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 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.
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 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.
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 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.
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/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.
Hi all,
Tomorrow Laura Boggia will tell us about her masterthesis she completed at IBM with Ivano Tavernelli, entitled 'Quantum Machine Learning for Anomaly Detection in High Energy Physics'. See below for the abstract. The talk will take place at 2pm in F31.1 or on Zoom: https://ethz.zoom.us/j/362994444.
Best,
Ladina
%%%%%
Abstract:
The advent of quantum computers gave rise to research for new applications that can be efficiently executed with the use of a quantum processor. Quantum Machine Learning (QML) is a prominent application for quantum devices and is described as the intersection between machine learning and quantum computation. High Energy Physics (HEP), as a computationally intensive domain of research, is a natural candidate for the application of QML. The search of new physics beyond the Standard Model (SM), that was initiated after the discovery of the Higgs particle, can potentially benefit from this new computing paradigm. We investigate the use of a QML protocol, namely Quantum Support Vector Machine (QSVM), for unravelling physics beyond the processes that can be described by the SM. The main differentiation of a QSVM relies on the use of a quantum feature map for the embedding of the input data via quantum circuits that can be efficiently evaluated on a quantum computer. In our work, we start from data sets containing simulated SM events and we randomly distort the data to introduce anomalies. Training on these two classes of data, we prepare a QML model that can classify anomalies on a complete data set coming from an Large Hadron Collider (LHC) experiment (SM and anomalies included). We perform a parametric analysis and identify how different parameters of the QSVM influence the performance of our workflow and determine an optimal parameter configuration for our use case. We demonstrate the potential of QSVM to better classify and identify patterns that will eventually lead to the understanding of new physics in HEP experiments. We confirm our findings with the use of a data set containing anomalous events caused by a graviton or Higgs particle and we also perform an experiment on an IBM quantum computer available in the cloud.
Hi all,
Tomorrow our visitor Lev Vaidman will tell us about 'Experimental demonstrations of exotic quantum measurements'. See below for the abstract. The talk will take place at 2pm in HIT F31.1 or on Zoom: https://ethz.zoom.us/j/362994444.
Best,
Ladina
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Abstract:
I will report first demonstrations of various types of quantum measurements. Nonlocal measurement - measurement of a property of a composite quantum system with spatially separated parts. Protective measurement - measuring expectation value of an observable with a single click. Robust weak measurement - measuring weak value of an observable with a single click. Modified interaction-free measurement: measurement that tells us that the place is empty without any particle passing through it.
Hi all,
Tomorrow our visitor from NUS Josep Lumbreras will tell us about ''Multi-armed quantum bandits'’.
See below for the abstract. The talk will take place at 2pm in HIT F31.1 or on Zoom: https://ethz.zoom.us/j/362994444.
Best,
Ladina
%%%%%
Abstract:
We initiate the study of tradeoffs between exploration and exploitation in online learning of properties of quantum states. Given sequential oracle access to an unknown quantum state, in each round, we are tasked to choose an observable from a set of actions aiming to maximize its expectation value on the state (the reward). Information gained about the unknown state from previous rounds can be used to gradually improve the choice of action, thus reducing the gap between the reward and the maximal reward attainable with the given action set (the regret). We provide various information-theoretic lower bounds on the cumulative regret that an optimal learner must incur, and show that it scales at least as the square root of the number of rounds played. We also investigate the dependence of the cumulative regret on the number of available actions and the dimension of the underlying space. Moreover, we exhibit strategies that are optimal for bandits with a finite number of arms and general mixed states. If we have a promise that the state is pure and the action set is all rank-1 projectors the regret can be interpreted as the infidelity with the target state and we provide some support for the conjecture that measurement strategies with less regret exist for this case.
Hi all,
Tomorrow our visitor from NUS Roberto Rubboli will tell us about ''Fundamental Limits on Correlated Catalytic State Transformations'’.
See below for the abstract. The talk will take place at 2pm in HIT F31.1 or on Zoom: https://ethz.zoom.us/j/362994444.
Best,
Ladina
%%%%%
Abstract:
Determining whether a given state can be transformed into a target state using free operations is one of the fundamental questions in the study of resources theories. Free operations in resource theories can be enhanced by allowing for a catalyst system that assists the transformation and is returned unchanged, but potentially correlated, with the target state. While this has been an active area of recent research, very little is known about the necessary properties of such catalysts. Here, we prove fundamental limits applicable to any correlated catalytic transformation by showing that a small residual correlation between catalyst and target state implies that the catalyst needs to be highly resourceful. In fact, the resources required diverge in the limit of vanishing residual correlation. We develop our results in a general resource theory framework and discuss its implications for the resource theory of athermality, the resource theory of coherence and entanglement theory.
https://arxiv.org/abs/2111.13356