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The paradigm of Quantum Information Science (QIS) is that quantum devices made of systems such as atoms and photons, can outperform the present-day technology in key applications ranging from computing power and communication security to precision measurements. Quantum information processing and the measurement and control of individual quantum systems are central topics in QIS, lying at the intersection of quantum mechanics with ‘classical’ disciplines such as information theory, probability and statistics, computer science and control engineering.

This course gives an introduction to QIS, emphasising the differences and similarities between the classical and the quantum theories. After a short review of the necessary probabilistic notions, the first part introduces the operational framework of quantum theory involving the fundamental concepts of states, measurements, quantum channels, instruments. This includes some of the influential results in the field such as entanglement and quantum teleportation, Bell's theorem and the quantum no-cloning theorem. The second part covers at least two topics from: quantum Markovian evolutions, quantum statistics, continuous variable systems.

Beginning with a careful review of core theoretical ideas and techniques in quantum theory designed to consolidate your knowledge, this engaging module will then introduce you to key advanced methods used to describe the quantum coherent devices that underpin emerging technologies such as the quantum computer.

Starting from the essential model systems of the quantum oscillator and two-level system, you will go on to discover how they are combined to form the famous Jaynes-Cummings model describing coherent light-matter interactions. By the end of the module you will also have learnt about quantum superconducting circuits, which form the basis of some of the most powerful quantum computers currently available. You will be introduced to the concept of quantum decoherence that describes the essential role that a system’s surroundings can play in destroying signatures of its quantum behaviour.

The ideas and methods covered in this module are widely used elsewhere on the course and it will equip you to begin exploring the fast-growing research literature on quantum devices. The module will be taught in a flexible way, with weekly in-person workshop sessions combined with a range of bespoke online resources so that you can focus on mastering the core topics which are less familiar to you before going on to more advanced ones.

Quantum metrology seeks to uncover the ultimate precision bounds for measuring physical parameters such as gravity, acceleration and magnetic fields. It aims to devise protocols and statistical methodology for achieving these bounds by exploiting intrinsic properties of quantum systems and dynamics.

The module will provide you with an introduction to quantum metrology with an emphasis on the conceptual issues and theoretical methodology. We will start by introducing fundamental concepts of statistical inference, which will then be extended to the quantum domain, to equip you with key mathematical tools and techniques in quantum estimation and metrology. Building on this foundation we will explore applications of current relevance to quantum technology such as quantum tomography, quantum phase estimation, and the Heisenberg limit. This will provide you with a solid background in statistical aspects of quantum metrology.

As quantum systems are sensitive to noise and perturbations, it is important to understand and counteract the effects of quantum errors in quantum technology applications. The final part of the module will investigate the theory of quantum noisy channels and apply it to the study of realistic metrology models. This will bring you close to current research topics at the intersection of quantum statistics, error correction and machine learning.

As the title of this block course might suggest, we will look in some detail at the interaction between light and matter. The module will have some focus on atomic physics, because atoms are the simplest form of matter that interacts with visible light. Our aim is to go beyond the simplistic model of photon absorption and emission. We will revise classical electromagnetic waves, move on to a quantum treatment and discuss some interesting effects and applications ranging from photon anti-bunching to laser cooling.    

The material will cover: 

1. revision of electromagnetic waves, classical atom models, heuristic quantum mechanics and Einstein coefficients
2. atomic spectra, Stark and Zeeman effects, polarization of fields, static vs. time varying fields
3. coherent light-atom interaction with quantised atoms, two-level atoms, Rabi oscillations
4. decoherence, optical Bloch equations, Bloch sphere and density matrix formalism
5. atomic line shapes, forces exerted by light on atoms
6. light propagation in atomic media, absorption and refractive index. 

The dissertation is an extended piece of research, in an area covered by the taught modules. It typically features a topic at the forefront of contemporary quantum research. The project will be largely self-directed, with oversight and support provided by a supervisor from the School of Mathematical Sciences, Physics and Astronomy or the Faculty of Engineering.

