See below for a list of this year's industrially co-supervised and co-sponsored PhD projects.

## Experimental Projects

#### QMO2401: Spin qubits in silicon MOS devices - Quantum Motion

- Location: Quantum Motion (London)
- Employer Supervisor: Fernando Gonzalez-Zalba / Alberto Gomez-Saiz / David Wise
- UCL Supervisor: John Morton / Andreas Demosthenous

Silicon-based approaches to quantum computing offer advantages such as high qubit density, record qubit coherence lifetimes for the solid state, and the ability to leverage the advanced nanofabrication methods of CMOS technologies. Two-qubit gate fidelities for spin qubits in silicon now exceed 99.5% and registers of up to 6 qubits have been made so far. By integrating CMOS quantum devices on-chip with ‘classical’ digital and analogue electronics, arrays of up to 1024 quantum dots have been addressed and rapidly characterised in just 5 minutes. These advances open up many exciting research opportunities for spin-qubits based on silicon MOS (metal-oxide-semiconductor) devices, fabricated using the same processes used routinely across the IC industry today. A PhD on this topic could take one of several directions, depending on the background of the candidate. A project could involve: 1) working with Quantum Motion’s IC team on the design and test of CMOS circuits and devices at cryogenic temperatures - for this project, experience in device validation and/or analogue circuit design would be beneficial; 2) working with the Intelligent Automation team on the automated tune-up of quantum dots in multi-gate QD arrays - for this, a basic understanding of machine learning techniques would be helpful; 3) working with the Quantum Hardware team to measure qubit properties such as single- and multi- qubit gate fidelities, understand their relation to device design, and help validate and refine fault-tolerant architectures based on spin qubits in silicon.

This project would suit a student reading Physics, Electrical Engineering, or a related subject in Engineering / the Physical Sciences. Particular experience of relevance will depend on the direction the student would like to take in the PhD project - understanding and/or experience in at least one of the following topics would be beneficial: quantum computing, measuring quantum devices, cryogenic measurements, analogue circuit design, machine learning, microwave engineering.

#### TOS2401: Semiconductor quantum light sources at telecom wavelength for quantum communication networks - Toshiba Europe

- Location: Toshiba Europe (Cambridge)
- Employer Supervisor: Andrea Barbiero
- UCL Supervisor: Paul Warburton

Quantum networks, where information is encoded in single and entangled photons and transmitted over long distances through optical fibre, have the potential to transform secure communication and distributed quantum computing. To enable this vision, new hardware is required. This includes devices known as quantum light emitters, which provide the telecom wavelength photonic qubits to carry quantum information across optical fibre. Semiconductor quantum dots (QDs) are considered one of the most promising candidates for the development of those emitters thanks to their ability to generate single and entangled photons on demand in a wide wavelength range. However, many challenges remain, including efficient extraction of every photon to maximise quantum bit rates, high coherence to enable strong photon-photon interactions, and deterministic integration of QDs in optimized photonic structures to further improve and tailor their emission properties while maximizing the fabrication yield and scalability. The combination of all these desirable features is challenging and has not been reported so far. The project will be part of the activities of the Quantum Information Group of Toshiba Europe Limited based in Cambridge, exploring the deterministic integration of QDs in optimised nanophotonic devices for the development of quantum network ready photon emitters at telecom wavelength. The experimental activities will initially focus on the design, fabrication, and optimisation of semiconductor nanophotonic devices. After producing optimal quantum light emitters, the student will work on their integration into fibre-connected systems, and into a fibre-based network connecting multiple nodes. The student will be part of an experienced and supportive team of scientists, with day-to-day lab supervision and the chance to interact with external partners in industry and academia.

We are seeking passionate applicants holding (or expecting to receive) a first-class or upper second-class degree in Physics, Electronic Engineering, or a similar subject. A background in optics, semiconductor physics, or quantum physics is preferable. Candidates should demonstrate familiarity with a programming language for data analysis (e.g. MATLAB or Python) and the desire to work collaboratively in a multidisciplinary team undertaking cutting-edge experimental research.

#### UNQ2401: Networked multi-module trapped ion quantum computing - Universal Quantum

- Location: Universal Quantum, Brighton
- Employer Supervisor: Winfried Hensinger
- UCL Supervisor: TBC

