum computer. It explains the need for scalable qubit systems, proper initialization into well-defined states, and long coherence times to avoid decoherence. The session also highlights the importance of precise control using high-fidelity quantum gates and accurate qubit-specific measurement (readout). Additionally, it briefly covers extra requirements for quantum communication, including reliable transmission of qubits and conversion between flying and stationary qubits.

Section 2.3: NMR and Nuclear Qubits
This lecture introduces nuclear magnetic resonance (NMR) and explains how nuclear spins can be used as qubits for quantum computing. It describes how spin-½ nuclei in a strong magnetic field form two-level systems (|0⟩ and |1⟩) and how resonance with radio-frequency waves enables precise control, including superposition and spin flips. The session also covers implementation of DiVincenzo criteria—initialization (via pseudo-pure states), control (RF pulses and spin–spin interactions), and readout (signal detection and Fourier transform). Finally, it demonstrates how multi-qubit systems and quantum gates can be built using molecules, culminating in an example of factorizing a number using an NMR-based quantum algorithm.

Section 3.1: Qubits out of Nitrogen-vacancy centres in diamonds

This lecture explains how nitrogen-vacancy (NV) centers in diamond can be used to build qubits for quantum computing. It describes the structure of NV centers, their spin-based energy levels, and how microwave and optical techniques enable qubit control, initialization (via optical pumping), and readout (through spin-dependent fluorescence). The session highlights that NV centers satisfy key DiVincenzo criteria, offering room-temperature operation, efficient initialization, and strong measurement capability. It also discusses coherence properties, experimental setups (confocal microscopy + EPR), and scaling approaches using nearby nuclear spins. Finally, applications such as quantum sensing, single-photon sources, and small multi-qubit registers are introduced.

Section 3.2: Superconducting Qubits

This lecture introduces superconducting qubits, starting from the basics of superconductivity where resistance drops to zero below a critical temperature due to the formation of Cooper pairs. It explains how these paired electrons behave as bosons and enable lossless current flow. The lecture then describes how superconducting circuits, especially Josephson junctions and SQUIDs—are used to build nonlinear LC (transmon) qubits with well-defined two energy levels. It also covers qubit control using microwave pulses and readout via resonator frequency shifts. Finally, it highlights initialization through ultra-low temperature cooling and notes their scalability and use in modern quantum computers.

Section 3.3: Photonic Qubits

This lecture introduces photonic qubits, explaining how photons, exhibiting wave-particle duality, can be used for quantum information processing. It describes two main encoding methods: polarization encoding (horizontal/vertical states) and spatial/path encoding using beam splitters and interferometers. The lecture covers implementation of single-qubit gates using optical elements like wave plates, while highlighting the challenge of two-qubit gates due to weak photon interactions. It also discusses measurement using single-photon detectors and the advantages of photonic systems, such as room-temperature operation and suitability for quantum communication.

Section 4.1: Classical Gates vs Quantum Gates

This lecture introduces classical and quantum logic gates, highlighting key differences between them. Classical gates (like OR, AND, NAND, NOR) are irreversible and operate strictly on binary states (0 or 1). In contrast, quantum gates are reversible, represented by unitary operators, and act on qubits that can exist in superposition. The lecture explains fundamental single-qubit gates (NOT, Hadamard, Phase) and two-qubit gates like CNOT, which enable interactions between qubits. It also demonstrates how combining gates (e.g., Hadamard + CNOT) generates entanglement, a crucial resource for quantum computing.

Section 5.1: Quantum Teleportation

This lecture explains the concept of quantum teleportation, where a quantum state is transferred from one location to another without physically moving the particle. It uses entanglement (Bell states) shared between two parties and quantum gates (CNOT and Hadamard) to enable the process. After measurement, classical information is sent, allowing the receiver to reconstruct the original quantum state using simple operations. The original state disappears from the sender and reappears at the receiver, preserving quantum information. This technique is important for quantum communication and information transfer in quantum computing systems.

Section 6.1: Quantum Parallelism

This lecture introduces the basics of quantum algorithms, starting with essential concepts like classical Boolean functions and quantum oracles. It explains how quantum systems use superposition to evaluate multiple inputs simultaneously, leading to the idea of quantum parallelism. The session highlights how a single application of a quantum oracle can compute outputs for multiple inputs at once. However, it also discusses the limitation of measurement, where not all computed results can be directly accessed. Overall, the lecture sets the foundation for understanding algorithms like the Deutsch algorithm.

