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Reformulation of the No-Free-Lunch Theorem for Entangled Data Sets
[article]
2020
arXiv
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The No-Free-Lunch (NFL) theorem is a celebrated result in learning theory that limits one's ability to learn a function with a training data set. ...
This motivates a reformulation that accounts for the degree of entanglement in the training set. ...
One such fundamental result is the No-Free-Lunch (NFL) theorem [12] [13] [14] [15] [16] . ...
arXiv:2007.04900v1
fatcat:7clzaz2g6vgjtl4bn6qnfjquom
A World without Pythons would be so Simple
[article]
2021
arXiv
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As a corollary, we establish the Simple Entropy proposal for the holographic dual of the area of a marginally trapped surface as well as a similar holographic dual for the outermost extremal surface. ...
This is the converse of the Python's lunch conjecture, which proposes that operators with support between the minimal and outermost (quantum) extremal surfaces - e.g. the interior Hawking partners - are ...
This is analogous to a type of no-hair theorem: the set of holographic black holes with a stationary bifurcation surface is identical to the highly limited set of states with local modular Hamiltonians ...
arXiv:2102.07774v2
fatcat:bsyzafmkp5gynb3ynzmino5c7m
Universal Adversarial Examples and Perturbations for Quantum Classifiers
[article]
2021
arXiv
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We prove that for a set of k classifiers with each receiving input data of n qubits, an O(ln k/2^n) increase of the perturbation strength is enough to ensure a moderate universal adversarial risk. ...
In this paper, we study the universality of adversarial examples and perturbations for quantum classifiers. ...
Now the quantum no free lunch theorem is described as below. Lemma B1. ...
arXiv:2102.07788v1
fatcat:u6hes6uysbdbtoyplhs3mzk3hi
Bell's Universe: A Personal Recollection
[article]
2016
arXiv
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where some geometric aspects of the quantum states are illustrated. ...
Finally, I describe the huge influence Bell had on my own work, in particular on entanglement and Bell inequalities in particle physics and their experimental verification, and on mathematical physics, ...
Acknowledgments First of all, I am grateful to Mary Bell for the generosity of sharing her memories of her scientific career and her life with John. ...
arXiv:1605.08081v1
fatcat:vszdiopdfbai7hsqgrhomxmjbe
Holographic spacetime, black holes and quantum error correcting codes: A review
[article]
2021
arXiv
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We review quantum error correction and relevant recovery maps with toy examples based on tensor networks, and discuss how it provides the desired framework for bulk reconstruction in which apparent inconsistencies ...
have led to the reproduction of the Page curve of the Hawking radiation from black holes. ...
/IFCPAR grant no 6304-3. ...
arXiv:2110.14669v1
fatcat:huvytzq5rnf2zgzfxp7hjchg64
Computability and Complexity of Unconventional Computing Devices
[article]
2017
arXiv
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We discover that all these claims rely on the provision of one or more unphysical resources. ...
No Free Lunch theorem Wolpert and Macready (1997) prove "no free lunch" (NFL) theorems related to the efficiency of search algorithms. ...
Possibly there is a Quantum No-Free-Lunch theorem stating that digital quantum gate circuits need quantum error correction and AQO needs to manoeuvre adiabatically through a complicated energy landscape ...
arXiv:1702.02980v2
fatcat:pikmc4gtuncztofsjw6as7vetu
Resource Theories as Quantale Modules
[article]
2021
arXiv
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It describes the utility of systems with probabilistic behavior for the task of distinguishing between hypotheses, which said behavior may depend on. ...
We aim to counter the tendency for specialization in science by advancing a language that can facilitate the translation of ideas and methods between disparate contexts. ...
Theorem 4.22 (generalized cost). Given the same set-up as in theorem 4.21, let S be a
left-invariant subset of T . ...
arXiv:2112.02349v1
fatcat:fxn7ukraszbs5dntm355m3pxie
Laws beyond spacetime
[article]
2021
arXiv
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In fact, the challenges run so deep that the survival of the investigated analyses into the era of quantum gravity is questionable. ...
However, it is unclear that naturalistic forms of Humeanism can maintain their commitment to there being no necessary connections among distinct entities. ...
