Hi all,
Tomorrow Yanglin Hu will tell us about his semester project, entitled
"Confined Relativistic Quantum Clock". See below for the abstract. The zoom
link is https://ethz.zoom.us/j/362994444.
Best,
-joe
Title: Confined Relativistic Quantum Clock
Abstract: A potentially detectable quantum modification to time in
delocalised clocks are proposed previously in order to examine the
correctness of quantum gravity theory. Here we aim to further investigate
the possibility to design an experiment. We derive the Hamiltonian of a
relativistic quantum clock in the electromagnetic field in the Rindler
spacetime. Based on that, we calculate the time dilation of a quantum clock
in a Penning trap. The numerical result shows that the time dilation is
detectable for a confined quantum clock. We also explore the effect of
decoherence via a heat bath of harmonic oscillators on a free quantum
clock. The decoherence does not change the time average of the clock.
Results till now show that designing an experiment to detect the quantum
modification to time are a possibility.
Hi all,
Tomorrow Sven Jandura will tell us about his semester project at IBM,
entitled "Time Propagation of a Wave Packet using a Variational Quantum
Simulator". See below for the abstract. The zoom link is
https://ethz.zoom.us/j/362994444.
Best,
-joe
Abstract: Quantum computers can speed up the calculation of the time
evolution of quantum states, a task that is classically hard because
just storing the wavefunction of a state of multiple particles requires
resources exponential in the number of particles. Here we present a
variational hybrid quantum-classical algorithm based on McLachlans
variational principle that approximates the time evolution of particles
moving in arbitrary potentials. We then numerically study the
performance of this algorithm on a free Gaussian wave packet in one
dimension and the scattering of a Gaussian wave packet on an Eckart
barrier. We find that for a free particle the number of parameters in
the variational form used by us can be significantly smaller than the
real dimension of the Hilber space, while for the Eckart barrier it has
to be close to the real dimension of the Hilbert space to obtain an high
fidelity approximation.
Hi all,
Tomorrow Boxi Li will tell us about his master thesis at TU Delft, entitled
"Efficient Optimization of Cut-offs in Quantum Repeater Chains". See below
for the abstract. Zoom link: https://ethz.zoom.us/j/362994444.
Best,
-joe
Abstract:
Quantum communication enables the implementation of tasks that are
unachievable with classical resources. However, losses on the communication
channel preclude the direct long-distance transmission of quantum
information in many relevant scenarios. In principle quantum repeaters
allow one to overcome losses. However, realistic hardware parameters make
long-distance quantum communication a challenge in practice. For instance,
in many protocols an entangled pair is generated that needs to wait in
quantum memory until the generation of an additional pair. During this
waiting time the first pair decoheres, impacting the quality of the final
entanglement produced. At the cost of a lower rate, this effect can be
mitigated by imposing a cut-off condition. For instance, a maximum storage
time for entanglement after which it is discarded. In this work, we
optimize the cut-offs for quantum repeater chains. First, we develop an
algorithm for computing the probability distribution of the waiting time
and fidelity of entanglement produced by repeater chain protocols which
include a cut-off. Then, we use the algorithm to optimize cut-offs in order
to maximize secret-key rate between the end nodes of the repeater chain. We
find that the use of the optimal cut-off extends the parameter regime for
which secret key can be generated and moreover significantly increases the
secret-key rate for a large range of parameters.
arXiv preprint: http://arxiv.org/abs/2005.04946
Hi all,
Tomorrow we again have two master thesis talks, this time by Romain Moyard
and Christian Bertoni. Romain worked with Raban on circuit optimization,
and Christian worked with me on information theory and renormalization.
Titles and abstracts for their talks are below. Here's the zoom link:
https://ethz.zoom.us/j/362994444
Best,
-joe
----------------
Romain Moyard ~
Title: Implementation, improvement and testing of an efficient template
matching algorithm
Abstract: Given a large and a small quantum circuit, an algorithm to find
all maximal matches of the small circuit, called template, in the large
circuit under consideration of pairwise commutation relations between
quantum gates was suggested by Iten et al. in arXiv:1909.05270. In this
talk, we present the result of the implementation of this algorithm into
the software library Qiskit-terra. We check its correctness by comparing it
with another, less efficient, algorithm that finds all the maximal matches.
We find two kinds of cases that were not correctly handled in the efficient
matching algorithm and correct them. Our implementation shows that the
average time complexity of the algorithm scales much better than the
theoretical worst-case time complexity. In addition, we present different
heuristics to speed up the matching algorithm with the trade-off of
probably not finding all maximal matches. We apply the matching algorithm
for circuit optimization on random circuits and also on benchmark circuits
that are already heavily optimized. In both cases, we can significantly
improve the implementation cost of the circuits. Finally we present an
adapted version of the algorithm that finds all maximal gate sequences
acting on a given qubit set in a circuit. This is promising for peephole
optimization.
Preprint: arXiv:1909.05270
------
Christian Bertoni ~
Title: Information theory and renormalization in statistical mechanics
Abstract: Renormalization in statistical mechanics is a process in which a
system is mapped to a different scale. It arises naturally when considering
phase transitions, since statistical systems exhibit scale invariance at
criticality. It is natural to think that this process eliminates
information, and that it should have an information theoretic
interpretation. In this talk I will present two different ways in which
tools from information theory can be applied to the problem of
renormalization, focusing on the question of whether one can select an
appropriate renormalization map by using simple information theoretic
criteria.
Hi all,
Tomorrow we are back from the summer break with two master thesis talks (of
25 minutes each). The speakers are Ludovico Machet, who worked with
Jinzhao, and Tim Möbus, who worked with David. See below for titles and
abstracts. We start as usual at 1500 on zoom, at
https://ethz.zoom.us/j/362994444.
Best,
-joe
++ Ludovico Machet: "On the gravitational action and horizon entropy in
Causal Set Theory”.
Abstract: The formulation of a quantum theory of gravity has been one of
the major challenges for theoretical physicists in the last century. In
this framework, the Causal Set Theory (CST) approach saw recent and rapid
progress with the discovery of a discrete equivalent for the
Einstein-Hilbert action. In this talk, after a rapid introduction of the
CST formalism, I will describe the derivation of the causal set action,
illustrate its continuum limit and how it can extract geometric information
from the causal set structure. I will then focus on the presence of
boundary terms in the continuum limit of the action and extend the
discussion to a general curved space time. I will show that the action of a
causal diamond in a Riemann normal neighbor effectively localizes to the
null-null joint.
I will then discuss how the information encoded in a causal set can be
useful to define a kinematical gravitational entropy. I will first consider
the Horizon Molecules proposal, then I will introduce the Spacetime Mutual
Information concept. I will argue that the SMI follows an area law when
evaluated on causal diamonds cut by causal horizons. This result is
promising in the search for a quantity giving a kinematical, then
dynamical, discrete entropy for causal horizons in CST.
Preprint: https://arxiv.org/abs/2007.13192
++ Tim Möbus: "On Chain Rules for Quantum Rényi Divergences".
Abstract:
The chain rule of the Rényi divergence, in its classical form, decomposes
the divergence on a multipartite system into a sum of conditional
divergences with respect to certain subsystems. The aim of this master
thesis is to recap the existing chain rule results for the minimal and
maximal quantum Rényi divergences, compare them, and discuss the role of
the regularisation. Especially, the case $\alpha=\frac{1}{2}$ is
investigated and counterexamples for the minimal divergence show the
non-additivity of the channel divergence and the necessity of the
regularisation of the chain rule. For that purpose, we introduce
semi-definite programs and prove a SDP representation for the channel
divergence.