Quantum Computation, Quantum Theory and AI
... Quantum computers were first envisaged by Nobel Laureate physicist Feynman [47] in 1982. He conceived that no classical computer could simulate certain quantum phenomena without an exponential slowdown, and so realized that quantum mechanical effects should offer something genuinely new to computati ...
... Quantum computers were first envisaged by Nobel Laureate physicist Feynman [47] in 1982. He conceived that no classical computer could simulate certain quantum phenomena without an exponential slowdown, and so realized that quantum mechanical effects should offer something genuinely new to computati ...
Concepts and Methods of Mathematical Physics - math.uni
... Exercise 1: Show that for any vector space V and any linear map φ ∈ End(V ), we have V ∼ = ker(φ) ⊕ Im(φ). Show that V /ker(φ) ∼ = Im(φ). Hint: Choose a basis B1 = {e1 , .., ek }, ei = φ(gi ) of Im(φ) and complete it to a basis B = B1 ∪ {f1 , ..., fn−k } of V . By subtracting suitable linear combina ...
... Exercise 1: Show that for any vector space V and any linear map φ ∈ End(V ), we have V ∼ = ker(φ) ⊕ Im(φ). Show that V /ker(φ) ∼ = Im(φ). Hint: Choose a basis B1 = {e1 , .., ek }, ei = φ(gi ) of Im(φ) and complete it to a basis B = B1 ∪ {f1 , ..., fn−k } of V . By subtracting suitable linear combina ...
Deterministic probability: neither chance nor credence
... heads. Yet you remain quite sure, despite all this evidence, that the chance of heads this time is 50%. To what degree should you believe the proposition that the coin falls heads […]? Answer. […] 50% […]. To the extent that uncertainty about outcomes is based on certainty about their chances, it is ...
... heads. Yet you remain quite sure, despite all this evidence, that the chance of heads this time is 50%. To what degree should you believe the proposition that the coin falls heads […]? Answer. […] 50% […]. To the extent that uncertainty about outcomes is based on certainty about their chances, it is ...
Statistical Mechanics: Entropy, Order Parameters and Complexity
... Ensembles: The trick of statistical mechanics is not to study a single systems, but a large collection or ensemble of systems. Where understanding a single system is often impossible, calculating the behavior of an enormous collection of similarly prepared systems often allows one to answer most que ...
... Ensembles: The trick of statistical mechanics is not to study a single systems, but a large collection or ensemble of systems. Where understanding a single system is often impossible, calculating the behavior of an enormous collection of similarly prepared systems often allows one to answer most que ...
Observation of Quantum Oscillations between a Josephson Phase Qubit
... probability was previously measured by applying microwaves at a frequency !31 for a duration of 80 –100 ns. If the qubit is initially in state j1i, the !31 signal causes a transition to state j3i, quickly followed by the qubit tunneling into the right-hand well. In this way, the qubit measurement co ...
... probability was previously measured by applying microwaves at a frequency !31 for a duration of 80 –100 ns. If the qubit is initially in state j1i, the !31 signal causes a transition to state j3i, quickly followed by the qubit tunneling into the right-hand well. In this way, the qubit measurement co ...
here
... and symmetric spaces, to appear in Annales Institut Henri Poincare (Prob.Stat.) 69) D.Applebaum, R.Banuleos, Probabilistic approach to fractional integrals and the Hardy-Littlewood-Sobolev inequality, to appear in Proceedings of 9th Isaac Congress (Springer) 70) D.Applebaum, S.Blackwood, The Kalman- ...
... and symmetric spaces, to appear in Annales Institut Henri Poincare (Prob.Stat.) 69) D.Applebaum, R.Banuleos, Probabilistic approach to fractional integrals and the Hardy-Littlewood-Sobolev inequality, to appear in Proceedings of 9th Isaac Congress (Springer) 70) D.Applebaum, S.Blackwood, The Kalman- ...
Models of quantum computation and quantum programming
... Models of quantum computation and quantum programming languages • Boolean circuits [38] defined in terms of logical gates and used to compute Boolean functions f : {0, 1}m 7→ {0, 1}n ; they are used in complexity theory to study circuit complexity. • Lambda calculus defined by Church [39] and used ...
... Models of quantum computation and quantum programming languages • Boolean circuits [38] defined in terms of logical gates and used to compute Boolean functions f : {0, 1}m 7→ {0, 1}n ; they are used in complexity theory to study circuit complexity. • Lambda calculus defined by Church [39] and used ...
Mathematical Analysis of Evolution, Information, and Complexity
... Library of Congress Card No.: applied for British Library Cataloguing-in-Publication Data: A catalogue record for this book is available from the British Library. Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deut ...
... Library of Congress Card No.: applied for British Library Cataloguing-in-Publication Data: A catalogue record for this book is available from the British Library. Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deut ...
annual report 2015 - ARC Centre of Excellence for Engineered
... Quantum technologies are likely to touch all aspects of our lives, from computation to climate science. Our research community has compelling potential applications in mind, but the field is very young and the potential for new inventions based on quantum principles is large. Over the horizon, we fo ...
... Quantum technologies are likely to touch all aspects of our lives, from computation to climate science. Our research community has compelling potential applications in mind, but the field is very young and the potential for new inventions based on quantum principles is large. Over the horizon, we fo ...
Algebraic Topology Foundations of Supersymmetry and Symmetry
... basic techniques of Fourier analysis and convolution products. A natural generalization of such molecular, partial symmetries and their corresponding analytical versions involves convolution algebras – a functional/distribution [197, 198] based theory that we will discuss in the context of a more ge ...
... basic techniques of Fourier analysis and convolution products. A natural generalization of such molecular, partial symmetries and their corresponding analytical versions involves convolution algebras – a functional/distribution [197, 198] based theory that we will discuss in the context of a more ge ...
Quantum Computing
... It turns out that information theory and quantum mechanics fit together very well. In order to explain their relationship, this review begins with an introduction to classical information theory and computer science, including Shannon’s theorem, error correcting codes, Turing machines and computatio ...
... It turns out that information theory and quantum mechanics fit together very well. In order to explain their relationship, this review begins with an introduction to classical information theory and computer science, including Shannon’s theorem, error correcting codes, Turing machines and computatio ...