Hi all,
Apologies, I'm terribly late with this week's email. Today at 2pm we hear
from Arne Thomson on "Comparing Quantum Neural Networks and Quantum Support
Vector Machines". See below for the abstract. The talk will be on zoom:
https://ethz.zoom.us/j/362994444
Best,
Joe
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We prove a polynomial speedup compared to [Liu, Arunachalam, and Temme “A
rigorous and robust quantum speed-up in supervised machine learning
<https://www.nature.com/articles/s41567-021-01287-z>”] for training of
noisy quantum support vector machines via the dual optimization problem. We
introduce the Pegasos algorithm as an alternative and derive bounds on its
runtime, which scales favorably. In addition, we analyze quantum neural
networks numerically from the same perspective.
Hi all,
Sorry for the late notice, I'm only slowly coming out of summer mode!
Tomorrow at 11 am we will have our first talk of the QIT Seminar in a
while, from Noah Berner on "Quantum Bayesian Neural Networks". See below
for the abstract. There's also a preprint available already, in case you
want to read more: https://arxiv.org/abs/2107.09599.
We're in the usual zoom room for the QIT Seminar:
https://ethz.zoom.us/j/362994444.
Next week we return to our usual time on Tuesdays at 2pm.
Best,
Joe
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Quantum machine learning promises great speedups over classical algorithms,
but it often requires repeated computations to achieve a desired level of
accuracy for its point estimates. Bayesian learning focuses more on
sampling from posterior distributions than on point estimation, thus it
might be more forgiving in the face of additional quantum noise. We propose
a quantum algorithm for Bayesian neural network inference, drawing on
recent advances in quantum deep learning, and simulate its empirical
performance on several tasks. We find that already for small numbers of
qubits, our algorithm approximates the true posterior well, while it does
not require any repeated computations and thus fully realizes the quantum
speedups.
Hi all,
Johannes Bausch from Cambridge will give this week's QIT Seminar, which
will take place Thursday morning at 11am. He'll tell us about "Complexity,
Quantum Information and Quantum Algorithms"; see below for the abstract.
Usual zoom channel: https://ethz.zoom.us/j/362994444
Best,
Joe
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Abstract: Loosely speaking, complexity theory is the study of how hard or
easy it is to answer certain computational problems. I will be presenting
three areas of quantum theory in this context. First I will focus on the
study of error correction codes in the communication context, utilizing
novel computational techniques such as neural network quantum states and
graph states to push known noise thresholds beyond the state-of-the-art.
The next topic will be on many-body systems, utilizing spectral techniques
to prove that various macroscopic properties such as ground state energies,
spectral gaps, or phase diagrams can be hard to compute, or even
undecidable. Finally, I will focus on the algorithmic side of quantum
computation, and present our recent work on improving quantum simulation of
the Fermi Hubbard model, and recurrent (quantum) neural networks.
Hi all,
Tomorrow Jinzhao will tell us about "The refined quantum extremal surface
prescription from the asymptotic equipartition property". See below for the
abstract. Usual time and place: 2pm https://ethz.zoom.us/j/362994444.
Best,
Joe
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The quantum extremal surface prescription, born out of the Ryu Takayanagi
formula in AdS/CFT, is a general rule of computing entanglement entropy in
gravity. Its usefulness is highlighted in the recent black hole Page curve
calculation. In this talk I will introduce the recent refinement of the
QES prescription, showing the significance of the smooth conditional
min/max-entropies. Inspired by the asymptotic equipartition property, I
will sketch a path integral derivation of it in the context of holography
with a novel replica trick. In the end, I will show that the derivation
implies the correction also applies beyond AdS/CFT and in particular to the
Page curve.
Hi all,
Tomorrow Michał Bączyk will tell us about his master's thesis on "Black
Hole Holographic Models in the framework of Gaussian Quantum Information",
supervised partly by Mischa. See below for the abstract. We'll start at 2pm
on zoom: https://ethz.zoom.us/j/362994444.
Best,
Joe
%%%%%%%%%
Title: Black Hole Holographic Models in the framework of Gaussian Quantum
Information
Abstract:
In this work, we make the first step towards introducing the operational
quantum information notions into the framework of Conformal Field Theories
and AdS/CFT correspondence. We provide an original toolkit for
investigating the action of Bosonic Gaussian channels on the QFTs
incorporated into the language of Gaussian Quantum Information.
Specifically, we study the quench protocol dynamics for the case of vacuum
state of 1D harmonic chain system and the TFD state. These are Gaussian
states that have meaningful dual descriptions in the language of AdS/CFT
correspondence. To evaluate the character of the free and interrupted by
channels evolution we calculate numerically for the systems of interest
quantum entropies and fidelities all using recent advances in the Gaussian
Quantum Information.
Hi all,
Tomorrow Severin Tschui will present his master's thesis with Zhikuan Zhao
from the computer science department, entitled "Supervised Classification
with Quantum Embeddings", and Arman Pour Tak Dost will present his semester
project with Mischa, entitled "Quasi-Ideal clocks and their environments".