A modular quantum computer architecture is of critical importance for the development of practical quantum computers as it is impossible to fit sufficiently many qubits on a single quantum computing module. We recently succeeded in demonstrating a new modular quantum computing architecture based on electric field links between quantum computing modules. We managed to demonstrate a connection rate of 2423 1/s with a success fidelity of transporting ions from one module to another of 99.999993% both values constituting world records in transmission speed and fidelity. We showed that the link does not measurably impact the phase coherence of the qubit making use of a Ramsay experiment. Our measurement places an upper bound on loss of phase coherence per link of 5x10-4 (Nature Communications 14, 531 (2023)). The actual infidelity is expected to be orders of magnitude lower evidenced by other more precise measurements carried out for linear ion transport. The microchips in this setup also contains current carrying wires which permit the creation of strong magnetic field gradients on the surface of the microchip. While previous experiments were limited to a two qubit-gate fidelity of 98.5% because of the magnetic field gradient of only 24 T/m, our chip can produce up to 150 T/m (Quantum Sci. Technol. 7, 034003 (2022)), enabling entangling gates with fidelity above the relevant fault-tolerant threshold. As part of this project, the student will demonstrate a fully networked multi-chip quantum computer performing all relevant operations on the device. This demonstration will include the realization of high-fidelity two-qubit gates on a chip, ion transport, including the demonstration of diabatic ion transport between the two quantum computing modules along with a full characterization of entanglement that can be generated across two quantum computing microchips. We will carry out a universal set of quantum computing operations in order to qualify the prototype device as a fully programmable multi-module quantum computer.

Student interested to learn a broad set of skills who is interested in an experimental project.

## Non-experimental Projects

#### BLU2401: Characterization of hardware-induced noise in superconducting qubits - Bluefors Oy

- Location: Bluefors, Helsinki
- Employer Supervisor: Massimo Borrelli
- UCL Supervisor: Paul Warburton

Superconducting qubits have emerged as the dominant platform for quantum computing, quantum sensing, and fundamental research. Their operability requires however stable millikelvin temperatures to limit the amount of both classical and quantum noise resulting in relaxation and decoherence. While chip-design and fabrication methods affect the qubit quality, the surrounding cryogenic infrastructure has an immense impact on qubit controllability. Most importantly, understanding how the I/O control system hardware introduces losses and imperfections within the sample space is of paramount importance regardless of the type of quantum processor unit. The Quantum Applications Department at Bluefors has an active and ongoing program on optimization of control and measurement of superconducting qubits. We are looking for a highly motivated PhD candidate to perform research in the following areas of focus:

- Detailed modelling and characterization of drive lines and drive line noise using tools of microwave engineering, RF simulations and measurements.
- Integration with models from quantum information and open quantum systems theory and related simulation tools, e.g., QuTip, to create a holistic description encompassing quantum and classical physics.
- Development of diagnostic tools for noise characterization, power sensing and amplification, and RF components for applications in quantum science.

The core of the research work will be predominantly theoretical and computational, although the candidate will be advised to learn and carry out some experimental work also. Moreover, participation to international conferences and schools will be strongly encouraged. The main place of work will be Bluefors headquarters in Helsinki (Finland).

We are looking for the following set of skills. Must have: A solid knowledge of quantum theory and good knowledge of superconducting qubits. Solid skills in mathematical and numerical modelling. Good knowledge of standard Python libraries; knowledge of QuTip is a big plus. Nice to have: Some knowledge of microwave theory and/or RF design is a big plus. Some knowledge of cryogenics is a big plus. Some lab experience is a nice-to-have. Good communication skills. Good writing and presentation skills.

#### PHA2401: Achieving large scale quantum algorithms by divide and conquer - Phasecraft

- Location: Phasecraft (London or Bristol)
- Employer Supervisor: Raul Santos Sanhueza
- UCL Supervisor: Toby Cubitt

Quantum simulation of materials or long-time quantum dynamics require simulating systems with increasing number of qubits or time to achieve accurate predictions, which make them challenging to implement on near-term, small-scale quantum devices. This project will explore and extend a number of techniques (such as circuit knitting [1,2], entanglement forging [3] or perturbative quantum simulation [4]) aiming to cut down the size of quantum circuits into smaller subcircuits by exploiting the structure of quantum simulation of local physical Hamiltonians. This will include building an understanding of the relationship between the classical complexity of said techniques and the physical properties that relate to it. In this project the conditions to reconstruct efficiently the expectation of an observable from the classical post-processing of each subcircuit’s prediction will also be investigated. Given that said conditions can be satisfied by controlling the amount of entanglement being generated, the project will investigate a number of candidates where it is expected they can be obtained. Natural candidates would include systems with low entanglement growth, or focusing on perturbative simulation where the strength of the perturbation introduced over solvable states is controlled.

[1] S. Bravyi, G. Smith, and J. A. Smolin. Trading classical and quantum computational resources. Phys. Rev. X, 6:021043, 2016. DOI: 10.1103/PhysRevX.6.021043.

[2] T. Peng, A. W. Harrow, M. Ozols, and X. Wu. Simulating large quantum circuits on a small quantum computer. Phys. Rev. Lett., 125:150504, 2020. DOI: 10.1103/PhysRevLett.125.150504.

