# APPLIED QUANTUM COMPUTING IV (HOW TO MAKE A QUBIT AND TOPICS IN QUANTUM MECHANICS) - 2024/5

Module code: PHYM070

## Module Overview

This module comprises two independent halves, on How to Make a Qubit, and Topics in Quantum Mechanics.

• Quantum technologies, including quantum computing, rely on the quantum mechanical principles of superposition and entanglement. Furthermore, this superposition and entanglement needs to be controlled in useful ways. In this module you will learn about what physical systems allow quantum technology production, and their limitations. Quantum computers are only one type of device that uses these principles, and several other technologies are being created that are also enhanced by use of superpositions. Others include atomic clocks and Magnetic Resonance Imaging, MRI. We will also learn about the errors that inevitably build up in quantum computers when quantum superpositions are disturbed, and the strategies that might be built in to correct them.

• Quantum Mechanics topics are essential building blocks for our understanding of many physical systems. The module assumes basic knowledge in quantum mechanics from the Introduction to Quantum Computing, but will provide a review at the beginning. Topics include a review of quantum mechanics, operator methods and applications to the harmonic oscillator, spin & angular momentum, symmetries in quantum mechanics.

### Module provider

Mathematics & Physics

GINOSSAR Eran (Maths & Phys)

### Module cap (Maximum number of students): N/A

Workshop Hours: 2

Independent Learning Hours: 68

Lecture Hours: 20

Tutorial Hours: 10

Guided Learning: 30

Captured Content: 20

Semester 2

N/A

## Module content

Indicative content for the How to Make a Qubit part:

• Qubit platforms. The DiVicenzo criteria specify the ingredients needed to build a quantum computer. We will perform a comparative study the characteristics of a variety of quantum technology platforms that provide the requisites (likely to include, but not limited to: Harmonic oscillators; Ion Traps; Photons; NMR; diamond NV; semiconductor spins).

• Error correction. Not only do we need strategies to reduce errors in quantum computers for qubits with low fidelity, strategies for correction are essential, and this has important implications for the number of qubits required in a practical computer.

• Other quantum technologies. We will also investigate the possibilities for other applications of quantum technology such as: Atomic Clocks; Magnetic Resonance Imaging; Sensors) [NB some specific hardware systems and applications are not included here because they will be explored in detail in other modules].

• Latest research. The list of platforms covered, the details of their comparison, and the applications in quantum technology will be kept up-to-date with the latest research in the field.

Indicative content for the Topics in Quantum Mechanics part:

• Review of Quantum Mechanics with Dirac Notation: We will revisiting the principles and mathematical formalism of quantum mechanics. Students will review key concepts such as wavefunctions, operators, and observables, and explore how they are represented in Dirac notation.

• The Ladder Operator Method: The ladder operator method is a powerful technique used to study quantum systems with discrete energy levels, such as harmonic oscillators and angular momentum systems. Students will learn how ladder operators enable the calculation of energy eigenstates, energy spectra, and transition probabilities between states.

• Symmetries in Classical and Quantum Mechanics: Students will examine how symmetries manifest in physical systems and how they are described mathematically. They will learn about symmetries such as translation, rotation, and time reversal, and understand their implications for conservation laws and the behavior of quantum systems.

• Angular Momentum and Spin: Angular momentum is a fundamental property in quantum mechanics that arises from the rotational symmetry of physical systems. Students will explore the quantization of angular momentum and its role in describing the behavior of particles with intrinsic spin, such as electrons. They will learn about the commutation relations and eigenstates associated with angular momentum operators, and how they are connected to observable quantities.

## Assessment pattern

Assessment type Unit of assessment Weighting
Coursework Q Mechanics assignment 50
Examination Qubits exam (1hr30mins) 50

## Alternative Assessment

In cases where an alternative re-assessment to an in-class group presentation is required, the alternative assignment will be an individual report/dissertation.

## Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate:

• adaptability, collaboration skills resulting in team contributions to group outcomes (Qubits).

• individual knowledge and problem-solving abilities (Qubits and Q Mech).

