Hi all,
Tomorrow Kai Ott will tell us about his semester project with Mischa Woods and Joe Renes, entitled 'Understanding Quantum Clocks: Measures of Precision and Entropy Production'. See below for the abstract. The talk will take place at 2pm in HIT F 32 or on Zoom: https://ethz.zoom.us/j/362994444.
Best,
Ladina
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Recent work on quantum clocks has shown quantum-over-classical advantage in time-keeping. In particular, in the limit of large dimensions, quantum ticking clocks can achieve …
[View More]arbitrary precision $R_1$ at vanishing entropy production $\Sigma_1$ per tick, while for classical clocks there is a fundamental trade-off between precision and entropy production per tick, i.e. for any desired precision, there is an associated minimal entropy production. In this work, we show that another type of precision $I_1$ defined via the relative entropy can be made arbitrarily large at vanishing entropy production even for classical ticking clocks of finite dimension. Then, we investigate optimal classical clocks, which achieve the minimum entropy production per tick for a given precision $R_1$. We give closed form solutions for their precision, discuss symmetries, and state how their parameters should be chosen to truly be optimal. Lastly, we relate the classical case to the quantum case to explain the approximate quadratic precision advantage of the latter over the former.
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Hi all,
Tomorrow Manuel John will tell us about his master thesis at IBM, entitled 'Optimizations of Quantum Classification Algorithms’.
See below for the abstract. The talk will take place at 2pm in HIT J 53 or on Zoom: https://ethz.zoom.us/j/362994444.
Best,
Ladina
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Computers are well known for their ability to sieve through vast amounts of data. They are
ubiquitous in today’s world, as specially designed algorithms have the ability to analyze, understand,
and group data and ideas …
[View More]into distinct categories. Naturally, promises arising from provable speed-ups
of quantum algorithms in relevant problem settings also motivate the search for quantum machine
learning algorithms. In this thesis, we embed data in quantum states with the use of parametrized
quantum circuits, which act as mappings of the original data to Hilbert space. We then compare
the datapoints by evaluating the fidelity between embedded datapoints and improve existing
classifiers by evaluating functions of the fidelity, which introduce non-linear decision boundaries
in Hilbert space. This allows us to classify ensembles of pure states and mixed states, and we
achieve results on real-world datasets competitive with those of a classical support vector machine.
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Hi all,
Tomorrow our visitior Thomas Galley will tell us about ''Quantum reference frames for general groups in the perspective neutral approach: the role of symmetry and gauge''. See below for the abstract. The talk will take place at 2pm in F 31.1 or on Zoom: https://ethz.zoom.us/j/362994444.
Best,
Ladina
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Title:
Quantum reference frames for general groups in the perspective neutral approach: the role of symmetry and gauge.
Abstract
Quantum reference frames are used to obtain a …
[View More]description of a certain subset of physical subsystems relative to a reference system, in the absence of external relata. In this talk I will first introduce changes of quantum reference frames for general groups in the “purely perspective dependent” approach. Following this I will show how to derive changes of quantum reference frames for general groups from a “perspective neutral state” which is a state which encodes all the different perspectives. In this approach one begins with a physical Hilbert space which is invariant under the action of the gauge group G. One can recover the perspective of a given reference system from a physical state via a conditioning map. The perspective dependent states obtained via this conditioning map lie in a space called the reduced physical Hilbert space of the subsystems relative to the reference system. The reduced Hilbert of a given subsystem naturally depends on the choice of reference system. One can recover changes of quantum reference frame between different perspectives via these conditioning maps and their inverses. In a final part of the talk I discuss in more detail the difference between gauge and symmetry, and show that in the case where there is an action of the gauge group only, then the reduced Hilbert space of a given subsystem is not just dependent on the choice of reference frame, but also the orientation of that reference frame.
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Hi all,
Tomorrow we will have two talks. Carla Ferradini will tell us about her semester project with Vilasini, entitled 'A causal modelling framework for classical and quantum cyclic causal structures' and Arman Pour Tak Dost will tell us about his master thesis with Mischa Woods entitled 'Quantum advantages in low-dimensional timekeeping'. See below for the abstracts. The talks will take place at 2pm in F31.1 or on Zoom: https://ethz.zoom.us/j/362994444.
