Summer research opportunities for undergraduate students.

The UCL EPSRC Centre for Doctoral Training in Delivering Quantum Technologies offers paid summer research placement opportunities for undergraduate students. These placements are an excellent way for students to gain experience working in a lab on a research project and obtain research experience during the summer months. During the project, you will be based within the research group of your academic supervisor and provided with relevant training as required.

Each summer we are offering research bursaries to work on projects of up to 8 weeks with academic staff and PhD students from the Centre for Doctoral Training. These projects will provide direct and relevant research experience to interested undergraduates. The projects are especially beneficial to students who are considering doing a PhD and want to get a better understanding of what doing research in quantum technologies involves. Previous experience is not required, only enthusiasm and the intention to learn.

The key details:

- Placement Length: Up to 8 weeks
- Placement Dates: Between June and August 2024
- Location: UCL, Bloomsbury, London
- Funding: Placements include a bursary of £3437 (£1718.50 per month)
- Application Deadline: 23:59 (UTC) Sunday, 31st March 2024

#### Eligibility criteria

To apply for these placements:

- You must be enrolled on an undergraduate degree programme at a UK university (e.g. BSc, BEng, MSci, MEng)
- You must currently either be in the second year of a three-year course or the third year of a four-year course
- You cannot also apply for admission to the Centre for Doctoral Training’s MRes+PhD programme this year
- No previous experience is required: we welcome applications from students who have not done an internship or research placement before

We particularly welcome applications from women, people with disabilities, and candidates from minority ethnic and socially disadvantaged groups as they are under-represented within STEM disciplines. UCL is committed to equality of opportunity, supports and encourages under-represented groups, and values diversity.

#### Available projects

- Project 1: Using Genetic Algorithms to Improve Quantum Annealing
**Supervisor Details:**Prof. Paul Warburton, London Centre for Nanotechnology, UCL**Summary of main research project:**Whether a quantum annealer is capable to successfully ﬁnd the optimal solution strongly depends on the intrinsic characteristics of the problem we want to address (size, structure of the energy landscape, presence of higher order couplings, etc.) as well as on how the problem is “prepared” to be solved (choose of the embedding, anneal schedule, eventual presence of catalysts etc.). The aim of the project is to use heuristic algorithms to optimise these latter parameters. The primary focus will be on using genetic algorithms, which are metaheuristic algorithms inspired by the process of natural selection.**Summary of undergraduate scholar’s project:**The project is separated into three steps:1. Use genetic algorithms to solve various optimisation problems: Genetic algorithms are powerful tools to solve optimisation problems, especially when the search space is very large (e.g. 10^26 ) and the solutions are very rare (e.g. 1:10^10 ). The goal of this part is to benchmark how effective they are in solving problems which are notoriously hard and eventually compare them with other methods.

2. Simulate the evolution of quantum systems: In this intermediate part the student will use numerical and analytical tools to simulate quantum systems. Starting from simple configurations (two level systems or spin chains) up to more complicated systems, as spin glasses, which is often the case in quantum annealing. The aim is to test how performances change depending on the choice of the parameters involved in the annealing.

3. Use genetic algorithms to improve the performance of quantum annealers: In this part the student will use the tools learned in the first part to find the optimal values of the parameters involved in the annealing. Using these techniques on various problems and parameters, the ultimate goal is to to test in which extent genetic algorithms can be useful in the context of quantum annealing Use genetic algorithms to improve the performance of quantum annealers.

