Abstract
Quantum algorithms exponentially faster than their classical equivalents exist for code breaking, quantum chemistry, knot theory, group theory, and are speculated to exist for diverse applications including machine learning and artificial intelligence. I review these applications and the current state of knowledge on how to build a practical quantum computer.
I report about our recent achievements on integrated photonic quantum circuits. For the fabrication we use direct laser-inscription, which allows complex three-dimensional waveguide architectures on chip for using multiple degrees of freedom, in particular diffraction control and birefringence.
Significant efforts have been made to interface cold atoms with micro- and nano-photonic systems in recent years. Originally, it was envisioned
that the migration to these systems from free-space atomic ensemble or
Stoquastic Hamiltonians are characterized by the property that their off-diagonal matrix elements in the standard product basis are real and non-positive. Many interesting quantum models fall into this class including the Transverse field Ising Model (TIM), the Heisenberg model on bipartite graphs, and the bosonic Hubbard model.
A pure quantum state of N subsystems with d levels each is called
k-uniform, if all its reductions to k qudits are maximally mixed.
These states form a natural generalization of N-qudits GHZ states
which belong to the class 1-uniform states.
Position verification allows us to verify the position of a device in space (e.g., for enabling access to location based services). Unfortunately, position verification is known to be insecure in principle using only classical cryptography. We show how position verification can be achieved using quantum communication.
I will talk about a classic lemma due to Jordan (1875) that is
frequently used in quantum computing. Jordan's lemma says that given
any two orthogonal projectors, there is a way to partition the
underlying vector space into 1- and 2-dimensional subspaces that are
invariant under the action of both projectors. This simple lemma has
applications in several areas of quantum computing. In this talk will
discuss the lemma, its proof, and explain some selected applications in
A masters and a PhD student at the Institute for Quantum Computing have each received thesis honours at the 2014 University of Waterloo convocation.
The Institute for Quantum Computing presented five students with awards for excellent research and outreach activity.