I am a research fellow working on quantum-enhanced machine learning and applications of high-performance learning algorithms in quantum physics. Trained as a mathematician and computer scientist, I received my PhD from the National University of Singapore. Currently I work as the Academic Director of the Quantum Machine Learning Initiative in the Creative Destruction Lab in the University of Toronto. Previously I worked in the Quantum Information Theory group in ICFO-The Institute of Photonic Sciences and in the University of Borås. I did longer research stints at several institutions, including the Indian Institute of Science, Barcelona Supercomputing Center, Tsinghua University, the Centre for Quantum Technologies in the National University of Singapore, and the Quantum Information Group in the University of Tokyo. I serve in an advisory role for various startups, and I am a member of the NUS Overseas Colleges Alumni.

## Current Interests

**Quantum-enhanced machine learning**: Current and near-future quantum technologies have a potential of improving learning algorithms. Of particular interest are algorithms that have a high computational complexity or that require sampling. The latter type includes many probabilistic graphical models in which not only the training phase, but also the inference phase has been infeasible at scale, prompting a need for quantum-enhanced sampling. This in turn will enable deep architectures for probabilistic models, as well as scalable implementations of statistical relational learning, both of which go beyond the black-box model of neural networks and shift the focus towards explainable artificial intelligence. While speedup is the primary consideration, we also investigate the fundamental limits of statistical learning theory in the framework of quantum physics.

**Quantum many-body systems, optimization, and machine learning**: Identifying the ground state of a
many-particle system whose interactions are described by a Hamiltonian
is an important problem in quantum physics. During the last decade,
different relaxations of the previous Hamiltonian minimization problem
have been proposed. These algorithms include the lower
levels of a general hierarchy of semidefinite programming (SDP)
relaxations for non-commutative polynomial optimization, which provide a lower bound on the
ground-state energy, complementing the upper bounds that are obtainable using variational methods. The latest developments step away from optimization, and introduce machine learning as an ansatz for ground-state energy problems and for the study of quantum phase transitions. In fact, strong links between quantum many-body physics (tensor networks in particular) and deep learning are being established. We are developing a set of theoretical and numerical tools to pursue these synergies. Sponsored by the ERC grant QITBOX, by the Spanish Supercomputing Network (FI-2013-1-0008 and FI-2013-3-0004) and by the Swedish National Infrastructure for Computing (SNIC 2014/2-7 and 2015/1-162) and a hardware donation by Nvidia Corporation.

## Past Projects

**Trotter-Suzuki Approximation**
(2012, 2015-2017): The Trotter-Suzuki decomposition leads to an efficient algorithm
for solving the time-dependent Schrödinger equation and the
Gross-Pitaevskii equation. Using existing
highly optimized CPU and GPU kernels, we developed a distributed version
of the algorithm that runs efficiently on a cluster. Our implementation
also improves single node performance, and is able to use multiple GPUs
within a node. The scaling is close to linear using the CPU kernels,
whereas the efficiency of GPU kernels improve with larger matrices. We
also introduced a hybrid kernel that simultaneously uses multicore CPUs
and GPUs in a distributed system. The distributed extension was carried out while visiting the the Barcelona Supercomputing
Centre funded by
HPC-EUROPA2. Generalizing the capabilities of kernels was carried out by Luca Calderaro sponsored by the Erasmus+ programme. Computational resources were granted by the Spanish Supercomputing Network (FI-2015-2-0023 and FI-2016-3-0042), the High Performance Computing Center North (SNIC 2015/1-162 and SNIC 2016/1-320), and a hardware grant by Nvidia.

**Pericles**
(2013-2017): Promoting and Enhancing Reuse of Information throughout the
Content Lifecycle taking account of Evolving Semantics (Pericles) is an
integrated project in which academic and industrial partners have come
together to investigate the challenge of preserving complex digital
information in dynamically evolving environments, to ensure that it
remains accessible and useful for future generations. We address
contextuality and scalability within the project. Contextuality refers
to probabilistic framework that considers the broader and narrower
context of the data within a quantum-like formulation, whereas
scalability allows executing algorithms on massive data sets using
heterogeneous accelerator architectures. Funded by European Commission Seventh Framework Programme (FP7-601138).

**ChiP-SL** (2013-2014): Big data asks for scalable algorithms, but
scalability is just one aspect of the problem. Many applications also
require the speedy processing of large volumes of data. Examples include
supporting financial decision making, advanced services in digital
libraries, mining medical data from magnetic resonance imaging, and also
analyzing social media graphs. The velocity of machine learning is often
boosted by deploying GPUs or distributed algorithms, but rarely both. We
are developing high-performance supervised and unsupervised statistical
learning algorithms that are accelerated on GPU clusters. Since the cost
of a GPU cluster is high and the deployment is far from being trivial,
the project Cloud for High-Performance Statistical Learning (ChiP-SL)
enables the verification, rapid dissemination, and quick adaptation of
the algorithms being developed. Funded by Amazon Web
Services.

**SQUALAR**
(2011): High-performance computational resources and distributed systems
are crucial for the success of real-world language technology
applications. The novel paradigm of general-purpose computing on
graphics processors offers a feasible and economical alternative: it has
already become a common phenomenon in scientific computation, with many
algorithms adapted to the new paradigm. However, applications in
language technology do not readily adapt to this approach. Recent
advances show the applicability of quantum metaphors in language
representation, and many algorithms in quantum mechanics have already
been adapted to GPU computing. Scalable Quantum Approaches in Language
Representation (SQUALAR) aimed to match quantum-inspired algorithms with
heterogeneous computing to develop new formalisms of information
representation for natural language processing. Co-funded by Amazon Web
Services.

**SHAMAN** (2010-2011) was an integrated project on large-scale digital
preservation. As part of the preservation framework, advanced services
aid the discovery of archived digital objects. These services are based
on machine learning and data processing, which in turn asks for scalable
distributed computing models. Given the requirements for reliability,
the project took a middleware approach based on MapReduce to perform
computationally demanding tasks. Since memory organizations which are
involved in digital preservation potentially lack the necessary
infrastructure, a high-performance cloud computing component was also
developed. Funded by Framework Programme
7.