Quantum Technologies Doctoral Training Partnership 2024-25

With funding from the Engineering and Physical Sciences Research Council (EPSRC), Kent is delighted to offer three PhD studentships within quantum technologies research as part of the Government National Quantum Strategy.

**These studentships are open to UK residents, there is a potential for up to one international scholarship (this includes EU) available under the projects led by Carlos Pérez Delgado, full international fees will be waived. All other projects are open to UK candidates only. Please see Annex B of the UKRI Training Grant Guidelines for international eligibility details. **

These studentships include a doctoral stipend (equivalent to the Research Councils UK National Minimum Doctoral Stipend, £19,237 - 2024/25 rate), tuition fees at the postgraduate home rate (£4,786 for 2024/25) and access to further research funding.

If you would like to pursue a PhD in quantum technologies, you can apply to one of our EPSRC projects, full project details are listed below. Applicants are strongly encouraged to contact the supervisors to discuss the projects in more detail.

**Step 1 **

Apply for a PhD at Kent: each project listed below will have its own 'Apply' button. Click on the relevant 'Apply' button and follow the online instructions.

As part of the process, students should include the following:

- reasons for study, your interest in the project and your background experience – please indicate which project you are interested in applying to,
- provide details/evidence of qualifications,
- provide a copy of your CV,
- provide two academic references.

**Step 2**

Once you have applied through the University of Kent online application portal (KentVision), you must email your Application ID number, your full name and the project title to kentgrc@kent.ac.uk. This step is to confirm that you wish to apply for an EPSRC studentship.

**Have
you already applied to Kent or are you a current Kent PhD student? **

If you have already applied or have a deferred offer, or you are a current PhD student at Kent and you wish to transfer onto one of the quantum technology projects, please contact the project supervisor to inform them you wish to be considered for the EPSRC scholarship. You must also email your details to kentgrc@kent.ac.uk along with an updated CV, reasons for study, your interest in the project and your background experience.

Using Quantum Computers to Develop Quantum Advantage in Coordinated Exploration Tasks

Cybersecurity Applications of Present and Near-term (NISQ) Quantum Computers

Topological state preparation on NISQ quantum computers

NISQ quantum algorithms for modelling 2d quantum matter

Quantum Optical Coherence Tomography for Biomedical Imaging

Quantum Harmonic Analysis for Functional Data

Quantum Software Engineering

*Supervisors: Dr Jorge Quintanilla Tizón (School of Physics & Astronomy) and Professor Paul Strange (School of Physics & Astronomy) *

Non-signalling coordination of spatially-separated units is useful when communication is hindered, for instance, by environmental factors, high latency, or spectrum saturation, or when it is not desirable for security reasons. In particular, a "rendezvous problem" involves two agents trying to find each other as quickly as possible without knowing each other's locations. Similarly, "graph domination" involves coordinating several units to explore as much of a search space as possible. Developing optimal protocols is often highly non-trivial.

Very recently [P. Mironowicz New. J. Phys. (2023)] it has been found that if the "players" in one of these "games" share an entangled quantum memory there are non-signalling strategies available to them that surpass any possible non-quantum strategy. Our group in Kent have obtained the first explicit protocols for quantum-assisted rendezvous and we have demonstrated the quantum advantage using real IBM quantum hardware [J. Tucker, P. Strange, P. Mironowicz, and J. Quintanilla, manuscript in preparation]. No such results exist yet for graph domination.

The proposed project will focus on the graph domination task. We will develop protocols achieving quantum advantage and demonstrate them using quantum computers. Our work will be directly informed by a wide range of potential applications, for instance in asteroid mining, drone swarm formations and cognitive radio networks, to name a few examples.

Initially, we will tackle simple scenarios where optimal protocols can be obtained theoretically. Subsequently we will address more realistic situations, requiring complex wave functions, using hybrid algorithms (classical and quantum computers working in tandem). In this approach, inspired by quantum eigensolvers, the classical machine tries different protocols using an evolutionary algorithm but the evolving wave function (which is difficult to simulate numerically) is held in a quantum processor.

The applicant should have a first degree in Physics, Mathematics, Computer Science or other related STEM field.

*Supervisors: Carlos Pérez Delgado (School of Computing) and Dr Jorge Quintanilla Tizón (School of Physics & Astronomy)*

Quantum cybersecurity studies applications of quantum technologies to cybersecurity, both offensive and defensive. This project focuses on cybersecurity applications of current and near future quantum devices, such as NISQ (Noisy Intermediate Scale Quantum) computers. The student will join an existing vibrant research group led by Carlos Perez Delgado already exploring such applications–a notable recent example is the vulnerability of Bitcoin and other cryptocurrencies to quantum attacks.

The goal of the student will be to identify new potential cybersecurity vulnerabilities that can be exploited using current and near future quantum technologies, and to research new ways to bolster the security of systems using nascent quantum technology. Some examples of the former include quantum-technological attacks against various online systems, cloud computing, cryptocurrencies and blockchains, banking systems, and other networking systems. Some examples of the latter include quantum key-distribution and quantum cryptography, quantum secure computation, and other quantum online collaboration protocols.

