Quantum Interaction Approach in Cognition, Artificial Intelligence
... concept theory and, specifically, the study of ‘how concepts combine’. This failure was explicitly revealed by Hampton’s experiments [43], [44] which measured the deviation from classical set-theoretic membership weights of exemplars with respect to pairs of concepts and their conjunction or disjunc ...
... concept theory and, specifically, the study of ‘how concepts combine’. This failure was explicitly revealed by Hampton’s experiments [43], [44] which measured the deviation from classical set-theoretic membership weights of exemplars with respect to pairs of concepts and their conjunction or disjunc ...
Objectives Chapter 4 Objectives, continued Chapter 4 Bohr Model of
... • In 1926, Austrian physicist Erwin Schrödinger developed an equation that treated electrons in atoms as waves. • Together with the Heisenberg uncertainty principle, the Schrödinger wave equation laid the foundation for modern quantum theory. • Quantum theory describes mathematically the wave proper ...
... • In 1926, Austrian physicist Erwin Schrödinger developed an equation that treated electrons in atoms as waves. • Together with the Heisenberg uncertainty principle, the Schrödinger wave equation laid the foundation for modern quantum theory. • Quantum theory describes mathematically the wave proper ...
Local coordinate, wave vector, Fisher and Shannon information in
... authors [1–3]. Here the formalism of Luo [1] is applied and generalized for N-electron systems. Luo showed that the real part of the local value of a quantum observable is the expectation value of the quantum observable, while the imaginary part comprises the fluctuation closely related to the Fisher ...
... authors [1–3]. Here the formalism of Luo [1] is applied and generalized for N-electron systems. Luo showed that the real part of the local value of a quantum observable is the expectation value of the quantum observable, while the imaginary part comprises the fluctuation closely related to the Fisher ...
quantum computer graphics algorithms
... measuring a superposition state (containing all values f (x) ) has the effect of collapsing the superposition in one of the basis states, thus only giving the value of the function for one single value for x . Quantum computing needs more than parallelism in order to be useful: the ability to extrac ...
... measuring a superposition state (containing all values f (x) ) has the effect of collapsing the superposition in one of the basis states, thus only giving the value of the function for one single value for x . Quantum computing needs more than parallelism in order to be useful: the ability to extrac ...
Experiments in “Quantum Erasure” and “Delayed
... set of entangled photons is observed to have interacted in separate areas ‘Main’ and ‘Test’ of the same experiment. We use a double-slit apparatus with a crystal placed in front of both openings. We direct one of the two entangled photons to a normal screen Main and the other to the Test area. ...
... set of entangled photons is observed to have interacted in separate areas ‘Main’ and ‘Test’ of the same experiment. We use a double-slit apparatus with a crystal placed in front of both openings. We direct one of the two entangled photons to a normal screen Main and the other to the Test area. ...
Quantum computing and mathematical research
... How to control the (initial) quantum states? How to create the appropriate environment for the quantum mechanical system to evolve without observing? How to “fight” decoherence (the interaction of the system and the external environment)? How to use the phenomena of superposition and entanglement ef ...
... How to control the (initial) quantum states? How to create the appropriate environment for the quantum mechanical system to evolve without observing? How to “fight” decoherence (the interaction of the system and the external environment)? How to use the phenomena of superposition and entanglement ef ...
A Complete Characterization of Unitary Quantum
... Our results on Matrix Inversion • Classically, we know that n x n Matrix Inversion is in log2(n) space, but don’t believe it can be solved in classical log(n) space • k(n)-Well-conditioned Matrix Inversion • Input: Efficient encoding of 2k x 2k PSD matrix A, and s,t∈{0,1}k : ...
... Our results on Matrix Inversion • Classically, we know that n x n Matrix Inversion is in log2(n) space, but don’t believe it can be solved in classical log(n) space • k(n)-Well-conditioned Matrix Inversion • Input: Efficient encoding of 2k x 2k PSD matrix A, and s,t∈{0,1}k : ...
Facilitator`s Guide PDF
... participants the visualization of atomic orbitals for hydrogen at http://www.falstad.com/qmatom/. Use the “real orbitals” and start at n=1, moving to n=2 and n=3. Then change the value of l. (Optional: The changing color represents the phase of the wave—this is what’s “waving.” The probability densi ...
