Quantum Science and Technology MSc

The notion of information is at the heart of modern science and technology, from internet applications to secure communication and artificial intelligence. While such “classical” information is represented by bits and can be encoded in currents in a computer chip, or tiny holes in a CD, at the most fundamental level, information can be encoded in the state of quantum systems such as atoms and photons. This module gives an introduction to some of the key ideas and techniques in Quantum Information and Computation, which lie at the foundation of current applications in Quantum Technology.

During the first three weeks we will review the mathematical formalism of quantum mechanics including the notions of states, measurements and composite systems. You will familiarise yourself with the notion of qubit which is the building block of quantum information. After this we will explore several protocols in Quantum Information such as teleportation, superdense coding and quantum key distribution.

We will then discuss a fundamental result called the Bell Theorem, which provides an experimental method to establish whether nature can be described by “classical” probabilistic theories. These findings highlight the key importance of the notion of entanglement for quantum applications.

In the third part you will learn about quantum circuits and quantum computation and study a few examples of quantum algorithms. The last part of the module focuses on how to describe the evolution of systems interacting with the environment, leading to the concept of quantum channel. This will be then applied to the study of error correction protocols in quantum computers.

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.

This module covers the exciting interactions between light and matter – in particular atoms, that enable many of the fascinating technological applications of quantum physics.

You’ll begin by exploring atoms, the simplest units of matter that engage with visible light to lay a solid foundation for understanding more complex interactions. The module starts with a recap of basic quantum-mechanical concepts; following that you will develop fundamental concepts such as the optical bloch equations and explore fascinating phenomena including photon anti-bunching and the science behind laser cooling. You will cover topics including:

• Spectra and Effects: Learn about atomic spectra and witness the intriguing Stark and Zeeman effects. You'll also discuss the polarization of fields and the differences between static and time-varying fields
• Semi-classical atom-light interactions: Explore coherent interactions between light and quantised atoms, including the fascinating dynamics of two-level atoms and Rabi oscillations
• Decoherence and Dynamics: understand the complexities of decoherence, optical Bloch equations, the Bloch sphere, and the density matrix formalism. These concepts are important for understanding atomic behaviour under observation
• Forces and Phenomena: Analyse how light influences atomic movement through discussions on atomic line shapes and the forces exerted by light on atoms
• Light in Atomic Media: The module concludes with an examination of how light propagates through atomic media, focusing on absorption and changes in the refractive index

The module is designed to increase your theoretical knowledge and to show you the practical applications and phenomena that shape our understanding of quantum physics and allow the exploitation of quantum processes for 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.

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.

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.

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.

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.

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

The purpose of this module is to provide an introduction to the concepts and methods of modern machine learning. The first part will cover basics of supervised learning including linear models, logistic regression, bias-variance decomposition and regularisation. The second part deals with unsupervised learning, and convers clustering, dimensional reduction, principle components analysis, mixture models and expectation maximisation. The third part is on reinforcement learning which includes dynamical programming, and an introduction to Markov decision processes.

The theory is applied to a variety of problems of linear and non-linear regression, classification, density estimation, data generation and optimal control. It will be a combination of fundamental concepts and hands-on application to a selection of example problems.

The module will be taught via two classes per week, comprising topical discussions, concrete examples of ML in science and lectures on the statistical foundations of ML

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
• reinforcement learning
• 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.

Statistical machine learning is a topic at the interface between statistics and computer science. It relates to models that can adapt to and make predictions based on data. This module builds on principles of statistical inference and linear regression to introduce a variety of methods of clustering, dimension reduction, regression and classification. Much of the focus is on the bias-variance trade-off, and on methods to measure and compensate for overfitting. You will learn in a practical way, using R extensively in studying contemporary statistical machine learning methods. A highlight of the module is applying them to tackle challenging real-world situations.