[3] A. Eddins, M. Motta, T. P. Gujarati, S. Bravyi and A. Mezzacapo. Doubling the size of quantum simulators by entanglement forging. PRX Quantum 3 (2022) 010309. DOI:10.1103/PRXQuantum.3.010309

[4] J. Sun, S. Endo, H. Lin, P. Hayden, V. Vedral, and X. Yuan. Perturbative Quantum Simulation Phys. Rev. Lett. 129, 120505 2022. DOI:10.1103/PhysRevLett.129.120505

Strong background in theoretical physics, theoretical computer science, or mathematics. Some knowledge of theoretical condensed matter physics is desirable (but not a necessary requirement)

#### PHA2402: Fermionic Code Deformation and Gauge Fixing - Phasecraft

- Location: Phasecraft (London or Bristol)
- Employer Supervisor: Joel Klassen
- UCL Supervisor: Lluis Masanes

A necessary step in the simulation of materials on quantum computers is an encoding of fermions into qubits. Typically the choice of encoding is made at the compilation step, and this choice remains fixed during the course of quantum computation. This project aims to explore the algorithmic benefits that may be gained by allowing an active deformation of the fermionic code during the course of the computation. A simple example of this is a fermionic swap network, wherein the mode ordering convention of the particular encoding is actively modified during the course of the circuit. However more sophisticated protocols are possible wherein the stabilizers of the encoding undergo active transformations for the purposes of achieving more efficient circuit operations. The mathematical form of these kinds of transformations has strong parallels with existing methods related to code deformation and gauge fixing, and I expect these mathematical methods can be transferred with minimal modification. The project would begin by a study of a concrete case of fermionic code deformation related to routing simple stabilizers -- coined "fermionic wormholes" -- with the aim of delineating the domain of their practical applicability. The project would then proceed by trying to generalize these methods with the aid of existing literature on gauge fixing and code deformation.

Strong background in theoretical physics, theoretical computer science, or mathematics.

#### PHA2403: Quantum Enhanced Simulation of Materials- Phasecraft

- Location: Phasecraft (London or Bristol)
- Employer Supervisor: Glenn Jones
- UCL Supervisor: Toby Cubitt

Classical materials simulation has a number of limitations when considering the complex interactions present between electrons. Development in the field of quantum computing algorithms are close to the point where early demonstrations of simulation on materials are possible. These new approaches can help us tackle classical challenges, ranging from a poor description of band gaps in metal oxides (battery and catalysis applications), to incorrect prediction of material surface properties. This PhD will work on state-of-the-art developments in the field of quantum simulation of materials and will apply these upcoming algorithms to some of the first simulations of their kind.

Strong background in theoretical physics, theoretical computer science, or mathematics. Some knowledge of theoretical condensed matter theory beneficial (but not a requirement).

#### PHA2404: Fault-resilient quantum algorithms - Phasecraft

- Location: Phasecraft (London or Bristol)
- Employer Supervisor: Toby Cubitt
- UCL Supervisor: Lluis Masanes

The biggest current obstacles to practical quantum computation are errors and noise. Although we have known since the 1990s that, theoretically, fault-tolerant quantum computation provides a solution, the overhead in terms of the number of gates and qubits is prohibitive. Thousands or of qubits and gates would be required to implement even a single fault-tolerant gate. Recently, I showed that there are certain quantum algorithms that are inherently fault-resilient: the output is guaranteed to be close to the correct state even in the presence of noise and faulty gate implementations, but without requiring any overhead. Currently, the known fault-resilient algorithms are not practical. The aim of this project is to develop the nascent theory of fault-resilient algorithms, and apply it to practical algorithms that would be suitable for implementation on current or near-term quantum computing hardware.

Strong background in theoretical physics, theoretical computer science, or mathematics.

#### RIV2401: Efficient approaches to higher accuracy decoding for quantum error correction – Riverlane

- Location: Riverlane (Cambridge)
- Employer Supervisor: Earl Campbell
- UCL Supervisor: Dan Browne

Higher accuracy decoders lead to higher error correction noise thresholds. While qubits are still noisy, higher accuracy decoders are crucial for realising sub-threshold QEC experiments. Longer-term, higher-accuracy decoders can reduce the number of qubits needed to reliably execute quantum algorithms. This PhD project aims to develop new decoders with higher accuracy while keeping them efficient in terms of running time and memory resources. Existing decoders like MWPM and Union-Find are very fast, but not so accurate. In contrast, tensor-network decoders have optimal accuracy, but are very inefficient and are too slow beyond 49 qubit QEC codes. There are a variety of two-stage belief-propagation algorithms, such as belief-matching and BP-OSD, which achieve higher accuracies and are more scalable than tensor-network decoding. Experimenting with different two-stage approaches to belief propagation will be the project’s starting point. Other ways to boost accuracy include using extra (beyond binary) measurement data such as “soft” or “leakage” information. Riverlane collaborates with several world-leading hardware companies providing theory support on their QEC experiments, and there will be opportunities to run your decoders on experimental data. Riverlane also works on building hardware decoders based on FPGAs and ASICs. If the project yields any innovations that are suitable for hardware, this is an additional avenue for expanding the project.

Undergraduate degree subject can be physics, mathematics or computer science. Abstract reasoning and strong computational skills both essential for this project.