# APPLIED QUANTUM COMPUTING I (QUANTUM SIMULATION AND QUANTUM OPTIMIZATION) - 2025/6

Module code: PHY3070

## Module Overview

This module comprises two independent halves, on Quantum Simulation (QSim), and on Quantum Optimization (Q Opt).

• The quantum simulation part of this module introduces students to the use of quantum computers in the simulation of physical systems using mapping of Hamiltonians from standard quantum mechanics to a representation suitable for application on quantum computers, along with a study of wavefunction ansatz design, algorithms, and error mitigation and correction.

• Quantum optimization is expected to take over a large number of demanding computational tasks, because it is capable of performing computations faster than their classical counterparts. Among many potential applications in logistics, aerospace, traffic control and in finance, which includes include pricing, risk management, and portfolio optimizations in financial markets, and indeed some banks have been investing in developing quantum computer algorithms.

### Module provider

Mathematics & Physics

### Module Leader

STEVENSON Paul (Maths & Phys)

## Overall student workload

Independent Learning Hours: 61

Lecture Hours: 25

Laboratory Hours: 8

Guided Learning: 31

Captured Content: 25

Semester 1

N/A

## Module content

Indicative content for the Quantum Simulation part:

• Quantum systems for simulation. Suitable example quantum many-body systems are discussed, drawing from examples in chemistry (e.g. molecular systems), condensed matter (e.g. spin systems), and nuclear physics. Representation of the Hamiltonian is described in second quantization notation.

• Hamiltonian Encoding. Methods of encoding Hamiltonians on quantum computers are presented, mapping from the second quantized notation to qubit spins via the Jordan-Wigner and other mapping methods, discussing and exploring the relative merits of different methods, dependent on the problem at hand and the quantum hardware available.

• State encoding. Methods of preparing entangled ansatz states representing many-body quantum wave functions for use in quantum simulation or optimization algorithms.

• Simulation algorithms. Methods of extracting physical information from the combination of wave function and Hamiltonian: Time-evolution and Trotterization; variational methods including the Variational Quantum Eigensolver.

• Error Mitigation. Sources of error in quantum simulation and methods for assessing and reducing error on current quantum hardware.

• Latest research. The latest research will be used to update content to take account of hardware capabilties and algorithms.

Indicative content for the Quantum Optimization part:

• Introduction to Quantum computing. This half-module will begin with a brief introduction to quantum computing with quantum circuits as well as discussing quantum annealing, both being relevant strategies for quantum optimization.

• The Quantum Approximate Optimization Algorithm (QAOA)

• Quantum annealers (QA)

• Case studies of quantum optimization. The application of QAOA and QA and to applications and potential use cases such as in finance, logistics, communications, computer vision.

• Latest research. The latest research will be used to update content to take account of hardware capabilities and algorithms.

## Assessment pattern

Assessment type Unit of assessment Weighting
Oral exam or presentation Quantum Simulation Project 50
Coursework Quantum Optimization Coursework 50

N/A

## Assessment Strategy

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

• individual knowledge, skill, and problem-solving abilities (Q Sim, Q Opt).

• The ability to use quantum optimizers for given simple optimization problems (Q Opt).

• The ability to analyse the suitability of a given optimization problem for quantum optimization and devise a strategy to choose the correct algorithm (Q Opt).

Thus the summative assessment for this module consists of:

• The Quantum Simulation project assessed by oral means, in which students will demonstrate synthesis and application of the module content covering LO 1-4) (Q Sim).

• The Quantum Optimization coursework, covering LO4-6 (Q Opt).

Formative assessment:

• On-line class quizzes will precede the oral assessment to give students formative feedback on progress (Q Sim).

• There is feedback from tutorial assignments (Q Opt).

Feedback:

• Students will receive immediate verbal feedback during computational laboratory hours where they will be working on problems, with help from staff. Some of these sessions will be dedicated to working on the project assignment (Q Sim) .

• Verbal feedback is provided by the lecturer during the tutorials (e.g., when exercises are worked out), (Q Opt).

• One-to-one advice in open office hours (Q Sim and Q Opt).

## Module aims

• To give students a comprehensive introduction to the ideas of quantum simulation (Q Sim).
• To ensure students can use the second quantisation notation of quantum mechanics, and translate Hamiltonians to Pauli form for implementation on quantum computers (Q Sim).
• To embed strategies and techniques for making suitable wave function ansatzes (Q Sim).
• To impart a range of standard algorithms and ensure students can use them in unseen cases (Q Sim).
• To equip students with the understanding of the key difference between a classical and a quantum computers (Q Opt).
• To equip students with the understanding of the types of optimization challenges in industry and finance which can be handled by quantum optimization algorithms (Q Opt).
• To equip students with the basic understanding of the different approaches and quantum algorithms and how real-life problems could be translated and solved by quantum processors and quantum annealers (Q Opt).

## Learning outcomes

 Attributes Developed 001 To understand, to be able to explain, and to use, the second quantization formalism in quantum mechanics (Q Sim). KC 002 To be able to map general Hamiltonians into qubit / Pauli matrix form (Q Sim). KC 003 To be able to make suitable wave function ansatzes, with physical insight from a problem at hand (Q Sim). KC 004 To understand quantum simulation and optimization algorithms and to be able to implement them with an understanding of errors and actual quantum advantage associated with real quantum computers (Q Sim and Q Opt). KCPT 005 Demonstrate an understanding of the principles of quantum circuits and quantum annealing (Q Opt). KCT 006 Demonstrate working knowledge of applying quantum computing to optimization problems (Q Opt). KCP

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:

• give students the skills to take a physical problem and map it onto the formalism of quantum computation (Q Sim).

• Introduce basics of quantum circuits and quantum annealing (Q Opt).

• Introducing the structure and flow of quantum algorithms for optimization and how they achieve the desired speedup compared to classical algorithms (Q Opt).

• Give the students skills to translate a real-world optimization problem into a form that is suitable for processing on quantum processors (Q Opt).

• Introduce students to the challenges and limitations of current hardware and how to decide on suitability of using quantum optimization (Q Opt).

Thus the learning and teaching methods include:

• a combination of traditional lecture-based sessions to cover background theory, (Q Sim and Q Opt).

• hands-on sessions in a computer laboratory to work through examples of quantum simulation. During some of the computer lab sessions, the students will have an opportunity to have supervised time working on the assessment associated with this part of the module (Q Sim).

• Typeset notes, containing exercises and examples, will be provided (Q Opt).

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: PHY3070

## Other information

Sustainability. This will be discussed in terms of quantum simulation scaling with problem size much better than classical algorithms, hence that the hardware and resource implications for quantum simulation are, in principle, much less than with classical computing resources (Q Sim). Optimization of resources is a central topic of discussion in quantum optimization, and this has a wider set of applications in resource management, crucial for sustainability (Q Opt).

Digital capabilities. The module covers advanced (quantum) computational/simulation methods, which are wholly a subset of digital capabilities (Q Sim).

Resourcefulness and Resilience: In development of the simulation project/presentation students will develop ability to solve an extended challenge, and the necessary self-reliance (Q Sim).  The knowledge on how to optimize (as applied here to various logistics, traffic, communications, finance and science) will be beneficial in a range of applications, thus enhancing the resourcefulness of the students (Q Opt).

Global and Cultural capabilities: The module will provide ideas 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 (Q Opt).

Employability: The simulation project will allow students to develop time-management, project planning and communication/presentation skills (Q Sim). This module teaches the structures of financial markets, along with the concepts of portfolio management, valuation, and risk management. All of these will significantly enhance the employability of the students in financial and related industries (Q Opt).

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 2025/6 academic year.