This series consists of weekly discussion sessions on foundations of quantum Theory and quantum information theory. The sessions start with an informal exposition of an interesting topic, research result or important question in the field. Everyone is strongly encouraged to participate with questions and comments.
I discuss a technique - the quantum adversary upper bound - that uses the structure of quantum algorithms to gain insight into the quantum query complexity of Boolean functions. Using this bound, I show that there must exist an algorithm for a certain Boolean formula that uses a constant number of queries. Since the method is non-constructive, it does not give information about the form of the algorithm. After describing the technique and applying it to a class of functions, I will outline quantum algorithms that match the non-constructive bound.
TBA
We show that if the ground state energy problem of a
classical spin model is NP-hard, then there exists a choice parameters of the
model such that its low energy spectrum coincides with the spectrum of
\emph{any} other model, and, furthermore, the corresponding eigenstates match
on a subset of its spins. This implies that all spin physics, for example all
possible universality classes, arise in a single model. The latter property was
recently introduced and called ``Hamiltonian completeness'', and it was shown
In a topological
quantum computer, universality is achieved by braiding and quantum information
is natively protected from small local errors. We address the problem of
compiling single-qubit quantum operations into braid representations for
non-abelian quasiparticles described by the Fibonacci anyon model. We develop a
probabilistically polynomial algorithm that outputs a braid pattern to
approximate a given single-qubit unitary to a desired precision. We also
classify the single-qubit unitaries that can be implemented exactly by a
Transversal
implementations of encoded unitary gates are highly desirable for
fault-tolerant quantum computation. It is known, however, that
transversal gates alone cannot be computationally universal. I will show
that the limitation on universality can be circumvented using only
fault-tolerant error correction, which is already required anyway. This
result applies to ``triorthogonal'' stabilizer codes, which were recently
introduced by Bravyi and Haah for state distillation. I will show that
We introduce two relative entropy quantities called the min- and max-relative
entropies and discuss their properties and operational meanings.
These relative entropies act as parent quantities for tasks such as data compression, information
transmission and entanglement manipulation in one-shot information theory. Moreover, they lead us to define entanglement monotones which have interesting operational interpretations.
Expressions of several information theoretic quantities involve an optimization over auxiliary quantum registers. Entanglement-assisted version of some classical communication problems provides examples of such expressions. Evaluating these expressions requires bounds on the dimension of these auxiliary registers. In the classical case such a bound can usually be obtained based on the
We
show that particle detectors, such as 2-level atoms, in non-inertial motion (or
in gravitational fields) could be used to build quantum gates for the
processing of quantum information. Concretely, we show that through
suitably chosen non-inertial trajectories of the detectors the interaction
Hamiltonian's time dependence can be modulated to yield arbitrary rotations in the
Bloch sphere due to relativistic quantum effects.
Ref. Phys.
Rev. Lett. 110, 160501 (2013)
A recent development in
information theory is the generalisation of quantum Shannon information theory
to the operationally motivated smooth entropy information theory, which
originates in quantum cryptography research. In a series of papers the first
steps have been taken towards creating a statistical mechanics based on smooth
entropy information theory. This approach turns out to allow us to answer
questions one might not have thought were possible in statistical mechanics,
I will discuss a
path-integral representation of continuum tensor networks that extends the
continuous MPS class for 1-D quantum fields to arbitrary spatial dimensions
while encoding desirable symmetries. The physical states can be interpreted as
arising through a continuous measurement process by a lower dimensional virtual
field with Lorentz symmetry. The resultant physical states naturally obey
entropy area laws, with the expectation values of observables determined by the