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.
Hi all,
Tomorrow Giulia Mazzola will tell us about her master thesis at IBM, on
"Simulating Yang-Mills Lattice Gauge Theories on Digital Quantum
Computers". See below for the abstract. Here's the link:
https://ethz.zoom.us/j/362994444.
Best,
-joe
Abstract:
Gauge theories represent the most successful description of elementary
particles and their fundamental interactions. In computing the real-time
dynamics in lattice gauge theories however, standard classical numerical
methods suffer from an exponential scaling of the required resources with
growing system size and thus, display severe limitations for the simulation
of real-time phenomena. Quantum computers might provide a potential
framework to tackle this problem as lattice gauge theories can be
efficiently represented using resources which are polynomial in the system
size. Here, we review different encoding schemes for non-abelian Yang-Mills
lattice gauge theories with dynamical fermionic matter such as quantum
chromodynamics in arbitrary dimensions on digital circuit-based quantum
computers. On the other hand, we apply promising variational quantum
algorithms for near-term quantum computation to study the groundstate
properties of small abelian lattice gauge theory systems like quantum
electrodynamics in (1+1)- and (2+1)-spacetime dimensions. Specifically, we
investigate the performance of physically motivated variational forms that
preserve the gauge symmetry of the theory, thereby allowing for an
efficient sampling in the physical Hilbert space of states. Therewith, we
demonstrate the phenomenon of flux-string breaking in form of a phase
diagram and further present the results of simulations on real
superconducting quantum hardware as a proof-of-principle. By generalizing
this scheme to non-abelian Yang-Mills theories, such gauge invariant
variational forms might be included in variational real-time evolution
algorithms, providing a potential path towards simulating real-time
dynamics of lattice gauge theories on near-term quantum devices.
Hi all,
Tomorrow Anne-Catherine de la Hamette will tell us about her master thesis
with Thomas Galley at Perimeter Institute, entitled "Quantum reference
frames: a relational approach to quantum theory". See the abstract below
for more details. Zoom link: https://ethz.zoom.us/j/362994444.
Best,
-joe
Abstract
Reference frames are essential in the description of physical phenomena.
Often used implicitly, they appear as idealized classical systems.
Following a more fundamental approach and considering them as physical
systems subject to the laws of quantum mechanics, they become quantum
reference frames (QRFs). A rigorous treatment of QRFs is indispensable both
in the construction of a relational theory of quantum mechanics and of
quantum gravity. Not only do the properties of QRFs give rise to numerous
applications in quantum information; they are also expected to improve our
understanding of observer-dependent settings such as the Wigner's friend
experiment.
In this talk, we present a relational formalism based on the group and
representation theoretic nature of reference frames. By identifying
coordinate systems with elements of a symmetry group G, we define a general
operator for reversibly transforming between QRFs associated to the group
G. We explore the properties of this operator in different cases and show
how it gives rise to transformations between coordinate systems which are
`in a superposition' relative to other coordinate systems. Finally, we
apply the relational formalism and the change of reference system developed
in this work to the Wigner's friend thought experiment.
Hi all,
Tomorrow Ladina Hausmann will tell us about her semester project with
Nuriya and Lídia, "On multi-agent logical paradoxes in
epistemically-restricted hidden variable theories". See below for the
abstract. The zoom link is https://ethz.zoom.us/j/362994444.
Best,
-joe
Abstract: The Frauchiger-Renner paradox shows that inconsistencies appear
when multiple agents reason about each other in quantum mechanics [1]. But
is this a distinct feature of quantum theory, or can other physical
theories exhibit similar paradoxes? We know that it is possible to find a
paradoxical setting in box world, a theory less local than
quantum mechanics, for a specific model of physical agents [2].
In this project we investigate multi-agent logical paradoxes in Spekkens'
toy theory. Spekkens' toy theory exhibits many phenomena of quantum
mechanics, but is a non-contextual local hidden variable theory [3]. The
quantum-like effects stem from an epistemic restriction akin to the
uncertainty principle, and a measurement disturbance rule.
We were able to prove that there is no Frauchiger-Renner-like paradox in
Spekkens' toy theory. In addition, we refined the formalism of Spekkens'
toy theory and were able to model agents' physical memories and
deterministic reasoning.