**Essential skills which the undergraduate scholar must have in order to undertake the project successfully:**Previous experience with coding (preferably Python) and basis of quantum mechanics.- Project 2: Simulation of quasi-periodic Hamiltonians
**Supervisor Details:**Prof. Arijeet Pal, UCL Department of Physics and Astronomy**Summary of main research project:**Analogue quantum simulation using atoms, molecules and photons has opened the possibility to realise and probe many-body quantum states, leading to the discovery of new non-equilibrium phases of matter. One of the frontiers of modern quantum many-body physics is to understand how quantum systems reach thermal equilibrium. Significant effort is being devoted to characterise out-of-equilibrium quantum phases, such as many-body localization (MBL) in which thermalisation is arrested in the presence of strong disorder and inter-particle interactions. In this project, we focus on quasi-periodic lattices where the correlated nature of the potential is expected to stabilise the MBL phase in two and higher dimensions. These systems can be readily realised in contemporary quantum simulation experiments using cold atoms. We will investigate the properties of these lattices using numerical and analytical tools for characterizing the Hamiltonians to study the emergence of erogodicity and localisation. Concepts from condensed matter physics and quantum information science will be combined to provide complementary perspectives of these phenomena.**Summary of undergraduate scholar’s project:**The undergraduate project will involve the simulation of quasi-periodic Hamiltonians first using exact diagonalisation and later, using more advanced methods such as tensor networks and perturbative techniques. We’ll initially focus on the non-interacting limit of the two-dimensional 8-fold quasi-crystal lattice and its localisation properties in the single-particle dynamics. In particular, the project would involve understanding the role of resonances in the localisation transition which could form the basis for renormalisation group calculations. Subsequently, we aim to study the effect of repulsive interactions on the stability of localisation. The project will be targeted at understanding ongoing cold atom experiments in Cambridge.Analytical methods: The student will develop an understanding of second-quantisation to construct many-body quantum Hamiltonians and perturbation techniques to construct excited eigenstate properties.

Numerical methods: Significant portion of the project will require programming in Python/Julia to simulate many-body Hamiltonians, which will provide them with a background in linear algebra packages. The student will also learn how to use tensor network libraries to run matrix product state simulations of quantum dynamics.

Outputs: Characterization of the instabilities of localization in quasiperiodic potentials and the resulting non-equilibrium dynamics. Develop a deep conceptual understanding of physical processes of thermalization and localization and their implications for analogue quantum simulation experiments.

**Essential skills which the undergraduate scholar must have in order to undertake the project successfully:**Quantum Physics, Condensed Matter Theory, Quantum Information, A programming language like Python/Julia, including working knowledge of numerical libraries such as Numpy/Scipy.- Project 3: Design and Simulation of Scalable Superconducting Quantum Computers
**Supervisor Details:**Prof. Paul Warburton, London Centre for Nanotechnology, UCL**Summary of main research project:**Superconducting quantum computers face two major issues: i) their low scalability and ii) the short coherence times of superconducting transmon qubits. The aim of this project is to explore the feasibility of a quantum computing architecture that mitigates against both of these issues by using more scalable superconducting control hardware and superconducting qubits that are more resilient to noise. The project will focus on the dynamic Hamiltonian simulation of one and two qubit operations using this architecture, moving from an ideal case to a more realistic model with decoherence and timing errors.**Summary of undergraduate scholar’s project:**Initially the student will simulate an ideal SFQ (Single Flux Quantum) driven fluxonium qubit to get familiarized with the techniques used in the rest of the project. Once this is done the student will explore errors that are introduced due to leakage into higher states and timing errors of various one qubit gates and how this will influence the design of hardware.The next stage of the project will simulate how two qubit gates are performed using SFQ circuits and what additional errors or design considerations arise when taking this into account.

Additionally the student will explore how non-uniform pulse sequences effect the fidelity of single and two qubit operations and if the advantages of using fluxonium qubits still hold in this scenario.

The output of this project will be a comprehensive theoretical benchmark of one and two qubit operations of a SFQ-driven fluxonium-based superconducting quantum computer. This will include its advantages of an equivalent transmon-based design, the errors that are introduced from timing errors, leakage and Josephson junction variation, and what design considerations need to be taken into account to mitigate these errors.

