The Need for Structure in Quantum Speedups
... OR function (because of Grover’s algorithm). On the other hand, as soon as we allow non-total functions, we can get enormous gaps. Aaronson [2] gave a Boolean function√f : S → {0, 1} for which R(f ) = N Ω(1) , yet Q(f ) = O (1).4 Other examples, for which R(f ) = Ω( N ) and Q(f ) = O(log N log log N ...
... OR function (because of Grover’s algorithm). On the other hand, as soon as we allow non-total functions, we can get enormous gaps. Aaronson [2] gave a Boolean function√f : S → {0, 1} for which R(f ) = N Ω(1) , yet Q(f ) = O (1).4 Other examples, for which R(f ) = Ω( N ) and Q(f ) = O(log N log log N ...
Topological Field Theories in 2 dimensions
... objects in the derived category of X. This method has been essentially confirmed for projective toric manifolds by Abouzaid [Ab], who proves the required mirror symmetry (B-side on X is equivalent to A-side on the Landau-Ginzburg model) without a priori reference to exceptional objects (and, in part ...
... objects in the derived category of X. This method has been essentially confirmed for projective toric manifolds by Abouzaid [Ab], who proves the required mirror symmetry (B-side on X is equivalent to A-side on the Landau-Ginzburg model) without a priori reference to exceptional objects (and, in part ...
Lecture 11 Identical particles
... Until now, our focus has largely been on the study of quantum mechanics of individual particles. However, most physical systems involve interaction of many (ca. 1023 !) particles, e.g. electrons in a solid, atoms in a gas, etc. In classical mechanics, particles are always distinguishable – at least ...
... Until now, our focus has largely been on the study of quantum mechanics of individual particles. However, most physical systems involve interaction of many (ca. 1023 !) particles, e.g. electrons in a solid, atoms in a gas, etc. In classical mechanics, particles are always distinguishable – at least ...
Topic 13: Quantum and nuclear physics
... For light having a wavelength of 500. nm we have E = hc/ = (6.6310-34)(3.00108)/(50010-9) = 3.9810-19 J. ...
... For light having a wavelength of 500. nm we have E = hc/ = (6.6310-34)(3.00108)/(50010-9) = 3.9810-19 J. ...
Fully nonlocal quantum correlations
... The standard nonlocality scenario consists of two distant systems on which two observers, Alice and Bob, perform respectively ma and mb different measurements of da and db possible outcomes. The outcomes of Alice and Bob are respectively labeled a and b, while their measurement choices are x and y, ...
... The standard nonlocality scenario consists of two distant systems on which two observers, Alice and Bob, perform respectively ma and mb different measurements of da and db possible outcomes. The outcomes of Alice and Bob are respectively labeled a and b, while their measurement choices are x and y, ...
61, 062310 (2000)
... Quantum no-cloning theorem 关1兴, which asserts that unknown pure states cannot be reproduced exactly by any physical means, is one of the most astonishing features of quantum mechanics. Wootters and Zurek 关1兴 have shown that the cloning machine violates the quantum superposition principle. Yuen and D ...
... Quantum no-cloning theorem 关1兴, which asserts that unknown pure states cannot be reproduced exactly by any physical means, is one of the most astonishing features of quantum mechanics. Wootters and Zurek 关1兴 have shown that the cloning machine violates the quantum superposition principle. Yuen and D ...
Quantum mechanics near closed timelike lines
... (i.e. , the existence of negative delays) makes no fundamental difference to the behavior of a network unless there is a closed path for infor mation. Such a path is not necessarily the trajectory of any carrier in the network because bits on different carriers interact and can exchange information ...
... (i.e. , the existence of negative delays) makes no fundamental difference to the behavior of a network unless there is a closed path for infor mation. Such a path is not necessarily the trajectory of any carrier in the network because bits on different carriers interact and can exchange information ...
From Quantum Gates to Quantum Learning
... – Measurement also makes X the new state and so interferes with computational processes – X is determined with some probability, implying uncertainty in the result ...
... – Measurement also makes X the new state and so interferes with computational processes – X is determined with some probability, implying uncertainty in the result ...
A tutorial on Quantum Cohomology
... which uses additive homology theory and applies to functions with nondegenerate critical points, and the Lusternik-Shnirelman inequality #(critical levels) > cup-length (X) which applies to functions with isolates critical points of arbitrary complexity and requires a multiplicative structure. – Suc ...
... which uses additive homology theory and applies to functions with nondegenerate critical points, and the Lusternik-Shnirelman inequality #(critical levels) > cup-length (X) which applies to functions with isolates critical points of arbitrary complexity and requires a multiplicative structure. – Suc ...
Reflection Symmetry and Energy-Level Ordering in Frustrated Spin
... Perron-Frobenius theorem: The lowest eigenvalue of any connected matrix having negative or vanishing off-diagonal elements is nondegenerate. Correponding eigenvector is a positive superposition of all basic states. After the rotation of all spins on one sublattice on ...
... Perron-Frobenius theorem: The lowest eigenvalue of any connected matrix having negative or vanishing off-diagonal elements is nondegenerate. Correponding eigenvector is a positive superposition of all basic states. After the rotation of all spins on one sublattice on ...
1996 Orchestrated Objective Reduction of Quantum Coherence in
... quantum systems can "self-collapse"by growing and persisting to reach a critical mass/time/energy threshold related to quantum gravity. In the OR scheme, the collapse outcomes ("eigenstates" need not be random, but can reflect (in some non-computable way) a quantum computation occurring in the coher ...
... quantum systems can "self-collapse"by growing and persisting to reach a critical mass/time/energy threshold related to quantum gravity. In the OR scheme, the collapse outcomes ("eigenstates" need not be random, but can reflect (in some non-computable way) a quantum computation occurring in the coher ...
Document
... The purpose of physics is to study entities of the natural world, existing independently from any particular observer's perception, and obeying universal and intelligible rules. Many physicists (inc. me) look at certain and reproducible events as real, so we like : If, without in any way disturbing ...
... The purpose of physics is to study entities of the natural world, existing independently from any particular observer's perception, and obeying universal and intelligible rules. Many physicists (inc. me) look at certain and reproducible events as real, so we like : If, without in any way disturbing ...
The Meaning of Elements of Reality and Quantum Counterfactuals
... particles have opposite values,’’ in the example discussed above. Priorities ( 1) and ( 3) are not relevant because violations of physical laws are not considered. The counterfactual worlds are different from the actual world not because of ``miracles,’’ i.e., violations of physical laws, but becaus ...
... particles have opposite values,’’ in the example discussed above. Priorities ( 1) and ( 3) are not relevant because violations of physical laws are not considered. The counterfactual worlds are different from the actual world not because of ``miracles,’’ i.e., violations of physical laws, but becaus ...
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