Best,
Ladina
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Title:
A …
[View More]causal modelling framework for classical and quantum cyclic causal structures
Abstract:
In 1937 the theoretical existence of closed time-like curves (CTCs) as solutions in General Relativity was discovered. These are time-like curves that allow a particle to return to its starting point in space-time and, thus, seem to imply that time travel backwards in time is theoretically possible. This gives rise to several paradoxes such as the well-known grandfather paradox. Therefore, it is of physical interest to characterise and give a description of such closed time-like curves from a causal point of view and derive logically consistent solutions. The study of these solutions requires to introduce cyclic causal models and deduce how to evaluate probability distributions. Here, we provide a method that allows us to determine whether an arbitrary cyclic causal graph admits a logically consistent solution and eventually evaluate probabilities. This method can be used both in classical or quantum scenarios. In both cases, we prescribe how to reduce the initial causal graph to an acyclic one and then recover cyclicity through post-selection. Classically, we show that for an acyclic graph this reduces to the joint probability distribution that can be derived using the classical theory of acyclic causality. In the quantum scenario, we also show the equivalence between loop composition of the causal box framework and post-selected CTCs in our formalism. The obtained results do not only describe CTCs that may arise in exotic solutions of General Relativity, but also can be used to model ordinary feedback processes.
Title:
Quantum advantages in low-dimensional timekeeping
Abstract:
This presentation will discuss quantum advantages in timekeeping. We derive analytical formulas for the regularity of quantum clocks, numerically optimized to prove the quantum advantage in low dimensions. We provide heuristics based on a dynamical approach that reveals the clock as a damped harmonic oscillator. Further, we propose an experimental setup that uses weak coupling, spontaneous emission, and large decay rates to obtain a Lindblad equation beyond the rotating wave approximation, which can be viewed as a fingerprint of the energy-time uncertainty relation. Lastly, we provide a connection between clocks and the fundamental linewidth of lasers.
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Hi all,
Tomorrow we will have two talks. Eliot Jean will tell us about his master thesis with Vilasini and Ralph Silva, entitled 'Connecting the Multi-Time Formalism and Post-Selected Closed Timelike Curves' and Matthias Salzger will tell us about his master thesis with Vilasini entitled 'Connecting indefinite causal order processes to composable quantum protocols in a spacetime'. See below for the abstracts. The talks will take place at 2pm in F31.1 or on Zoom: https://ethz.zoom.us/j/…
[View More]362994444.
Best,
Ladina
%%%%%
Title:
Connecting the Multi-Time Formalism and Post-Selected Closed Timelike Curves
Abstract:
In this work, two different models are reviewed and relations between the two are derived. On the one hand, the multi-time formalism is a time-symmetric formulation of quantum mechanics. It allows to describe experiments with multiple preparation and measurement stages and, in particular, pre- and post-selected systems. On the other hand, the model of post-selected closed timelike curves (P-CTCs) is a particular quantum model for CTCs, which formalizes physically the notion of time travel. It was already shown that linear two-time states and linear P-CTCs are related to process matrices. This suggested that linear two-time states and linear P-CTCs are actually equivalent. What about the spaces of general two-time states, or even multi-time states, and general P-CTCs? It is shown that any pure two-time operator can be implemented up to proportionality using a circuit assisted by a single P-CTC. Furthermore, multi-time states and two-time operators can be related using a circuit involving at most the same number of P-CTCs as there are backward-evolving states in the related multi-time state. Finally, mixed two-time operators can be achieved using a mixture of P-CTC-assisted circuits.
Title:
Connecting indefinite causal order processes to composable quantum protocols in a spacetime
Abstract:
Process matrices provide a general framework to model quantum information processing protocols without assuming a fixed and acyclic background spacetime. However, it is an open question to characterize the subset of processes that are physically realizable in a fixed background spacetime. A related question is that process matrices are known to be non-composable while composability is a basic property of physical processes. A bottom-up approach to characterizing physical processes is given by the framework of quantum circuits with quantum control of causal order (QC-QC). On the other hand, a recent top-down approach to the problem connects to the framework of causal boxes, which models composable physical protocols in a background spacetime, while allowing for quantum states to be delocalized in space and in time. The subset of causal boxes that incorporate the set-up assumptions of the process framework correspond to so-called process boxes. Here we address the physicality and composability questions for process matrices by connecting these bottom-up and top-down approaches. We first give a procedure for modelling each QC-QC as a causal box. This allows us to define composition of QC-QCs in terms of composition of causal boxes and resolves the composability problem. We then consider the mapping from process boxes to QC-QCs. Our results suggest that the general class of processes that can be physically implemented in a fixed background spacetime are those that can be interpreted as QC-QCs. Intuitively, this result follows from the physical principle of relativistic causality in the background spacetime. This provides an avenue for exploring further connections between information-theoretic and spacetime related causality notions, and composability of physical experiments.
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