DrZhenyu Cai

Quantum computers promise profound advantages over conventional computers in applications like chemistry simulation, decryption, and machine learning. However, they are also much more susceptible to errors arising from imperfect manipulation and unwanted interaction with their surroundings. Indeed, these errors are the main obstacles preventing us from achieving quantum advantage — a milestone where quantum computers outperform traditional computers in practical tasks. Quantum error correction (QEC) is the canonical way to tackle these errors. It employs additional qubits to encode and protect the quantum information, offering a robust solution but at the cost of substantial hardware resources. Quantum error mitigation (QEM), on the other hand, uses additional noisy circuit runs to probe the damages caused by the noise in order to reverse them. The hardware requirement of QEM is low, but it cannot be scaled to arbitrarily large computations if applied alone. With the recent rapid advance of quantum hardware, two pivotal milestones lie ahead: the practical application of noisy intermediate-scale quantum devices using QEM, and the experimental validation of full QEC for long-term scalability. My research will centre around these two critical goals and beyond, developing a comprehensive error suppression framework incorporating both QEC and QEM to pave the way towards noise-resilient quantum computation. My project will start with designing a fundamental framework for QEM in the same spirit as those that existed in QEC. Such a framework can inspire novel constructions of QEM and QEC methods, with the help of the new space-time perspective on QEC. Recognising that QEC and QEM will co-exist for the foreseeable future to provide maximal error suppression power, I will explore the advantages of their combination. For different error suppression techniques, I will design bespoke quantum processor architectures taking into account the hardware constraints, and explore the possibility of tailoring a given error suppression scheme towards the hardware platform or optimising it accordingly for different applications. Zooming down to the lowest hardware level where a qubit is defined, I will look into the advantages of co-designing the qubit alongside the error suppression schemes. Another crucial aspect of error suppression is understanding the noise profile in a device, which I will refine by adapting noise characterisation protocols towards the QEM/QEC schemes on top, with the help of shadow tomography techniques. All of the novel error suppression schemes that I developed will be tested and validated in experiments via academic and industrial collaborators. At the end of this project, having worked on error suppression across different layers in the quantum computation stack, we can compile the results we have obtained into the first instance of a full-stack optimised error suppression strategy for a specific application scenario and hardware platform, and calculate the corresponding performance improvement and resource reduction achieved. Ultimately, my long-term vision is to generalise this instance into a full-stack error suppression pipeline for quantum computation that can automatically generate the optimised error suppression schemes for different hardware and tasks, ensuring reliable and scalable quantum computation in a wide range of use cases. This is of course a very challenging goal, but such a bespoke optimised error suppression strategy is a critical step towards finally unlocking the true potential of quantum computation for real-world applications.

The project Software Enabling Early Quantum Advantage (SEEQA, pronounced 'seeker') is a joint effort by Oxford, UCL, and Bristol, supported by multiple UK quantum startup companies and NQCC. The aim is to make the era of "quantum advantage" arrive sooner! "Advantage" means having real working quantum computers that can perform tasks that are either impossible, or prohibitively slow or expensive, by any conventional means. We'll know this era has arrived when we can solve otherwise-infeasible tasks in areas such as chemistry and materials discovery or in solving complicated resource allocation problems with near-zero waste. Although quantum computers have long promised this kind of advantage, it has not yet been realised. There are many reasons -- partly it is just that the prototype hardware needs more time to mature. But progress needs to be made in the practical theory to support quantum computing, to 'lower the bar' that the hardware needs to be able to reach. This is what SEEQA will do, in three main themes: 1. Figuring out how best to use state-of-the-art conventional computing power to help early quantum computers. There are two main ways: First, the conventional computers can actually help run the task that the quantum computer is performing. The task gets broken up into lots of small quantum computations, and the conventional computer gets all the results and puts them together to decide what to do next. The other way a conventional computer can help is by monitoring the quantum processor for errors: there is some detective work to do in order to infer the nature of the errors from the evidence that comes from monitoring, and a conventional computer needs to do this -- it's called decoding. 2. Coming up with new ways in which to handle or suppress errors. As mentioned, quantum computers (especially the early ones) suffer from 'noise' which means little imperfections in everything that is done. If not handled, the resulting errors will lead to useless outputs. There are many ideas for fighting errors, but SEEQA will address new possibilities. In particular, SEEQA will investigate the interface between two major approaches to find new solutions: The approaches are called Quantum Error Mitigation (QEM), which suppresses error damage, and Quantum Error Correction (QEC) which can totally fix errors but is currently very expensive in terms of number of components needed. Also, SEEQA will explore and advance some of the more recent and sophisticated ideas for handling measurement errors -- if you can't trust the output of the quantum computer you are very limited! 3. Finally, SEEQA will focus on the interrelationship between the architecture or protocol we would like to perform, and the available hardware architecture (including noise sources and other imperfections, the 'topology' which means the question of which qubits can directly 'see' other qubits, and so on). Although quite a bit is known about this, there remain a great many questions within the two themes (a) "what algorithms can run well on my architecture?", and (b) "what architectures can my algorithm run on?" Underpinning all this theoretical research, it will be vital to be able to test things out. The SEEQA project will have two kinds of provision: First, very efficient software that runs on conventional computers to 'pretend' to be quantum computers - exactly simulating them using the well-known laws of quantum physics. However it will only ever be possible to work with small emulated quantum computers because the quantum state is so complex. So it is vital that SEEQA also has access to real prototype quantum processors -- and as many as possible because they are various types. Fortunately SEEQA has multiple letters of support, offering resources approaching £500k, from pioneering UK hardware companies that have working quantum prototypes right now. They will make available their experts and their devices to SEEQA in order to help us to succeed.