Quantum Computing - Computer Science
... with the actual world. The result is obtained by a probability if we try to see the result of computation, and we can obtain the probability that the result holds. The basic unit of information in quantum computers is called a qubit. It is based on superposition states in which both the states 0 and ...
... with the actual world. The result is obtained by a probability if we try to see the result of computation, and we can obtain the probability that the result holds. The basic unit of information in quantum computers is called a qubit. It is based on superposition states in which both the states 0 and ...
Linköping University Post Print Quantum contextuality for rational vectors
... The Kochen-Specker theorem from 1967 [1] states that the quantum predictions from a three-dimensional quantum system (a qutrit) are inconsistent with noncontextual hidden variables. The proof uses 117 directions in three dimensions, arranged in a pattern such that they cannot be colored in a particu ...
... The Kochen-Specker theorem from 1967 [1] states that the quantum predictions from a three-dimensional quantum system (a qutrit) are inconsistent with noncontextual hidden variables. The proof uses 117 directions in three dimensions, arranged in a pattern such that they cannot be colored in a particu ...
Quantum Mechanics
... • What is simple and beautiful in QM: Matter and light have the same description, a hybrid of wave and particle. • What is unfathomable in QM: How do we know when to “switch” between a particle description and a wave description? This switch seems to occur when we measure the position of a photon or ...
... • What is simple and beautiful in QM: Matter and light have the same description, a hybrid of wave and particle. • What is unfathomable in QM: How do we know when to “switch” between a particle description and a wave description? This switch seems to occur when we measure the position of a photon or ...
Fidelity as a figure of merit in quantum error correction
... order (in the error rate) as the reversible case. Other codes take advantage of the fact that in addition to correcting e errors, any occurrence of e + 1 errors can also be detected, so that such uncorrectable qubits can be discarded [16]. When more than e errors occur for a coded qubit, the ensuing ...
... order (in the error rate) as the reversible case. Other codes take advantage of the fact that in addition to correcting e errors, any occurrence of e + 1 errors can also be detected, so that such uncorrectable qubits can be discarded [16]. When more than e errors occur for a coded qubit, the ensuing ...
pptx
... Application: “No low-energy trivial states” conjecture [Freedman-Hastings] states that there exist Hamiltonians where all low-energy states have topological order. ∴ This can only be possible with low coordination number. ...
... Application: “No low-energy trivial states” conjecture [Freedman-Hastings] states that there exist Hamiltonians where all low-energy states have topological order. ∴ This can only be possible with low coordination number. ...
Outline of section 4
... This corresponds to expanding the wavefunction in the complete set of eigenstates of the operator for the physical quantity we are measuring and interpreting the modulus squared of the expansion coefficients as the probability of getting a particular result. This is the general form of the Born inte ...
... This corresponds to expanding the wavefunction in the complete set of eigenstates of the operator for the physical quantity we are measuring and interpreting the modulus squared of the expansion coefficients as the probability of getting a particular result. This is the general form of the Born inte ...
Quantum Fourier Transform for Shor algorithm. PPT format.
... to another vector of complex numbers 2. This is a one-to-one mapping, so inverse transform exists 3. This is not the same condition as in standard Fourier Transform where we transform binary vectors to binary vectors ...
... to another vector of complex numbers 2. This is a one-to-one mapping, so inverse transform exists 3. This is not the same condition as in standard Fourier Transform where we transform binary vectors to binary vectors ...
Microsoft Word _ arxiv paper - Philsci
... either immediately or through theorems incorporating the lower axioms. Alfred Tarski came to the same understanding independently of Gödel four years later: “All sentences constructed according to Gödel’s method possess the property that it can be established whether they are true or false on the ba ...
... either immediately or through theorems incorporating the lower axioms. Alfred Tarski came to the same understanding independently of Gödel four years later: “All sentences constructed according to Gödel’s method possess the property that it can be established whether they are true or false on the ba ...
Quantum Electronics
... our knowledge of the world, and be more productive in our work, quantum computing will continue that trend. But also, as some kinds of very difficult problems become practical to solve at all, this will change the kinds of things we can do. We know very little about how quantum mechanics works, and ...
... our knowledge of the world, and be more productive in our work, quantum computing will continue that trend. But also, as some kinds of very difficult problems become practical to solve at all, this will change the kinds of things we can do. We know very little about how quantum mechanics works, and ...
Witnessing quantumness of a system by observing only its classical
... distinguish ρ±̃ . This implies that ρ+ , ρ− , which is a contradiction. Hence, we conclude that in order to reproduce the above correlation functions, the classical system must have an additional observable T 0 that cannot be simultaneously sharp when T is. In our representation, that observable can ...
... distinguish ρ±̃ . This implies that ρ+ , ρ− , which is a contradiction. Hence, we conclude that in order to reproduce the above correlation functions, the classical system must have an additional observable T 0 that cannot be simultaneously sharp when T is. In our representation, that observable can ...
Probability amplitude
In quantum mechanics, a probability amplitude is a complex number used in describing the behaviour of systems. The modulus squared of this quantity represents a probability or probability density.Probability amplitudes provide a relationship between the wave function (or, more generally, of a quantum state vector) of a system and the results of observations of that system, a link first proposed by Max Born. Interpretation of values of a wave function as the probability amplitude is a pillar of the Copenhagen interpretation of quantum mechanics. In fact, the properties of the space of wave functions were being used to make physical predictions (such as emissions from atoms being at certain discrete energies) before any physical interpretation of a particular function was offered. Born was awarded half of the 1954 Nobel Prize in Physics for this understanding (see #References), and the probability thus calculated is sometimes called the ""Born probability"". These probabilistic concepts, namely the probability density and quantum measurements, were vigorously contested at the time by the original physicists working on the theory, such as Schrödinger and Einstein. It is the source of the mysterious consequences and philosophical difficulties in the interpretations of quantum mechanics—topics that continue to be debated even today.