See below for their abstracts. We'll start at 2pm on zoom:
https://ethz.zoom.us/j/362994444.
Best,
Joe
%%%%%%%%%
Speaker: Severin Tschui
Title: Supervised Classification with Quantum Embeddings
Abstract: The theory of supervised classification using quantum algorithms
is reviewed, focusing on the similarity between classical kernel machines
and a quantum classifier model. The model is based on identifying the
encoding of classical data in a quantum Hilbert space as a feature map,
termed quantum embedding. An ansatz is defined on how to realise such an
embedding using quantum circuits, and a code framework is provided which
handles the implementation and simulation. We apply the model to classify
four different data sets, finding that it reaches high training accuracy in
all cases but failing to generalise on two data sets with greater
dimension. We present a novel idea for assessing quantum embedding quality
and carry out a simulation to investigate its merits. The experiment did
not deliver statistically significant results to confirm or refute if the
method is viable.
Speaker: Arman Pour Tak Dost
Title: Quasi-Ideal clocks and their environments
Abstract: In this presentation, we motivate the axioms that clocks should
satisfy. They were already known but motivated from a different point of
view. It turns out that quantum clocks are more precise than classical
clocks. We want to investigate the physicality of this result and present
different approaches. We find a collision model that could potentially
realize the clock experimentally. Yet, there is a rescaling procedure
involved, the physicality of which remains for further investigations.
Hi all,
Tomorrow we have two master students finishing up, Julian Schuhmacher, who
was at IBM with Ivano Tavernelli, and Yanglin Hu, who was working with
Mischa. See below for their titles and abstracts. We'll start at 2pm on
zoom: https://ethz.zoom.us/j/362994444
Best,
Joe
Speaker: Julian Schuhmacher
Title: Towards large scale simulations with quantum computers and machine
learning potentials
Abstract:The simulation of materials with molecular dynamics (MD)
simulations is an important tool to understand and predict the properties
of materials. Historically, accurate MD simulations were driven by
computationally costly, yet still approximated, first-principles electronic
structures calculations like Density Functional Theory (DFT), and therefore
were limited to small system sizes and short simulation times. In the last
few years, the application of machine learning potentials, trained on DFT
or post-Hartree Fock data, allowed to run MD simulations at the accuracy of
ab initio methods, but at a fraction of the computational cost.
Speaker: Yanglin Hu
Title: Feasibility of Experimental Realizations of Quantum Effects in
Gravitational Time Dilation
Abstract: A potentially detectable quantum discrepancy to time dilation in
delocalized clocks was derived previously. However, no experiment was put
forward to experimentally test it. In this work, we investigate the
possibility to conduct a real experiment. The expectation value and the
variance of the quantum discrepancy are derived with the Lindblad equation
and second-order perturbation theory. Two experimental protocols based on
Strontium and Magnesium optical lattice clocks are proposed. Numerical
results show that it would be possible to detect the quantum discrepancy
with next-generation Magnesium optical lattice clocks. We also investigate
the effect of decoherence mechanisms on clock's accuracy. Upper bounds on
decoherence rates in order to detect the quantum discrepancy are also
given.
Hi all,
Tomorrow our new postdoc Vilasini will tell us about "Causality and its
compatibility with space-time structure". See below for the abstract. We
start at 2pm on zoom: https://ethz.zoom.us/j/362994444.
Best,
Joe
Abstract:
We often do not distinguish between the directions of causation and
(space-)time, even though causality can be defined operationally and
independent of a space-time structure. Separating the concepts of causality
and space-time and characterising how they fit together would give crucial
insights into the different notions of causality such as operational
causality, relativistic causality and logical consistency. Motivated by
this, we develop a causal modelling framework for operationally
characterising causation in the presence of cyclic, fine-tuned and
non-classical causal influences. In the process, we distinguish between two
kinds of causal loops that can arise in our framework, depending on
operational detectability. We then define how this general class of causal
models can be embedded “compatibly” in a space-time structure i.e., without
leading to signalling outside the future. We derive necessary and
sufficient conditions for a causal model to be compatible with an embedding
in a space-time structure, and to rule out certain kinds of causal loops in
the model. In particular, this provides an operational framework for
analysing causality in the post-quantum “jamming” theories proposed in
[1,2], and generalises their results from Bell-type scenarios to arbitrary
causal structures. Furthermore, we show that post-quantum jamming can lead
to superluminal signalling, contrary to the claims of [1,2], we identify
missing assumptions in these claims as well as new features of post-quantum
theories that admit jamming non-local correlations.
Joint work with Roger Colbeck.
[1] Grunhaus, J., Popescu, S., Rohrlich, D. Phys. Rev. A53, 3781–3784
(1996).
[2] Horodecki, P. , Ramanathan, R. Nat. Comms. 10, 1701 (2019).