**Essential skills which the undergraduate scholar must have in order to undertake the project successfully:**Previous experience with coding (preferably Python) and basis of quantum mechanics.- Project 4: Quantum Error Correction with quasi-cyclic Codes
**Supervisor Details:**Prof. Dan Browne, UCL Department of Physics and Astronomy**Summary of main research project:**Implementing quantum error correction (QEC) is crucial for harnessing the full potential of quantum computers in the presence of inherent noise. QEC codes address this challenge by redundantly encoding information across multiple qubits. These codes enable the detection and correction of errors without directly measuring qubit states. This project will investigate a recently proposed family of quantum low-density parity check (qLDPC) codes that have a high qubit encoding rate and error threshold. The goal is to use a mixture of analytic and numerical techniques to construct quasi-cyclic codes and find the code parameters.**Summary of undergraduate scholar’s project:**The scholar will start with learning the basics of quantum error correction (QEC) theory, including the stabiliser formalism and surface codes. The scholar will also investigate CSS codes; construction of QEC codes from X and Z parity-check matrices.The scholar will then study the framework introduced by IBM Quantum to generate quasicyclic quantum low-density parity check (qLDPC) codes, partially reproducing the results with software. In this framework, a quasi-cyclic code is defined by two polynomials of matrices with three terms. This construction allowed the authors to produce novel QEC codes with desirable properties.

In this project, the scholar will be expected to investigate variations of the quasi-cyclic code formalism to generate other codes using different polynomials and classify their code parameters. In particular, the scholar will look at two-term polynomials and their relation with the toric code as well as exploring whether classical codes can be generated with this formalism. Based on the available time, the scholar could then investigate code constructions with four-term polynomials.

The scholar will be expected to produce Python code that (partially) automates the tasks above.

- Project 5: Using Electron Spins in Diamond for Ultrasensitive Disease Diagnostics
**Supervisor Details:****Summary of main research project:**At the McKendry group we have pioneered the use of quantum defects (nitrogen-vacancy centres) in nanodiamonds to produce a significant improvement in the sensitivity of lateral flow diagnostic tests. We do this via the optical readout and microwave based control of the electron spin states associated with the nitrogen-vacancy centre. This versatile system can be used to detect a broad range of infectious diseases as well as to gain a wide range of information about biological systems in general. Our interdisciplinary team combines researchers with expertise in Chemistry, Biomedical Engineering, Physics and Machine Learning in order to tackle the broad set of challenges posed by developing and optimising these technologies.**Summary of undergraduate scholar’s project:**The students project would consist of:

- A literature review of the relevant techniques
- Training in performing optical and diamond spin-based modulation measurements on a microscope
- Training in assay development
- Training in conjugating nanodiamonds with biomolecules for lateral flow based assays
- Training in microwave systems
- Performing some characteristic spin measurements of nanodiamonds on lateral flow assays
- Data analysis of time dependent fluorescent signals from the nanodiamond

We would expect the outcome to be a combination of the literature review and a summary and analysis of some of the measurements taken.

Essential

- A good understanding of solid-state physics and quantum mechanics
- Coding proficiency (Matlab or Python)
- The ability to learn and understand techniques from a broad set of disciplines

Desirable

- Experience with optical systems
- Experience in a wet lab
- Chemistry and/or a Biology A level

- Project 6: Impact of Network Topology on Repeater Usage in Quantum Networks
**Supervisor Details:**Prof. Alejandra Beghelli, UCL Department of Electronic & Electrical Engineering**Summary of main research project:**Quantum networks, a collection of interconnected devices exchanging quantum information, need to distribute entanglement between users before data can be teleported. When users are in geographically distant locations, quantum repeaters are needed to extend the reach of entanglement. However, quantum repeaters are envisaged to be costly and thus, not all network nodes can be equipped with them. This project will evaluate the impact of topology on the quantum repeater requirements. To do so, the intern is expected to modify Monte Carlo simulators developed by the research team to determine the number of repeaters required for a given performance.**Summary of undergraduate scholar’s project:**Week 1-2: Get familiar with the topic of quantum networks, quantum repeaters and Monte Carlo simulation.

Week 3-4: Get familiar with existing code. Reproduce previous results on quantum repeaters usage on grid topologies.