This module will provide you with skills that employers typically seek in graduates who enter the workplace. They include:

• problem solving
• oral and written communications
• teamwork
• technical skills

The notion of information is at the heart of modern science and technology, from internet applications to secure communication and artificial intelligence. While such “classical” information is represented by bits and can be encoded in currents in a computer chip, or tiny holes in a CD, at the most fundamental level, information can be encoded in the state of quantum systems such as atoms and photons. This module gives an introduction to some of the key ideas and techniques in Quantum Information and Computation, which lie at the foundation of current applications in Quantum Technology.

During the first three weeks we will review the mathematical formalism of quantum mechanics including the notions of states, measurements and composite systems. You will familiarise yourself with the notion of qubit which is the building block of quantum information. After this we will explore several protocols in Quantum Information such as teleportation, superdense coding and quantum key distribution.

We will then discuss a fundamental result called the Bell Theorem, which provides an experimental method to establish whether nature can be described by “classical” probabilistic theories. These findings highlight the key importance of the notion of entanglement for quantum applications.

In the third part you will learn about quantum circuits and quantum computation and study a few examples of quantum algorithms. The last part of the module focuses on how to describe the evolution of systems interacting with the environment, leading to the concept of quantum channel. This will be then applied to the study of error correction protocols in quantum computers.

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.

This module covers the exciting interactions between light and matter – in particular atoms, that enable many of the fascinating technological applications of quantum physics.

You’ll begin by exploring atoms, the simplest units of matter that engage with visible light to lay a solid foundation for understanding more complex interactions. The module starts with a recap of basic quantum-mechanical concepts; following that you will develop fundamental concepts such as the optical bloch equations and explore fascinating phenomena including photon anti-bunching and the science behind laser cooling. You will cover topics including:

• Spectra and Effects: Learn about atomic spectra and witness the intriguing Stark and Zeeman effects. You'll also discuss the polarization of fields and the differences between static and time-varying fields
• Semi-classical atom-light interactions: Explore coherent interactions between light and quantised atoms, including the fascinating dynamics of two-level atoms and Rabi oscillations
• Decoherence and Dynamics: understand the complexities of decoherence, optical Bloch equations, the Bloch sphere, and the density matrix formalism. These concepts are important for understanding atomic behaviour under observation
• Forces and Phenomena: Analyse how light influences atomic movement through discussions on atomic line shapes and the forces exerted by light on atoms
• Light in Atomic Media: The module concludes with an examination of how light propagates through atomic media, focusing on absorption and changes in the refractive index

The module is designed to increase your theoretical knowledge and to show you the practical applications and phenomena that shape our understanding of quantum physics and allow the exploitation of quantum processes for quantum technologies.

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.

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.

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.

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.

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

The purpose of this module is to provide an introduction to the concepts and methods of modern machine learning. The first part will cover basics of supervised learning including linear models, logistic regression, bias-variance decomposition and regularisation. The second part deals with unsupervised learning, and convers clustering, dimensional reduction, principle components analysis, mixture models and expectation maximisation. The third part is on reinforcement learning which includes dynamical programming, and an introduction to Markov decision processes.

The theory is applied to a variety of problems of linear and non-linear regression, classification, density estimation, data generation and optimal control. It will be a combination of fundamental concepts and hands-on application to a selection of example problems.

The module will be taught via two classes per week, comprising topical discussions, concrete examples of ML in science and lectures on the statistical foundations of ML

Statistical machine learning is a topic at the interface between statistics and computer science. It relates to models that can adapt to and make predictions based on data. This module builds on principles of statistical inference and linear regression to introduce a variety of methods of clustering, dimension reduction, regression and classification. Much of the focus is on the bias-variance trade-off, and on methods to measure and compensate for overfitting. You will learn in a practical way, using R extensively in studying contemporary statistical machine learning methods. A highlight of the module is applying them to tackle challenging real-world situations.

This module will provide you with skills that employers typically seek in graduates who enter the workplace. They include:

• problem solving
• oral and written communications
• teamwork
• technical skills