Lecture 8: Period Finding: Simon`s Problem over ZN 1 Problem
... most convenient to work with the oracle which behaves as follows: Of (|xi|bi) = |xi|b ⊕ f (x)i, where b is an m-qubit string. We have the promise that f is periodic; namely for some s ∈ ZN \ {0}, f (x) = f (x + s) for all x ∈ ZN . Otherwise, all of f ’s values are assumed to be distinct: that is, we ...
... most convenient to work with the oracle which behaves as follows: Of (|xi|bi) = |xi|b ⊕ f (x)i, where b is an m-qubit string. We have the promise that f is periodic; namely for some s ∈ ZN \ {0}, f (x) = f (x + s) for all x ∈ ZN . Otherwise, all of f ’s values are assumed to be distinct: that is, we ...
Factoring 51 and 85 with 8 qubits
... constitute a fully genuine implementation of order-finding (but not of factoring). The main point of this work, that the number of qubits required in the first register is greatly reduced for composites in the series (3), applies to either approach. Smolin, Smith, and Vargo16 recently addressed the ...
... constitute a fully genuine implementation of order-finding (but not of factoring). The main point of this work, that the number of qubits required in the first register is greatly reduced for composites in the series (3), applies to either approach. Smolin, Smith, and Vargo16 recently addressed the ...
Do not mess with time: Probing faster than light travel and
... example, think of the causal loops where at some point ones travels back in time to give to his/her past-self the numbers associated to some lottery. Several solutions have been proposed for such paradoxes (see e.g. for a detailed discussion Ref. 1) we shall here focus on the so called Hawking’s chr ...
... example, think of the causal loops where at some point ones travels back in time to give to his/her past-self the numbers associated to some lottery. Several solutions have been proposed for such paradoxes (see e.g. for a detailed discussion Ref. 1) we shall here focus on the so called Hawking’s chr ...
Advanced Quantum Mechanics - Department of Physics and
... is hermitean and the basic commutation relation is satisfied. We want to stress at this point the nonobservability of the wave function. It are the operators and their eigenvalues as outcome of measurements that are relevant. As far as the Hilbert space is concerned, one can work with any appropriat ...
... is hermitean and the basic commutation relation is satisfied. We want to stress at this point the nonobservability of the wave function. It are the operators and their eigenvalues as outcome of measurements that are relevant. As far as the Hilbert space is concerned, one can work with any appropriat ...
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... perspective would be deterministic, where all physical quantities describing a system can be simultaneously specified for all times. For example, students in classical electrodynamics courses are typically instructed to think of an electron as a localized particle with a well-defined position and mo ...
... perspective would be deterministic, where all physical quantities describing a system can be simultaneously specified for all times. For example, students in classical electrodynamics courses are typically instructed to think of an electron as a localized particle with a well-defined position and mo ...
Hydrogen Atoms under Magnification: Direct
... atomic and molecular orbitals [6,7]. In this Letter we will present experiments where the nodal structure of electronic wave functions of hydrogen atoms is measured, making use of a photoionization microscopy experiment, where photoelectrons resulting from ionization after excitation of a quasibound ...
... atomic and molecular orbitals [6,7]. In this Letter we will present experiments where the nodal structure of electronic wave functions of hydrogen atoms is measured, making use of a photoionization microscopy experiment, where photoelectrons resulting from ionization after excitation of a quasibound ...
CHAPTER 16: Quantum Mechanics and the Hydrogen Atom
... Heisenberg uncertainty principle • “Bohr orbit” idea violates the uncertainty principle! • Certain pairs of variables (e.g., x and px; E and t; r and L) can’t be known exactly at the same time • E.g., (∆x)(∆px) ≥ h/4π , where ∆x denotes an uncertainty in x, etc. Clearly both uncertainties can’t be ...
... Heisenberg uncertainty principle • “Bohr orbit” idea violates the uncertainty principle! • Certain pairs of variables (e.g., x and px; E and t; r and L) can’t be known exactly at the same time • E.g., (∆x)(∆px) ≥ h/4π , where ∆x denotes an uncertainty in x, etc. Clearly both uncertainties can’t be ...
Quantum Hall effect and the topological number in graphene
... tc = 1.5. If the chemical potential is in that gap, Hall conductivity is zero. In the graphene case, B = 400T corresponds to φ ≈ 0.005φ0 When ta = tb = 1 and tc = 2, two zero modes in the Brillouin zone merge into a confluent mode at H = 0[18]. In that case gaps are visible at every integer number n ...
... tc = 1.5. If the chemical potential is in that gap, Hall conductivity is zero. In the graphene case, B = 400T corresponds to φ ≈ 0.005φ0 When ta = tb = 1 and tc = 2, two zero modes in the Brillouin zone merge into a confluent mode at H = 0[18]. In that case gaps are visible at every integer number n ...
![arXiv:0803.3834v2 [quant-ph] 26 May 2009](http://s1.studyres.com/store/data/015940141_1-1e8e53e4d619ce68a74ed7b6b3742d1d-300x300.png)
Spontaneous emission of an excited two
... with Lorentzian type spectrum. The next step is to select parameters gj , ḡj , ωj and Γj to simulate the original damping terms and fluctuation terms. Now there are two spectral functions, not just one spectral function as in rotating-wave approximation, the simulation task will become more complica ...
... with Lorentzian type spectrum. The next step is to select parameters gj , ḡj , ωj and Γj to simulate the original damping terms and fluctuation terms. Now there are two spectral functions, not just one spectral function as in rotating-wave approximation, the simulation task will become more complica ...
Topological Insulators and Topological Semi-metals
... The in-plane band dispersions near the Weyl nodes k z k z are thus quadratic rather than linear, with a phase of 4π for the chiral spin texture. The two Weyl nodes form a single pair ...
... The in-plane band dispersions near the Weyl nodes k z k z are thus quadratic rather than linear, with a phase of 4π for the chiral spin texture. The two Weyl nodes form a single pair ...
Chapter 12 Path Integral for Fermion Fields
... A → A + dΛ this functions transforms as Φ → Φ + Λ. Using the identity 2iΣαβ = γ α γ β − δ αβ one sees that ...
... A → A + dΛ this functions transforms as Φ → Φ + Λ. Using the identity 2iΣαβ = γ α γ β − δ αβ one sees that ...
EE1 2006: Solution to homework assignment 6 Problem 1: (a) Show
... region when it is in the first excited state, n = 1? Compare your result with the corresponding probability for the ground state, which was shown to be 16%. Explain the trend. Solution: First find the classical turning for the oscillations of the classical harmonic oscillator when its energy is equa ...
... region when it is in the first excited state, n = 1? Compare your result with the corresponding probability for the ground state, which was shown to be 16%. Explain the trend. Solution: First find the classical turning for the oscillations of the classical harmonic oscillator when its energy is equa ...
