Research interests within the group span many areas of theoretical quantum information science. However, there are several areas which are of mutual interest to a significant number of group members.
The realisation that quantum systems can be used to encode information has lead to a revolution in the way we think about the limits of information processing, and in no area is that more clear than cryptography. While quantum cryptography is often used as a synonym for quantum key distribution, our research interests focus on quantum cryptography beyond key distribution. Quantum information techniques allow for a wide range of information theoretically secure cryptographic protocols for tasks which can either be accomplished with only computational security or cannot be accomplished at all using purely classical techniques.
Cryptographic interests within the group focus on problems associated with distributed computing, such as blind quantum computation, verified computation, homomorphic encryption systems and anonymous communication.
Architectures for quantum computation
Large scale quantum computers, if built, would offer tremendous computational speed-ups over classical algorithms for a range of problems, such as quantum simulation and integer factorization. However, before large-scale quantum computers become a reality, there are a number of challenges which must first be overcome. A wide variety of candidate systems have emerged which can be shown to support quantum information processing for a few qubits, but each has its own advantages and disadvantages. Systems which allow easy manipulation of individual qubits are often difficult to entangle, while systems with strong interactions often prevent direct addressing of individual qubits. Similarly, systems which can easily be measured also tend to decohere rapidly, where as systems which remain coherent for long periods are often difficult to measure or cool.
Within the group we are interested in developing new techniques for overcoming the barriers to scalable quantum computing. This research both includes developing techniques to overcome control limitations in quantum systems, by developing global control schemes which allow manipulation of individual qubits even when they cannot be addressed directly and by developing optical techniques to entangle non-interacting systems through measurement, and techniques for correcting for random errors occurring during computation using quantum error correction and fault-tolerance techniques.
Measurement-based quantum computation
Measurement-based quantum computation (MBQC) is a fundamentally quantum model of computation. In an MBQC, the computation is performed by making sequential and adaptive measurements on a fixed entangled quantum state. Since it is inherently reliant on entanglement to function, there is no direct classical analogue of the measurement-based model of computation, and hence MBQC provides a useful tool with which to view computational problems. Indeed, such an approach has already lead to significant advances in blind computations protocols, most of which are now measurement-based. MBQC also offers substantial advantages from an architectures point of view, since to implement a measurement-based computation, no entangling gates are necessary once the initial resource state has been created.
Within the group we are interested in almost every aspect of measurement-based computation. On the practical side, we are interested in architectures for implementing measurement-based computations and have developed techniques for growing resource states even in the presence of errors and failed entangling operations. We are also interested in more theoretical properties of MBQC, such as entanglement in cluster states and the flow and generalized flow structures which underly measurement orderings in deterministic measurement-based computations. Lastly, we are interested in using techniques from MBQC to develop new computational and cryptographic techniques.
Metrology is the art and science of measurement. All scientific endeavours begin and end in measurements. Measurements are how we know what the world looks like, and how it behaves. They are how we know the results of our computations, and how Bob acquires the messages sent by Alice. Unlike in the classical world, quantum mechanics imposes limitations on the precision of measurements even in the absence of noise. However, quantum states also allow for far more precise measurements than are possible using separable measurements, allowing us to surpass the shot noise limit. By studying quantum metrology we aim to not only uncover these fundamental limits, but also to develop techniques capable of making measurements which achieve this level of precision.
Within the group our research interests in metrology encompass many areas of quantum metrology. From a fundamental point of view, we are interested in the ultimate limits of precision both in noisy and noiseless systems. From a practical point of view this encompasses applications such as quantum illumination and imaging, single spin amplification, optical phase estimation and magnetic field measurements.
Quantum information theory
Reliable information transmission is an important building block in the design and construct of large scale quantum computers, systems and networks. In quantum information theory, we study variations on the problem of reliable information transmission, typically with a physical scenario in mind. Much of the analysis deals with the formal mathematical notion of quantum states, channels and various types of entropies. Typical quantities that we investigate are bounds on the rates of reliable transmission under different physical settings.