The topic could be based on a research investigation, a review of research literature, or a combination of these. You can choose among a range of topics proposed by supervisors or suggest an original topic yourself.

The project options cover the current research directions ranging from:

• quantum computing and error correction
• foundations of quantum information and quantum resource theory
• quantum sensing and metrology
• ultracold atom systems
• optomechanical devices
• open systems and measurements
• brain imaging with MEG
• diamond sensing and more

The dissertation offers an excellent introduction to exciting research, scientific writing and insights into how research is conducted. This makes it a solid basis for pursuing a PhD.

Quantum technologies feature a wide range of exciting applications from precision sensors to quantum computing and quantum simulators. These developments will shape our future and enable research and industry to go beyond what is possible today. This module will introduce you to contemporary research topics including quantum sensing, quantum simulators, quantum computing hardware (i.e. neutral atoms, photonics and Rydberg atoms) and quantum engineering. The module discusses real-life examples and topical areas of current interest. Many of these are close to the research topics of the module convenors and our industry partners.

We focus on experimental aspects and realisations of quantum technology in the lab. You will learn techniques that are applied in current quantum technologies and the module is an ideal preparation for a dissertation in this area. You will learn fundamental techniques such as:

• atomic physics
• measurement techniques
• phase estimation
• squeezing

You will also hear about precision sensing, interferometry, magnetometry, atomic clocks and experimental quantum information based on cold atoms. Other topics include photon storage and atom-photon interfaces and atoms in optical lattices.

Understanding different types of quantum technologies and how they interact with each other will be an excellent basis for a job in the quantum technology industry or further postgraduate research. Presentations by industrial partners and attending our careers fairs will complement your learning within this module.

This module will introduce the Python programming language and its associated ecosystem*. We focus on the elements most applicable to scientific computing.

You will begin by covering the essentials of pure Python, as well as installation, environment maintenance and version control issues. You will then be introduced to the 'numpy' module for efficiently dealing with array data, followed by plotting with 'matplotlib', and the various scientific tools in 'scipy7'.

We will consider various modules useful for different aspects of scientific programming including:

• data handling and analysis
• symbolic mathematics
• Monte Carlo sampling
• tools for Machine Learning
• producing graphical and online interfaces

Finally, you will cover areas of good software development, such as testing and profiling. We will also discuss approaches for dealing with very large amounts of data or speed critical applications.

Teaching will be workshop style, with lecture slides, examples, and exercises provided. We will use Jupyter notebooks for interactive learning during the teaching sessions.

 * Qualification criteria applies with a test of prior experience at the beginning of the course.

This module encompasses the two main topics of error-correcting codes and cryptography.

In digital transmission (as for mobile phones), noise/errors that corrupt a message can be very harmful. The idea of error-correcting codes is to add redundancy to the message so that the receiver can recover the correct message even from a corrupted transmission. As a simple but inefficient example, you could imagine sending the same message three times to mitigate errors. We will concentrate on linear error-correcting codes (such as Hamming codes), where encoding, decoding and error correction can be done efficiently. This leads to time and cost savings in real-world applications.

In cryptography, the aim is to transmit a message such that an unauthorised person cannot read. The message is encrypted and decrypted using a cipher system. There are two main types of ciphers: private (symmetric) and public key ciphers. We will discuss basic classical mono- and poly-alphabetic ciphers, and more modern public key ciphers arising from number theory, for example RSA. Key exchange protocols and digital signatures (DSA) are covered too.