In this talk, I will give an introduction to Spekkens' toy theory.
Additionally, I will present how memory update and reasoning work in the
toy theory. In the end, I'll discuss the Frauchiger-Renner paradox in
Spekkens' toy theory.
[1] Daniela Frauchiger and Renato Renner. Quantum theory cannot
consistently describe the use of itself. Nature Communications, 9(1),
sep 2018. doi:10.1038/s41467-018-05739-8.
[2] V Vilasini, Nuriya Nurgalieva, and Lídia del Rio.
Multi-agent paradoxes beyond quantum theory. New J. Phys.,
21(11):113028, nov 2019. doi:10.1088/1367-2630/ab4fc4.
[3] Robert W. Spekkens. Evidence for the epistemic view of
quantum states: A toy theory. Physical Review A, 75(3), mar
2007. doi:10.1103/physreva.75.032110.
Hi all,
Tomorrow we'll hear from Gillen Beck on "Conditional Mutual Information in
Quantum Circuits", his semester project with David Sutter. See below for
the abstract. Meeting link: https://ethz.zoom.us/j/362994444.
Best,
-joe
Abstract:
For a tripartite quantum state ρABC, the conditional mutual information is
an entropic value which quantifies the correlations between subsystems A
and C, conditioned on B. When this value is zero, the state can be
considered aquantum Markov chain, and there exists a map which can
precisely recover ρABC from ρAB alone. A related map exists for states with
small, but nonzero, conditional mutual information, which approximately
recovers ρABC, with the recovery fidelity approaching unity as the
conditional mutual information approaches zero. Motivated by the potential
of universal state recovery in the context of qubit loss and noisy
circuits, this project examined the evolution of conditional mutual
information through a few standard circuits: the quantum Fourier transform,
phase estimation, and Grover's search. I first present the general
findings, which suggest that recoverable settings can arise naturally in
quantum circuits. Lastly, I discuss both the potential application of the
recovery map as a new approach to circuit optimization, as well as the next
steps required to determine its viability.
Hi all,
Tomorrow Tony Metger will tell us about his master's thesis with Thomas
Vidick at Caltech. 1500 on zoom, https://ethz.zoom.us/j/362994444. See
below for title and abstract.
Best,
-joe
Title:
Self-testing of a single quantum device under computational assumptions
Abstract:
Self-testing is a method to characterise an arbitrary quantum device based
only on its classical input-output correlations. Prior works on
self-testing require the assumption that the quantum device is composed of
two non-communicating subsystems. Here, we replace this non-communication
assumption by a computational assumption. Specifically, we give a protocol
that allows a classical verifier to robustly certify that a single
computationally bounded quantum device must have prepared a Bell pair and
performed single-qubit measurements on it, up to a change of basis applied
to both the device's state and measurements. This means that under
computational assumptions, the verifier is able to certify the presence of
entanglement inside a single quantum device. To achieve this, we employ
techniques introduced by Brakerski et al. (2018) and Mahadev (2018) which
allow a classical verifier to constrain the actions of a quantum device
assuming the device does not break post-quantum cryptography.
Hi all,
Tomorrow Patrick Neuweiler will tell us about his master thesis at IBM, see
below for title and abstract. We'll start at 15:30 (note the slightly later
time) on zoom: https://ethz.zoom.us/j/362994444.
Best,
-joe
Title: Combinatorial Optimization with Variational Quantum Imaginary Time
Evolution
Abstract: While quantum computing can achieve exponential speed-ups for
many problems, it is unclear, what speed-up it can bring for NP-hard
Combinatorial Optimization problems. In this thesis, we investigate the
potential of Variational Quantum Imaginary Time Evolution (VarQITE), a
recently proposed quantum heuristic that can be used to solve classically
hard problems. The algorithm can always find the optimal solution using an
appropriate variational circuit of sufficient depth, potentially
exponential in the number of qubits. However, it is unclear how the minimum
required depth increases with the number of variables for a particular
problem. We run exact and shot-based quantum simulations, to find how the
requirements for a successful VarQITE scale with the problem size. While we
find that VarQITE performs well on the tested problems, it requires further
analysis on problems of increasing size to ultimately answer the question
of quantum advantage for combinatorial optimization.