The specific applications to be pursued will take into account the applicant’s background and interests.

The project will be carried out in collaboration with the group led by Jorge Quintanilla who will bring practical expertise in developing quantum computer (Qiskit) codes and running them on simulated and real quantum hardware (IBM). This includes in-house codes for the evolutionary development of application-specific quantum algorithms. We will use this technique to find quantum codes that address specific cybersecurity problems in the fields mentioned above.

The applicant should have a first degree in CS, physics, mathematics, or other related STEM field.

Home and International candidates are welcome to apply. Full international tuition fees will be waived for this project.

*Supervisors: Dr Gunnar Möller (School of Physics and Astronomy) and Dr Steffen Krusch (School of Mathematics, Statistics and Actuarial Science)*

The theoretical idea of topological states of matter, carrying an inherent robustness of their features to external influences, has inspired a huge effort in materials science aimed at identifying suitable compounds. However, the second quantum revolution of emerging quantum technologies has now opened an alternative pathway to creating states with topological features using unitary circuits: It was already demonstrated that currently available intermediate scale noisy quantum computers (NISQ) can be used to simulate the quantum states of famous topologically ordered phases such as Kitaev’s toric code model [1] and an S_3 non-Abelian theory [2]. The creation of these states raises numerous questions, e.g., whether these states truly carry the same inherent robustness as that of topological matter, how they relate to topological codes, a general understanding of the number of gate operations and measurements required to create such states, etc.

In this PhD project, we will design quantum circuits for creating a wider range of topological states, and critically examine the potential of using such states as a platform for realising robust quantum memories and gate operations. In particular, we will examine the question to which extent so-called `fast-forwarding’ techniques based on using measurements during state a preparation can be used in a scalable fashion to achieve large ensembles with topological order.

The preparation of topological states and exploration of braiding properties of excitations created within such systems is closely related to topological codes. However, focusing on the realisation of topological matter can provide more elementary challenges as compared to realising computations within a topological code [3]. Hence, we expect there to be an attractive near-term use of emulations of topological matter as a benchmark for quantum computers against stringent predictions derived from topological field theory.

- Satzinger, K. J. et al. Realizing topologically ordered states on a quantum processor. Science 374, 1237–1241 (2021).
- Iqbal, M. et al. Creation of Non-Abelian Topological Order and Anyons on a Trapped-Ion Processor. Preprint at http://arxiv.org/abs/2305.03766 (2023).
- Campbell, E. T., Terhal, B. M. & Vuillot, C. Roads towards fault-tolerant universal quantum computation. Nature 549, 172–179 (2017).

*Supervisor: Dr Gunnar Möller (School of Physics and Astronomy) *

First quantum computers have been realised and used to successfully demonstrate proof of principle for quantum computing. However, large quantum computers with sufficient fidelity to execute general-purpose quantum algorithms require significantly better hardware. Before reaching this goal, an important challenge remains to find effective algorithms which can perform well on near-term noisy quantum computers.

The challenge of designing effective algorithms compatible with limited numbers of qubits, fidelities and circuit depths is not dissimilar to the challenges posed to classical computers in treating the exponential complexity of quantum systems. In classical computing, the study of quantum information of many-body systems has led to single out tensor network approaches as a natural language for describing quantum mechanical bulk systems. It is already understood how one-dimensional classical matrix product states can be translated into quantum circuits. This approach additionally allows for the possibility to represent infinite systems by means of approximating the environment of the active computation region such that both can be stored in

a moderate number of qubits [1].

In this PhD project, we will generalise these ideas to seek efficient quantum algorithms for simulating quantum materials in higher dimensions. As a starting point, we will explore formulations in terms of isometric entangled pair states, which can be mapped straightforwardly onto unitary circuits [2]. Additionally, we will explore variational optimisation strategies of circuit elements to reduce required circuit depths relative to direct implementation of Hamiltonian

functionals [3]. To address a wider range of models, we will draw on the notion that duality transformations can be used to reduce the amount of entanglement [4], and thus potentially required circuit depths. We will tap into local expertise on dualities at Kent [5] to design circuit representation of duality transforms and explore their potential for designing efficient quantum

simulations of 2d materials.

- Barratt, F. et al. Parallel quantum simulation of large systems on small NISQ computers. npj Quantum Information 7, 1–7 (2021).
- Wu, Y., Anand, S., Lin, S.-H., Pollmann, F. & Zaletel, M. P. Two-dimensional isometric tensor networks on an infinite strip. Phys. Rev. B 107, 245118 (2023).
- Causer, L., Jung, F., Mitra, A., Pollmann, F. & Smith, A. Scalable simulation of non-equilibrium quantum dynamics via classically optimised unitary circuits. Preprint at http://arxiv.org/abs/2312.14245 (2023).
- Lootens, L., Delcamp, C., Ortiz, G. & Verstraete, F. Dualities in One-Dimensional. Quantum Lattice Models: Symmetric Hamiltonians and Matrix Product Operator Intertwiners. PRX Quantum 4, 020357 (2023).
- Moradi, H., Moosavian, S. F. & Tiwari, A. Topological holography: Towards a unification of Landau and beyond-Landau physics. SciPost Phys. Core 6, 066 (2023).