However, there is no free lunch: in the context of quantum gravity, primitivism and dispositionalism about laws face the difficulty (unknown to the Humeans) to articulate a non-temporal notion of nomic ...
arXiv:2111.04500v1
fatcat:i2gi2gdhojfclcxwxzialjrz3i
Information Causality, the Tsirelson Bound, and the 'Being-Thus' of Things
[article]
2017
arXiv
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In particular I first describe an argument, due to Demopoulos, to the effect that the so-called 'no-signalling' condition can be viewed as a generalisation of Einstein's principle that is appropriate for ...
I then argue that a compelling way to motivate information causality is to in turn consider it as a further generalisation of the Einsteinian principle that is appropriate for a theory of communication ...
Alice's data set. ...
arXiv:1708.08630v3
fatcat:tapg5giprnguvnbq4ydj6mev34
Schrödinger type equation for subjective identification of supply and demand
[article]
2018
arXiv
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The present authors have put forward a quantum game theory based model of market prices movements. ...
By using Fisher information, we present a construction of an equation of Schrödinger type for probability distributions for relationship between demand and supply. ...
The second one follow from the no free lunch principle.
Figure 1 : 1 The local minima of Fisher information. ...
arXiv:1812.11824v1
fatcat:d245vsqqvbcatjj3ymkypuvsse
On the learnability of quantum neural networks
[article]
2020
arXiv
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We consider the learnability of the quantum neural network (QNN) built on the variational hybrid quantum-classical scheme, which remains largely unknown due to the non-convex optimization landscape, the ...
This result implies the same learnability of QNN whether it is implemented on noiseless or noisy quantum machines. ...
The capacity of quantum neural networks. arXiv
preprint arXiv:1908.01364, 2019.
[30] Kyle Poland, Kerstin Beer, and Tobias J Osborne. No free lunch for quantum machine learning. ...
arXiv:2007.12369v1
fatcat:hlpzvycphjdj5puylo6jon7asi
Purely Bayesian counterfactuals versus Newcomb's paradox
[article]
2020
arXiv
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Based on this remark, I prove the existence of Newcomb-like problems for which an epistemic system necessarily expects the entity to make a counterfactually bad decision. ...
I prove that the counterfactual optimality of the 1-Box strategy depends on the player's prior on the predictor's additional data. ...
Acknowledgement The author is thankful for insightful discussions with El Mahdi El Mhamdi, among others. ...
arXiv:2008.04256v1
fatcat:wrxjkyns7baw5mkhlagno3o7ma
Entanglement and Quantum Information Transfer in Arrays of Interacting Quantum Systems
[article]
2009
arXiv
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for the spin system has an intuitive physical interpretation. ...
This thesis examines some of the more fundamental requirements of a successful quantum computation, namely the ability to transmit quantum information with maximum efficiency, and the creation of entanglement ...
According to the Jaynes principle, if the data set is compatible with a range of entanglements ǫ ∈ [ǫ − , ǫ + ], one should always assume ǫ = ǫ + . ...
arXiv:0909.0655v1
fatcat:e6w32nms3bhdpozyad34q6de5u
Generalization in Machine Learning via Analytical Learning Theory
[article]
2019
arXiv
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Moreover, the proposed theory provides a theoretical basis for a family of practically successful regularization methods in deep learning. ...
Unlike statistical learning theory, the proposed learning theory analyzes each problem instance individually via measure theory, rather than a set of problem instances via statistics. ...
Vikas Verma was supported by Academy of Finland project 13312683 / Raiko Tapani AT kulut. ...
arXiv:1802.07426v3
fatcat:7exfsfnk7bhq5nanydfkk7tyd4
Machine learning applications for noisy intermediate-scale quantum computers
[article]
2022
arXiv
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For our final application, we propose a variational algorithm in the area of approximate quantum cloning, where the data becomes quantum in nature. ...
In this Thesis, we develop and study three quantum machine learning applications suitable for NISQ computers, ordered in terms of increasing complexity of data presented to them. ...
Of particular importance are my PhD examiners, Raul Garcia-Patron Sanchez and Iordanis Kerenidis, for agreeing to give me a PhD at the end of the road. ...
arXiv:2205.09414v1
fatcat:bkkzng7zfza2ndpnhq4tiqp3wa
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