... participants the visualization of atomic orbitals for hydrogen at http://www.falstad.com/qmatom/. Use the “real orbitals” and start at n=1, moving to n=2 and n=3. Then change the value of l. (Optional: The changing color represents the phase of the wave—this is what’s “waving.” The probability densi ...
A REPORT ON QUANTUM COMPUTING
... environment (known as decoherence), a quantum computer can output results dependent on details of all its classical-like states. This is quantum parallelism - parallelism on a serial machine. But unlike classical bits, qubits can exist simultaneously as o and 1, with the probability for each state g ...
... environment (known as decoherence), a quantum computer can output results dependent on details of all its classical-like states. This is quantum parallelism - parallelism on a serial machine. But unlike classical bits, qubits can exist simultaneously as o and 1, with the probability for each state g ...
Unified and Generalized Approach to Quantum Error Correction David Kribs, Raymond Laflamme,
... Remark 1 The condition Eq. (9) is independent of the choice of basis fji ig that defines the family Pkl and of the operator-sum representation of E. In particular, under the P P changes j0k i l ukl jl iPand Fa b wab Eb , the scalars change to 0abkl a0 b0 k0 l0 ukk0 ul0 l waa0 wbb0 abkl ...
... Remark 1 The condition Eq. (9) is independent of the choice of basis fji ig that defines the family Pkl and of the operator-sum representation of E. In particular, under the P P changes j0k i l ukl jl iPand Fa b wab Eb , the scalars change to 0abkl a0 b0 k0 l0 ukk0 ul0 l waa0 wbb0 abkl ...
powerpoint
... The total angular momentum and only one of the three Cartesian components (z-component) can be determined exactly simultaneously. One component cannot exhaust the total momentum (because of “+1” in l(l +1) ). The angular momentum is quantized in both its length and orientation – it cannot point at a ...
... The total angular momentum and only one of the three Cartesian components (z-component) can be determined exactly simultaneously. One component cannot exhaust the total momentum (because of “+1” in l(l +1) ). The angular momentum is quantized in both its length and orientation – it cannot point at a ...
View slides
... test of the more stringent ETH. In the cases we study, a Krylov subspace of order 1,000 is enough to follow the evolution until thermalization. Given that, we can study much larger Hilbert spaces, up to order 15,000,000. (states still have 15,000,000 components). It is a different type of test becau ...
... test of the more stringent ETH. In the cases we study, a Krylov subspace of order 1,000 is enough to follow the evolution until thermalization. Given that, we can study much larger Hilbert spaces, up to order 15,000,000. (states still have 15,000,000 components). It is a different type of test becau ...
Observables and Measurements in Quantum Mechanics
... As we have seen, this is most succinctly done by treating the package of information that defines a state as if it were a vector in an abstract Hilbert space. Doing so provides the mathematical machinery that is needed to capture the physically observed properties of quantum systems. A method by whi ...
... As we have seen, this is most succinctly done by treating the package of information that defines a state as if it were a vector in an abstract Hilbert space. Doing so provides the mathematical machinery that is needed to capture the physically observed properties of quantum systems. A method by whi ...
Quantum teleportation
Quantum teleportation is a process by which quantum information (e.g. the exact state of an atom or photon) can be transmitted (exactly, in principle) from one location to another, with the help of classical communication and previously shared quantum entanglement between the sending and receiving location. Because it depends on classical communication, which can proceed no faster than the speed of light, it cannot be used for faster-than-light transport or communication of classical bits. It also cannot be used to make copies of a system, as this violates the no-cloning theorem. While it has proven possible to teleport one or more qubits of information between two (entangled) atoms, this has not yet been achieved between molecules or anything larger.Although the name is inspired by the teleportation commonly used in fiction, there is no relationship outside the name, because quantum teleportation concerns only the transfer of information. Quantum teleportation is not a form of transportation, but of communication; it provides a way of transporting a qubit from one location to another, without having to move a physical particle along with it.The seminal paper first expounding the idea was published by C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres and W. K. Wootters in 1993. Since then, quantum teleportation was first realized with single photons and later demonstrated with various material systems such as atoms, ions, electrons and superconducting circuits. The record distance for quantum teleportation is 143 km (89 mi).