Thus, the summative assessment for this module consists of:

• The Quantum Mechanics coursework assignment assesses Learning Outcomes 4-6. The assignment will consist of a set of problems, representing each of the topics. The problems will require detailed written solutions by which the students will demonstrate their understanding of the material and their problem solving abilities.

• The Qubits Exam will assess Learning Outcomes 1-3.

Formative assessment

• Formative assessment will be provided through SurreyLearn quizzes to assess recall of key points and basic problem solving skills (Qubits).

• Formatively assessed problem sheets (Qubits and Q Mech).

Feedback

• Verbal immediate feedback will be given in tutorials through in-class questions and discussions in tutorials (Qubits and Q Mech).

• One-to-one advice in open office hours (Qubits and Q Mech).

## Module aims

• The module aims to give an understanding of the variety of modern quantum computer hardware, with comparative analysis of the advantages, disadvantages, and likely applications of each (Qubits).
• Applications of quantum technology other than computers will also be explored, such as quantum sensing (Qubits).
• From a hardware perspective, it is very important to understand how imperfections in quantum technology affect the ability to deliver large scale computers, and this module will cover hardware error correction strategies (Qubits).
• The module aims to develop a deeper understanding of the consequences of the postulates of quantum mechanics, using Dirac notation, operator methods the role of symmetry (Q Mech).
• The principles learned will be applied to problems that can be solved analytically, which are important checks on the output of simple quantum computations (Q Mech).

## Learning outcomes

 Attributes Developed 001 Compare and contrast the advantages and disadvantages of different quantum hardware systems (Qubits). KC 002 Calculate the strength and sequence of perturbation pulses needed to produce specific operations with a variety of quantum technology platforms (Qubits). KC 003 Analyse and present specific advances made in recent scientific literature results relative to the state-of-the-art in the relevant topic (Qubits). KC 004 Recall the postulates of quantum mechanics, and apply them to simple two level systems (Q Mech). PT 005 Be able to use operators and commutation relations in analysing the simple harmonic oscillator, angular momentum, and spin (Q Mech). KC 006 Be able to explain how symmetries are used in quantum mechanics (Q Mech). C

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

## Methods of Teaching / Learning

The learning and teaching strategy is designed to:

• Expose students to the latest research in quantum technology hardware, including not only quantum computer hardware but also other technologies like quantum clocks, sensors etc (Qubits).

• Encourage critical thinking about hardware research results, in particular comparative assessment of benefits and barriers for any given technology (Qubits).

• Give understanding of the way that quantum computer gates are translated into signals to hardware in the various implementations (Qubits).

• Knowledge of strategies to deal with errors, in the present era of Noisy Intermediate Scale Quantum computing (Qubits).

• Enable students to understand the physics concepts involved in Quantum Mechanics, how to use mathematical tools to find analytical solutions (Q Mech).

• The student will understand how to use operator methods to analyse the simple harmonic oscillator, and angular momentum (Q Mech).

• The student will be able to represent operators as matrices and use standard matrix methods, for example to compute the eigenvalues and expectation values of operators (Q Mech).

Thus, the learning and teaching methods include

• Interactive lectures, (Qubits and Q Mech).

• tutorials to discuss problem sets, and class seminars to discussion about limitations and challenges in quantum technology (Qubits).

• Problem sets will be issued throughout the course to give practice at problem-solving in quantum mechanics (Q Mech).

• Workshops for group activities (Qubits).

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.

Upon accessing the reading list, please search for the module using the module code: PHYM070

## Other information

Digital Capabilities: In this module we study the hardware components of a revolution in digital capabilities: the quantum computer (Qubits and Q Mech).

Employability: The market for graduates in quantum computing is expected to rise significantly in the future as the technology becomes more established, and background knowledge of the variety of platforms with their various advantages and disadvantages will be very beneficial (Qubits).

## Programmes this module appears in

Programme Semester Classification Qualifying conditions
Applied Quantum Computing MSc 2 Compulsory A weighted aggregate mark of 50% is required to pass the module

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2024/5 academic year.