The principal field of quantum-information processing is quantum computing. The UK government has identified quantum computing as a priority and has promoted the country as a scientific superpower in quantum computing. As is tradition, the University of Cambridge has played a pivotal role in the development of the field. In 1992, Prof. Richard Jozsa (now at DAMPT) kick-started the field by proving the first quantum algorithm with an exponential speedup compared to its classical counterpart. Moreover, today’s leading qubit technology is based on Prof. Brian Josephson’s Nobel-Prize awarded work at the department. Current theoretical research in the field is largely centred around the development of quantum machine-learning algorithms, quantum simulation algorithms, fault-tolerant quantum computing and noisy intermediate-scale quantum (NISQ) computing. Recent years have seen an increasing interest in verification procedures for quantum computers. Enormous efforts are put in demonstrations of practical advantages of quantum computers, with the latest milestone achievement being Google’s 2019 *Nature* paper ‘Quantum supremacy using a programmable superconducting processor’. Theoretical questions regarding actual advantages of quantum algorithms are also under international scrutiny, amplified by the discovery of classical versions of, for example, the Harrow-Hassidim-Lloyd (HHL) algorithm and its derivatives. With the steady improvements of experimental quantum-computing systems, there is increased research into device-tailored methods for error correction and error mitigation. Within the next decades we will see a steady transition from classical computing to quantum computing, likely to revolutionise big-data problems and machine learning, as well as the simulations of physical systems. Chemically accurate quantum simulations of smaller molecules are within reach of current technologies.

The Cavendish Quantum Information group is currently working on various aspects of quantum machine learning and quantum algorithms. The group published the first methodologies for conducting generalised measurements in spin-based and gate-based quantum computers, an essentiality for many quantum-computing algorithms and quantum cryptography protocols. The group has developed state-of-the-art algorithms for quantum computational chemistry. The group’s algorithm for variational quantum eigensolver (VQE) chemistry calculations is, to this day, the most CNOT-efficient. In a collaboration with MIT, the Cavendish QI group has been developing exponentially faster quantum algorithms for the polar decomposition, a crucial component to quantum machine learning.

The group has received several EPSRC grants, industry funding, and Horizon 2020 funding to construct world-leading GPU servers for accurate real-space simulations of wave functions in realistic quantum potentials. In collaborations with industry (Hitachi Ltd) and experimental groups at the University of Grenoble and the University of Vienna, these GPU servers have been used to produce guiding simulations. The simulations have enabled, for example, the first experimental demonstration of a surface-acoustic-wave-driven single-electron directional coupler. Using GPU-accelerated high-performance computing, the group has designed device-specific protocols for entanglement generation between electron-spin qubits in semiconductor heterostructures. The simulation software is being continuously updated and further developed to improve performance and handle other interesting cases, such as topological insulators. Experimental groups working on quantum devices are welcome to submit proposals for joint projects where our group can provide state-of-the-art simulations of dynamics in realistic potentials.

Experimental work in the group investigating the interplay of magnetism and topology has important implications for quantum information processing. Using molecular beam epitaxy (MBE), the group is able to grow high quality thin films of topological insulators (TIs), a state of matter where the topology of the electronic band structure protects electrons from backscattering. The introduction of magnetism into this system unlocks an even more exotic state, known as the Chern Insulator, which is the only platform that can realise the quantum anomalous Hall effect (QAHE), that is the quantum Hall effect at zero external magnetic field. This state, when interfaced with a proximate superconductor, is a prerequisite for the elusive chiral Majorana edge mode, a particle that as its own antiparticle that can be exploited for use in fault tolerant, topological quantum computation. Using a custom-designed MBE chamber to grow these magnetic TIs, the group will grow high quality wafers that can be used in the processing of devices to realise a more stable QAHE at higher temperatures, a task that has so far proven extremely challenging. The group is also ideally set up to process and characterise such devices, using low-temperature electrical transport and non-invasive magneto-optic Kerr effect (MOKE) measurements, conducted with a probe designed and built by members of the group.

Performing molecular simulations with a variational quantum eigensolver (VQE) is a new field in quantum computation that was prompted by the emergence of noisy intermediate-scale quantum (NISQ) computers in the past decade. A VQE is a hybrid classical-quantum algorithm that, compared to other purely quantum algorithms, is more noise resistant and error tolerant. VQEs are suitable for implementation on early quantum computers. Simulations of small molecules, like nitrogen and water, are within reach today. In the next 5 years, given the steady growth in the size of the NISQ computers, we expect to see the first demonstration of practical quantum advantage. Using a VQE, it will be possible to simulate molecules that cannot be simulated by classical computers. This will unlock a number of applications based on VQE algorithms for simulating molecular and crystal systems used in chemistry, material science, and drug synthesis. An example of such an early application for VQEs is the simulation of the iron molybdenum cofactor molecule. A better understanding of this molecule is the key to optimising the production of ammonia for fertilisers, which currently consumes nearly 2% of the world’s energy output.

Numerical simulations of few-particle quantum systems are invaluable tools that can help guide experiments and explore fundamental theory. Behaviour of complex quantum systems with realistic experimental potentials are impossible to solve theoretically. Numerical simulations, however, can give us approximate solutions. With recent advances in graphics processing units (GPUs), which are perfectly suited for the task of physics simulations thanks to their parallel computing performance, it is now possible to simulate two or three particles in three dimensions on hundreds of lattice sites per dimension, which is a necessary condition for accurate results. This enables the investigation of many interesting physical problems, for example, the interactions between electrons confined to a two-dimensional electron gas, which could be used for quantum computing operations. The capability to investigate complex quantum systems will grow as new GPU hardware is developed. Examples of relevant research areas are semiconductor quantum devices, topological insulators, superconducting qubits, Majorana zero modes, and photonic circuits. As quantum computing develops rapidly, basic single- and two-qubit operations for novel implementations can be simulated.