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.
Hi all,
Tomorrow Johannes Weidenfeller will tell us about his thesis project with
Elisa on shallow quantum circuits: https://ethz.zoom.us/j/362994444. Here
is the abstract:
In a recent breakthrough, Bravyi, Gosset and König (Science, 2018) proved
an unconditional separation between the complexity classes of
constant-depth quantum circuits QNC0, also called *shallow quantum circuits*,
and their classical counterparts NC0. This result has since then been
extended to a number of different computational problems. In this talk, we
introduce so-called *higher-dimensional generalised GHZ states*, which are
multipartite entangled states in a superposition of pure GHZ-like states,
and explore their non-local properties. We further discuss the main ideas
behind proving a separation in the setting of *arithmetic problems*, which
generalise the *Parity Halving problem*, previously introduced by Watts,
Kothari, Schaeffer and Tal (STOC 2019).
“Quantum advantage with shallow circuits” (Sergey Bravyi, David Gosset, and
Robert König): https://arxiv.org/abs/1704.00690
"Exponential separation between shallow quantum circuits and unbounded
fan-in shallow classical circuits” (Adam Bene Watts, Robin Kothari, Luke
Schaeffer, and Avishay Tal): https://arxiv.org/abs/1906.08890
Best,
-joe