Week 5-6: Obtain new results in grids of decreasing connectivity (edge removal).

Week 7-8: Refine results, prepare final presentation to the research group.

Expected outputs:

- Modified Monte Carlo simulator documented
- Relationship between topology features and repeaters requirements
- Slides summarising work and findings.

- Project 7: Numerical Simulation of Non-Equilibrium Quantum Many-Body Systems
**Supervisor Details:**Prof. Marzena Szymanska, UCL Department of Physics and Astronomy**Summary of main research project:**Understanding dissipation and decoherence in many-body systems is critical to the development of quantum technologies. Despite rapid progress, accurate characterization of the non-equilibrium properties of realistic quantum systems remains a difficult problem, necessitating the development of new tools and simulation methods. Motivated by their potential technological impact, we concentrate on developing new quantum-inspired classical simulation methods for open many-body quantum systems, based on tensor network and quantum Monte Carlo techniques. Our methods have enabled the study of previously inaccessible models, such as dissipative spin chains with long-ranged interactions or collective dissipation.**Summary of undergraduate scholar’s project:**The student will employ state-of-the-art tensor network and quantum Monte Carlo methods developed by the Research Fellow and other group members to investigate the steady state and dynamical properties of dissipative strongly-correlated quantum manybody systems. Specifically, the student will be solving quantum master equations for the density matrix and studying the interplay between dissipation and interactions, including long-ranged interactions. Additionally, the student will be encouraged to contribute to the ongoing development of the aforementioned numerical methods (e.g. by incorporating new symmetries, models, sampling protocols) and will learn how to utilize HPC resources for scientific computing tasks (Bash, MPI).More ambitiously, the student may also have an opportunity to develop a novel computational method for open quantum many-body systems under the guidance of the Research Fellow, drawing on techniques from e.g. tensor networks, Monte Carlo, quantum trajectories, Krylov iterations, low-rank, or cluster mean-field approximations.

A significant portion of the research project will be dedicated to numerical simulation, implementation, and data analysis in Julia/Python. The student will be expected to produce a report summarizing their research project and present their findings to the rest of the group towards the end of their placement.

- Project 8: Witness Gravitational Entanglement in Large Spin Interferometry
**Supervisor Details: Prof. Sougato Bose,**UCL Department of Physics and Astronomy**Summary of main research project:**An experiment proposal to detect quantum entanglement generated by the gravitational interaction between two masses has been advanced aiming to witness quantum gravity for the first time – in a laboratory. In the original protocol, each mass is placed in a spatial superposition using a Stern-Gerlach interferometer – where a spin ½ is embedded in the mass, and a spin-dependent force is experienced by the mass when a magnetic gradient is applied. Following, the two masses are let interact via gravity: if gravity is quantum, the two masses become entangled. Entanglement can be detected by measuring quantum correlations in the embedded spins.**Summary of undergraduate scholar’s project:**The idea that the spin correlations can witness quantum gravity (QG) has shaken the discussion of the QG community which has been mainly theoretical, opening a path toward experiments. However, further analyses have shown that the proposed protocol is extremely challenging in an experimental setting. There is a need for further theoretical effort to find systems that could be more suitable for detecting gravitational entanglement.Recently, we generalized the protocol from a spin ½ to an arbitrary large spin. In the original protocol, the spin ½ and the magnetic gradient “splits” the mass into two paths. When a magnetic gradient is applied to an arbitrary spin (with total spin J), the mass is superposed in 2J+1 spatial points. When two masses are considered with the QG interaction, the entanglement generated increases with the spin value J. Hence, large spins are a promising system.

However, in our recent work, the entanglement is measured in terms of von Neumann entropy and the Negativity, which, for large spin, are impossible or hard to implement in an experimental setting. The student will research other observables that may detect gravitational entanglement in large spins, closing the gap between promising theory and experiment to witness QG.

We are looking for a student with a strong theoretical physics background, with skills in quantum mechanics. Coding skills (preferably in Python) are needed.