Emulation and optimisation of circuits for quantum simulation

Quantum computers are expected to provide an exponential speedup over traditional computers in performing certain tasks. As experimentalists begin to build prototype devices, it would be useful to be able to benchmark and verify them against simulations run on classical computers, but the purported exponential advantage of quantum computation presents an obvious practical barrier to doing so. On the other hand, it is known that a restricted class of quantum circuits, known as stabiliser circuits, can be efficiently simulated using only classical computational resources. It is expected that the classical simulation cost for more general quantum circuits will be in some sense exponential in the amount of non-stabiliser operations required. Related is the magic state model of quantum computation, where non-stabiliser resource states known as magic states are "injected" into a circuit in order to implement non-stabiliser operations. In many schemes for fault-tolerant quantum computation, the requirement for highly pure magic states produces a large experimental overhead whenever non-stabiliser operations are needed. It is therefore desirable to rigorously quantify the non-stabiliser resource involved in a given circuit. Earl Campbell and Mark Howard at the University of Sheffield previously developed a resource theory of non-stabiliser states based on a measure called robustness of magic. For those operations that can be implemented using magic state injection, the theory immediately yields a means to quantify their classical simulation overhead. Only certain operations can be implemented in this way, however, and it is less clear how best to quantify the non-stabiliser resource involved in more general circuits. The current focus of my project is to extend the framework to deal with general quantum operations. Longer term, we hope to use insights from this work to develop improved algorithms for simulating general quantum circuits, and to optimise circuit design to consume less non-stabiliser resource. We believe that the scenarios where these techniques might be most usefully applied include noisy quantum devices and certain quantum chemistry simulations.

Quantum technologies promise a transformation of the fields of measurement, communication and information processing. They present a particular opportunity since they are disruptive technologies: not only do they offer a chance for rapid growth but they also allow lesser participants in a field (such as the UK in IT) to become major players through appropriate risk-taking and manpower development. Students graduating from the InQuBATE Skills Hub will have the right mindset to work in the industries where quantum technologies will be applied, and help to break down the traditional barriers between those sectors to make this transformation happen. They will have all the necessary technical and transferable skills, plus a network of contacts with our partners, their fellow cohort members and the academic supervisors.

Our commercial partners are keen to help our students realise their potential and achieve the impact we expect of them, through the training they offer and their contributions to the centre's research. They include companies who have already developed quantum technologies to products in quantum communication (Toshiba) and optimization (D-Wave), large corporates who are investing in quantum technology because they see its potential to transform their businesses in aerospace, defence, instrumentation and internet services (Lockheed Martin, Google,) and government agencies with key national responsibilities (NPL). We want to see the best communication of our students' research, so our students will benefit from the existing training programme set up with a leading scientific publisher (Nature Publishing Group); we also want to see more of the future companies that lead this field based the UK, so we have partnered with venture capital group DFJ Esprit to judge and mentor the acceleration of our students' innovations toward the market.