Hi all,
Tomorrow Lorenzo Laneve will tell us about his semester project with Lídia,
entitled "Impossibility of composable Oblivious Transfer in relativistic
quantum cryptography". See below for the abstract. We start at 2pm on zoom:
https://ethz.zoom.us/j/362994444.
Best,
Joe
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https://arxiv.org/abs/2106.11200
Abstract: We study the cryptographic primitive Oblivious Transfer; a
composable construction of this resource would allow arbitrary multi-party
computation to be carried out in a secure way, i.e. to compute functions in
a distributed way while keeping inputs from different parties private.
First we review a framework that allows us to analyze composability of
classical and quantum cryptographic protocols in special relativity:
Abstract Cryptography implemented with Causal Boxes. We then (1) explore
and formalize different versions of oblivious transfer found in the
literature, (2) prove that their equivalence holds also in relativistic
quantum settings, (3) show that it is impossible to composably construct
any of these versions of oblivious transfer from only classical or quantum
communication among distrusting agents in relativistic settings, (4) prove
that the impossibility also extends to multi-party computation, and (5)
provide a mutual construction between oblivious transfer and bit commitment.
Hi all,
Tomorrow we will hear from Davide Materia on his master's thesis with Ivano
Tavernelli at IBM, entitled "DFT functionals trained with Quantum
Computers". See below for the abstract. We start at 2pm on zoom:
https://ethz.zoom.us/j/362994444.
Best,
Joe
%%%%%%
Abstract: In this thesis, we developed different methods for the training
and the optimization of a Density Functional Theory (DFT) exchange and
correlation functionals, vxc, which relies on the minimization of the
electronic density difference obtained by subtracting the approximated DFT
density with a reference one evaluated on a quantum computer. The
determination of accurate and universal DFT vxc functional represents an
unsolved problem in computational chemistry and despite many attempts
(based on theoretical as well as heuristic approaches) a general solution
that is applicable in all physical contexts is still lacking. The new
generation of DFT functionals are build combining different energy
contributions and energy corrections (such as exchange, correlation but
also van der Waals energy terms with different short and long range
behaviors) weighted by a number of parameters that are usually fitted to
minimize the errors on a set of properties (mainly relative energies) in a
training set of molecules and solid state systems.
In this work, motivated by the central role of the density in the
Hohenberg-Kohn theorem, we investigate the possibility to use directly the
electronic density of molecular systems to optimize the DFT functionals,
hoping for a greater universality of the new functional resulting from this
optimization.
Hi all,
There's no QIT Seminar this week. Next week we'll hear from Christophe
Piveteau on his latest research -- see below. That will be at 2pm on zoom:
https://ethz.zoom.us/j/362994444
Best,
Joe
Speaker: Christophe Piveteau
Title: Quantum message-passing algorithm for optimal and efficient decoding
Abstract: Recently, Renes proposed a quantum algorithm called belief
propagation with quantum messages (BPQM) for decoding classical data
encoded using a binary linear code with tree Tanner graph that is
transmitted over a pure-state CQ channel [Renes, NJP 19 072001 (2017)].
This algorithm presents a genuine quantum counterpart to decoding based on
classical belief propagation, which has found wide success in classical
coding theory when used in conjunction with LDPC or Turbo codes. More
recently Rengaswamy et al. [npj Quantum Information 7 97 (2021)]
numerically observed that, for a small example code, BPQM implements the
optimal decoder for determining the entire input codeword. Here we
significantly expand the understanding, formalism, and applicability of the
BPQM algorithm with the following contributions. First, we prove
analytically that BPQM realizes optimal decoding for any binary linear code
with tree Tanner graph. We also provide the first formal description of the
BPQM algorithm in full detail and without any ambiguity. In so doing, we
identify a key flaw overlooked in the original algorithm and subsequent
works which implies quantum circuit realizations will be exponentially
large in the code size. Although BPQM passes quantum messages, other
information required by the algorithm is processed globally. We remedy this
problem by formulating a truly message-passing algorithm which approximates
BPQM and has circuit complexity O(poly n,polylog 1/ϵ), where n is the code
length and ϵ is the approximation error. Finally, we also propose a novel
method for extending BPQM to factor graphs containing cycles by making use
of approximate cloning. We show some promising numerical results that
indicate that BPQM on factor graphs with cycles can significantly
outperform the best possible classical decoder.
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
%%%
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
%%%%%
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
%%%%%%%%%%%%%
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
%%%%%%%%
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.