# APPLIED QUANTUM COMPUTING I (FINANCE & TOPICS IN QUANTUM MECHANICS) - 2024/5

Module code: PHY3072

## Module Overview

This module comprises two independent halves, on Financial Derivatives, and Topics in Quantum Mechanics.

- Financial Derivatives. The first half of this module covers various applications of statistical physics to model share prices and financial markets. This mathematics is then applied to calculating prices for some examples of financial derivatives.
- 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

### Module Leader

GINOSSAR Eran (Maths & Phys)

### Number of Credits: 15

### ECTS Credits: 7.5

### Framework: FHEQ Level 6

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

## Overall student workload

Independent Learning Hours: 80

Lecture Hours: 20

Tutorial Hours: 5

Laboratory Hours: 5

Guided Learning: 20

Captured Content: 20

## Module Availability

Semester 1

## Prerequisites / Co-requisites

None

## Module content

Indicative content for the Financial Derivatives part:

**Introduction to Financial derivatives**: markets, speculation, hedging, investment; overview of derivatives and non-arbitrage pricing; types of interest rates used in the module.**Futures and Forwards**: forward contracts: over the counter agreements, underlying asset, future time, delivery price; future contracts: exchange traded, zero worth at inception; formulas for delivery price via non-arbitrage arguments.**Options (call and put)**: Definition, European vs American; Vanilla vs Exotic; pricing factors: asset price, interest rate, volatility, strike, time to maturity; call-put parity significance; construction of complex strategies using options. Overview of non-vanilla options (Exotics): binary, forward, compound, pathdependent, spread, Bermuda, customizable strategies with exotic options.**Binomial Model:**Basis of option pricing using Binomial model; Delta and its role in option values; extension to more periods and scenarios; calculation of option values using discounted expected values backward; sensitivities of option prices (Greeks); continuous time-pricing model.**Black-Scholes-Merton framework**: construction from probabilistic and non-arbitrage arguments; convergence of the binomial model to the Black-Scholes-Merton framework; analytical formulae for Greeks and their interpretation.**Volatility**: Spot (instantaneous), historical, and implied volatility; implied volatility surface: smile and skew effects, flattening with time to maturity.**Replicating portfolios**: using assets and risk-free investments; Delta hedging technique to reorganise portfolio to maintain a quantity of assets equal to Delta; application of Delta hedging to the binomial model and to Black-Scholes-Merton.

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 | Financial Derivatives assignment | 50 |

Coursework | Quantum Mechanics assignment | 50 |

## Alternative Assessment

None

## Assessment Strategy

The __assessment strategy__ is designed to provide students with the opportunity to demonstrate:

- individual knowledge and problem-solving abilities (Finance and Quantum Mechanics).
- Understanding of the concepts of derivative pricing, and underlying mathematics (Finance).

Thus, the

__summative assessment__for this module consists of:

- The Financial Derivatives coursework assignment involving real data analysis and modelling of financial instruments will assess Learning Outcomes 1-3.
- 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.

__Formative assessment__

- Formative assessment will be provided through tutorial sessions (Finance)
- Formatively assessed problem sheets (Quantum Mechanics)

__Feedback__

- Verbal immediate feedback will be given during computational laboratory hours where students will be working on problems, with help from staff (Finance)
- Verbal immediate feedback will be given during tutorials (Quantum Mechanics)
- One-to-one advice in open office hours (Finance and Quantum Mechanics)

## Module aims

- To expose the students to the fundamentals of financial derivatives, introducing theoretical concepts and practical applications using Python (Finance).
- To develop skills in pricing and analyzing various derivatives instruments (Finance)
- To enable students to construct and analyse complex strategies using derivatives (Finance).
- 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 (Quantum Mechanics).
- The principles learned will be applied to problems that can be solved analytically, which are important checks on the output of simple quantum computations (Quantum Mechanics).

## Learning outcomes

Attributes Developed | ||

001 | Understand the mathematics and models that underpin the analysis of financial data, including the properties of random variables, probability distributions and share price models and be able to assess their validity and remit. (Finance) | CKT |

002 | Know about a range of common financial derivatives, be able to explain financial terminology and produce pay-off and profit diagrams for forward contracts, put and call options (Finance). | CKP |

003 | Understand basic portfolio optimization theory and types of trading and traders (Finance). | CKT |

004 | Recall the postulates of quantum mechanics, and apply them to simple two level systems (Quantum Mechanics) | KT |

005 | Be able to use operators and commutation relations in analysing the simple harmonic oscillator, angular momentum, and spin (Quantum Mechanics) | CK |

006 | Be able to explain how symmetries are used in quantum mechanics (Quantum Mechanics) | 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:

- Help students develop an understanding of how the ideas of stochastic processes can be applied to financial derivatives. (Finance)
- Develop computational skills with a focus on financial data (Finance)
- Enable students to understand the physics concepts involved in Quantum Mechanics, how to use mathematical tools to find analytical solutions (Quantum Mechanics)
- The student will understand how to use operator methods to analyse the simple harmonic oscillator, and angular momentum (Quantum Mechanics).
- 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 (Quantum Mechanics).

Thus, the

__learning and teaching methods__include

- Interactive lectures to cover background theory (Finanice and Quantum Mechanics)
- hands-on sessions in a computer laboratory for computer-based problem solving (Finance)
- Problem sets will be issued throughout the course to give practice at problem-solving in quantum mechanics (Quantum Mechanics).

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.

## Reading list

https://readinglists.surrey.ac.uk

Upon accessing the reading list, please search for the module using the module code: **PHY3072**

## Other information

The School of Mathematics and Physics is committed to developing graduates with strengths in Employability, Digital Capabilities, Global and Cultural Capabilities, Sustainability, and Resourcefulness and Resilience. This module is designed to allow students to develop knowledge, skills, and capabilities in the following areas:

**Digital Capabilities**: Students will apply computational skills in Python to engage with and analyse complex financial datasets (big data). Bespoke software packages will also be used to present complex data clearly and understandable.

**Employability**: During the first part of the module, the leaders in the financial sector will visit either in person or online to share their experience and provide advice regarding graduate jobs and interviews. This module introduces students to the structures of financial markets, along with the concepts of financial derivatives, portfolio management, valuation, and risk management. All of these will greatly enhance student employability in financial and related industries.

**Sustainability**: Sustainable investing aiming at generating long-term financial returns while advancing sustainable solutions and outcomes are a central aspect throughout the module; we explore environmental, social, and governance investing as well as ethical and green investing throughout the module.

**Global and Cultural Capabilities**: Students will be introduced to real-life Quant professionals working in the city. In the second half of this module, students will be introduced to the idea of quantum computers and how they compare to their classical counterparts, along with the areas in which they may transform the world. These ideas, in turn, are beneficial towards enhancing global and cultural intelligence of the students.

## Programmes this module appears in

Programme | Semester | Classification | Qualifying conditions |
---|---|---|---|

Applied Quantum Computing MSc | 1 | Compulsory | A weighted aggregate mark of 40% 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.