Your study will be based on projects and presentations, guided by tutorial sessions. We will cover three general and interrelated sets of ideas and methods:

• Essential Elementary Quantum Mechanics: Qubits: quantum states and superpositions. Entanglement: exponential Hilbert space means exponential computing power. Other topics include projective measurements, bases, and tomography and unitary operators

• Quantum Circuits and Algorithms: From classical gates to quantum gates: Universal quantum gates. Graphical quantum circuit notation. Important one- two- and multi-qubit gates. Quantum algorithms and quantum parallelism

• Programming near-term Quantum Computers: Basics of qiskit python api for programming IBM quantum computers. Running quantum circuits on a simulated quantum computer. Running quantum circuits on a real quantum computer. Test basic quantum mechanics

This module provides an introduction to the theoretical and conceptual foundations of quantum field theory, which is a highly versatile and important subject in modern theoretical and mathematical physics. After a short review of some elementary aspects of classical field theory, the first part of this module introduces the crucial concept of relativistic field quantisation and develops perturbative methods leading to the famous Feynman diagrams. The more advanced component includes the study of renormalisation techniques for quantum field theories and a discussion of physical applications to quantum electrodynamics and the standard model of particle physics. 

This module (which is part of the “Quantum Information, Computation and  Metrology” pathway) provides an overview of relativistic quantum theory that is required for research in high energy physics, quantum gravity or relativistic quantum information. You will be supported to work independently as the assessment is designed to test your learning outcomes and encourage you to do independent reading and understanding key milestones. The project and final coursework test the study of topics studied independently and in greater depth.

This module gives you an introduction to how computers can learn from data. You’ll explore a variety of problems of linear and non-linear regression, classification, density estimation and data generation. It will be a combination of fundamental concepts and hands on application to a selection of example problems.

Deep learning has recently revolutionised fields such as computer vision, speech recognition, natural language processing, and many more. It is a class of machine learning which aims to ‘teach’ a computer an abstract representation of data. This representation is encoded by the weights of a neural network, which consists of many layers of non-linear processing.

This module will introduce the concepts and methods of modern deep learning, following on from (Machine Learning in Science Part I). Topics to be covered will include deep neural networks and supervised/supervised learning:

• convolutional NNs
• RNNs
• transformers
• large language models
• autoencoders
• GANs
• transfer learning
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• Markov decision processes
• cleaning data
• handling large data sets

Concepts will be applied to a group project (working in pairs) on autonomous driving.

It will be taught via two classes per week. These include topical discussions, concrete examples of M in science and lectures on the statistical foundations of ML.

This module gives and Introduction to fundamentals of robotics, and introduces students to: Direct Kinematics, Inverse Kinematics, Workspace analysis and specifying appropriate robotic manipulators for industrial processes.

This module aims to provide students with the essential knowledge and skills that will enable them to understand the current and next generation of characterisation methods and metrology techniques used to analyse additively manufactured structures. The level of understanding will permit the fundamental analysis, development and optimisation of the programme of study and data analysis, and evaluation of their potential application. 

The module will be mainly delivered in an intensive one week of lectures and laboratory classes.

This module is an extended version of Quantum Technology with the first part being identical. In addition, you will apply your knowledge to experimental settings and learn the skills necessary to work successfully in a Quantum Technology laboratory.

This includes:

• operating QT systems
• taking precision data
• reliable note taking
• advanced data analysis
• working with experimental setups
• working in a team

The module will prepare you for writing a dissertation in experimental quantum technologies.

Quantum metrology seeks to uncover the ultimate precision bounds for measuring physical parameters such as gravity, acceleration and magnetic fields. It aims to devise protocols and statistical methodology for achieving these bounds by exploiting intrinsic properties of quantum systems and dynamics.

The module will provide you with an introduction to quantum metrology with an emphasis on the conceptual issues and theoretical methodology. We will start by introducing fundamental concepts of statistical inference, which will then be extended to the quantum domain, to equip you with key mathematical tools and techniques in quantum estimation and metrology. Building on this foundation we will explore applications of current relevance to quantum technology such as quantum tomography, quantum phase estimation, and the Heisenberg limit. This will provide you with a solid background in statistical aspects of quantum metrology.

As quantum systems are sensitive to noise and perturbations, it is important to understand and counteract the effects of quantum errors in quantum technology applications. The final part of the module will investigate the theory of quantum noisy channels and apply it to the study of realistic metrology models. This will bring you close to current research topics at the intersection of quantum statistics, error correction and machine learning.