Section 6.2: Deutsch Algorithm

This lecture introduces the Deutsch algorithm, building on concepts like quantum parallelism and phase kickback. It explains how phase information from a quantum oracle can be encoded into a qubit to extract useful results. The algorithm solves the problem of determining whether a Boolean function is constant or balanced using just one query, unlike classical methods that require two. The lecture walks through the circuit step-by-step, showing how interference and measurement yield the answer. Overall, it demonstrates an early example of quantum computational speedup.

Section 6.3: Deutsch-Josza Algorithm

This lecture introduces the Deutsch–Jozsa algorithm, a generalization of the Deutsch algorithm, to determine whether a Boolean function is constant or balanced. Classically, this requires an exponential number of queries, whereas the quantum approach solves it with just one query to the oracle. The algorithm uses superposition, Hadamard gates, and quantum interference to encode the solution into the measurement outcomes. By measuring the data register, one can definitively identify whether the function is constant or balanced. The key takeaway is how quantum parallelism and interference enable significant computational speedup.

Section 6.4: Phase Estimation Algorithm

This lecture introduces the quantum phase estimation algorithm, which uses the Quantum Fourier Transform and its inverse to extract the phase (eigenvalue) of a unitary operator. It explains how phase information gets encoded into qubits via phase kickback using controlled unitary operations. By preparing superposition states and applying powers of the operator, the phase is accumulated across multiple qubits. Applying the inverse QFT then converts this phase information into a measurable binary output. Finally, measuring the first register yields an estimate of the phase, making this a foundational tool for many quantum algorithms.

Section 6.5: Grover's Algorithm

This lecture introduces Lov Grover’s quantum search algorithm for finding a target item in an unstructured dataset. It explains how an oracle identifies solutions by flipping their phase, without explicitly knowing them. Starting from an equal superposition, the Grover operator (oracle + inversion about the mean) amplifies the probability of the correct solution. Repeated iterations progressively increase the desired state’s amplitude. The algorithm achieves a quadratic speedup, requiring only O(√N) queries compared to the classical O(N).

Section 7.1: Towards Quantum Fourier Transform

This lecture introduces the basics of the Quantum Fourier Transform (QFT) by first revisiting the classical discrete Fourier transform and its role in analyzing frequency components of data. It defines QFT as a linear operator acting on quantum states expressed in an orthonormal basis and extends it to arbitrary superposition states. The lecture also derives the inverse QFT and emphasizes the need to convert the summation form into a product form for circuit implementation. Using binary representation and exponential identities, the QFT expression is transformed into a product of single-qubit states. This final form sets the foundation for constructing efficient quantum circuits in the next session.

Section 7.2: Circuit For Quantum Fourier TransformThis lecture derives the quantum circuit implementation of the Quantum Fourier Transform (QFT) using a two-qubit example and generalizes it to multiple qubits. It shows how Hadamard and controlled phase rotation gates (Rₙ) together produce the desired product-state form of the QFT. The circuit is efficient but outputs qubits in reversed order, requiring additional swap gates. The total gate complexity scales as O(n2)O(n^2)O(n2), which is exponentially faster than the classical Fast Fourier Transform’s O(n2n)O(n2^n)O(n2n). The lecture highlights QFT as a key building block for advanced quantum algorithms like phase estimation.

Section 8.1: Shor's Prime Factorisation Problem

This lecture introduces the integer factoring problem- finding factors p and q such that n=pq and explains why it is computationally hard classically but easy to verify, forming the basis of cryptographic systems like RSA. It shows how factoring can be reduced to finding the period (order) of a function in modular arithmetic. The lecture then explains how Peter Shor’s quantum algorithm uses quantum phase estimation and the Quantum Fourier Transform to efficiently find this period. Once the order is known, factors can be obtained using GCD computations. Overall, the algorithm provides a polynomial-time (probabilistic) quantum solution, offering a significant speedup over classical methods and reshaping complexity class boundaries.

Section 9.1 and 9.2: Programming with Quantum Simulator

This lecture focuses on the practical implementation of quantum computing concepts using Qiskit. It demonstrates how to create, manipulate, and visualize single- and multi-qubit systems using quantum gates like Hadamard, Pauli, and CNOT. The session also covers measurement techniques and the use of simulators to observe quantum behavior. Advanced topics include multi-qubit operations, entangled states like GHZ states, and implementing simple algorithms such as the Deutsch Algorithm. Overall, it bridges theory with hands-on coding to run quantum circuits on simulators and real quantum hardware.

Course Summary