*Supervisors: Dr Adrian Bradu (School of Physics and Astronomy) and Professor Andrew Hone (School of Mathematics, Statistics and Actuarial Science)*

Optical Coherence Tomography (OCT) is a noninvasive imaging technology allowing micron-resolution 3D imaging of biological tissues without physical contact. Unfortunately, the development of instruments capable of producing images with a resolution below 1 micrometre has stopped due to technical difficulties in manipulating the ultrawide spectra required to achieve high resolutions. The theory suggests that Quantum Optical Coherence Tomography (QOCT) can improve this resolution by a factor of two, significantly reducing dispersion and improving the images' sensitivity.

To some extent, the existing QOCT technique is equivalent to the classical time-domain OCT implementation because the mechanical scanning of the reference mirror senses the position of a scattering object within the sample. Since the coherence length of the biphotons used in QOCT is short, interference occurs only when the optical paths in the arms of the interferometer are equal, which is manifested as a peak or a dip in the measured dependence of the joint photon detection probability with the optical path difference between the arms of the interferometer. The main issue of this approach, as well as of the classical time-domain OCT, is the necessity of introducing mechanically scanned elements in the setup, which reduces the accuracy, sensitivity, and speed of the measurements.

**Objectives of this PhD project:
**

- Firstly, it aims to develop a theoretical model of a new quantum OCT approach that doesn't involve any moving parts. The strategy involves spectral tuning a source of biphotons. This approach is equivalent to the classical spectral domain OCT method.
- Secondly, building on the Applied Optics Group's existing equipment and expertise, the project will devise an experimental setup for a QOCT instrument to prove the theoretical model's findings.
- Thirdly, it aims to use the theoretical and experimental findings to extend the existing software procedures developed in the Applied Optics Group in classical OCT to create its equivalent QOCT procedures.
- Fourthly, the project will perform metrological characterisation of all relevant parameters of the images obtained and quantify the QOCT advantage over classical OCT.
- Finally, the developed instrument will be used to produce quantum optical biopsies of biological samples, including in-vivo retinal images. These images will then be compared with classical OCT images to evaluate the effectiveness of the QOCT approach.

Supervisors: Dr *Ana
Loureiro and **Professor Andrew Hone (School of Mathematics, Statistics and Actuarial Science)*

Quantum harmonic analysis (QHA) is the analysis of operators for time series analysis and signal processing. Modern industrial processes produce a vast amount of data in the form of time series, whether it be in manufacturing, communications technology, environmental monitoring, or the development of sustainable energy sources. Functional data analysis is a popular approach to capturing the properties of time series, taking into account that most of the processes considered are time dependent. Representing functional data raises many challenges, due to the requirement of considering infinite-dimensional function spaces.

To analyse the time-frequency content of functional data, one must address cross-correlation of the time-frequency content of data points. The most commonly used techniques involve spectral decomposition (based on classical harmonic analysis), especially time-frequency methods or functional principal component analysis (PCA). In contrast, QHA involves analysing operators on Hilbert spaces defined by integral transforms (reproducing kernels): it allows the classical notion of Fourier transform to be extended to operator algebras, with a corresponding concept of convolution between a pair of operators.

There is a clear advantage of using QHA as an alternative to time-frequency method analysis or functional PCA: it provides a data set-specific, stable representation of functional data. Moreover, taking an operator convolution in QHA permits an effective approach to data augmentation, whereby an initial data set can be expanded with synthetic data to produce a data set that is more realistic and/or more robust under small perturbations: this is useful e.g. in processing audio signals, where the basic features of the data should not be affected by small shifts.

The project will use QHA to analyse particular data sets from existing industrial colleagues working on large-scale simulation, and new industrial collaborations are expected to result.

*Supervisor: Carlos Pérez Delgado (School of Computing)*

In an effort to stave off a repeat of the "software crisis" of the 1960s, researchers have recently begun developing the field of quantum software engineering (QSE). If software engineering is, as defined by the IEEE, "the application of a systematic, disciplined, quantifiable approach to the development, operation, and maintenance of software, as well as to the study of these approaches; that is, the application of engineering to software," then quantum software engineering is the application of engineering to the development, operation, and maintenance of quantum software.

The goal of the student will be to help develop tools,
techniques, and methodologies for the development, operation and maintenance of
quantum software. The student will join a world-leading research group in QSE,
behind the development of the Q-UML quantum software modelling language, and
the Q-COSMIC standard metric for quantum software sizing.

The University of Kent is currently one of the leading research hubs for quantum software engineering. It is part of the Hub for Quantum Communication.

Home and International candidates are welcome to apply. Full international tuition fees will be waived for this project.