Measurement-based quantum computing and its relation to other quantum models

Lead Research Organisation: University of Edinburgh
Department Name: Sch of Informatics

Abstract

My research proposal focuses on the field of quantum computation and information theory, a rapidly growing cross-disciplinary field of great importance from both a fundamental and technological perspective. As predicted by Moore's law, the miniaturisation has been the key element in the highly successful quest for more powerful information processing devices in the recent decades. However these advances reach now a fundamental limit where one can no longer ignore microscopic quantum phenomena, and needs quantum engineering to take the challenge.Fortunately, various physical implementations bring quantum computers closer to a reality, while theoretical results exhibit several remarkable advantages of quantum computers over classical ones. It has been predicted that any large-scale overhaul of information science in the 21st century will have to include quantum information. This is evident from the launch of start-up companies which conduct research on quantum information processing such at Quantique, MagiQ and D-Waves, as well as from the creation of quantum research teams within well established firms such as IBM, Microsoft and HP.This research proposal specifically targets a novel form of quantum information processing, called measurement-based quantum computing (MQC), where the key twin notions that distinguish quantum information processing from its classical counterpart, that is Entanglement (creating non-local correlations between quantum elements),and Measurement (observing a quantum system), are the explicit driving force of computation. Such a new paradigm has been so far mainly investigated by physicists with a specific focus on implementation, involving many research groups in UK. I propose to investigate the more computational and mathematical sides, and exploit the main characteristic of this model, namely that any computation can be broken down into a round of global operations (involving more than one quantum element), and a subsequent round of only local ones (together with classical communication). This has potential consequences in the particular questions I wish to address: what is the depth complexity of such computations (how many low-level operations can be applied simultaneously), are there hitherto unknown classes of computations one can realise with strong constraints on the needed quantum resources (using a polynomial number of quantum elements), can we design new commitment protocols (some party is committing to a choice only to be revealed at a later time of his choice), and hiding protocols (some party is drawing on another's computing resources without revealing what for), and perhaps more ambitiously new MQC-specific schemes for redundant computations that will protect computations from errors induced by unavoidable contacts with the environment. A positive answer to one of the above questions would lend further credence in the MQC model as a strong contender in the elusive search for a scalable implementation of quantum computing.
 
Description We have explored the potential of quantum information
theory from its formal and foundational aspects
to actual cryptographic experiments through this grant. We have
developed the rigorous mathematical model underlying
the measurement-based quantum computing and information flow analysis paving the road for wider access to such models
among different sub-disciplines within computer science (more than 600 joint citations). Key highlights are described
next. We have invented the new cryptographic protocol of universal blind quantum computing (UBQC), demonstrating for the first time the possibility of preserving the privacy of computation using quantum properties. The UBQC
has received strong praise (more than 200 joint citations)
in the international quantum community as one
of the major breakthroughs of the last decade (Vazirani
QIP 2010, Aaronson Shtetl-Optimized 2011, Vedral
Physics Today 2012, Zeilinger QCMC 2012). In
collaboration with experimental lab in Vienna, we also adapted the theoretical work to the optical implementation. Within a week of the publication of the Science paper, more than 50 articles appeared in the international media (including BBC) describing the work as achieving secure quantum cloud
computing for the first time.

Security as discussed above, is only half the story
of a potential quantum era. A more pressing challenge
facing any kind of complex system and in particular
the emerging quantum technology, is practical verification. We developed a new approach for testing the correctness of any delegated quantum computing based on the ability to compute
with encrypted data, while hiding the underlying function.
We demonstrated, theoretically and experimentally, that measurement of the randomly prepared single qubits, encrypted from the actual computation, leads to an efficient quantum certification. After our Nature Physics publication, various media
(including a live BBC interview), praised the result
as a quantum leap in bringing quantum technology
closer to reality. We have since been at the forefront
of quantum verification, developing a spectrum of various
tests using technology available in quantum labs
across the world.
Exploitation Route We stand at a point in the development of science, technology and business practice where computational models coupled to unprecedented capacity to collect data are becoming vital tools in almost all sectors, from data-driven business models through to in silico modelling of whole biological organisms. At the same time we are seeing the early development of quantum computing devices that offer the capacity to solve problems that
are far beyond the limits of classical computation. Our developed verification and validation techniques and novel quantum enhanced secure cloud computing could be explored as a structural understanding of how to use these intermediate quantum systems for scientific and business benefit, contributing to the UK's global leading position in this computational revolution. This could provide
the knowledge and expertise to allow the UK science,
technology and business and the stakeholders to
verify, certify and evaluate today's quantum devices so
that we can effectively exploit tomorrow's.
Sectors Digital/Communication/Information Technologies (including Software),Security and Diplomacy