Matchgate and space-bounded quantum computations are equivalent
... ingredient for the classical simulability of the circuits (as indeed n.n. and next-n.n. actions are already universal for quantum computation [1]). Note that n.n. matchgate actions may be extended to arbitrary line pairs using the qubit SWAP operation on n.n. lines. However SWAP is not a matchgate ( ...
... ingredient for the classical simulability of the circuits (as indeed n.n. and next-n.n. actions are already universal for quantum computation [1]). Note that n.n. matchgate actions may be extended to arbitrary line pairs using the qubit SWAP operation on n.n. lines. However SWAP is not a matchgate ( ...
Half-integral weight Eichler integrals and quantum modular forms
... on R\{γ −1 ∞}. This provides one of the first examples of the burgeoning new theory of quantum modular forms, laid out by Zagier [22], which we review in Section 2.2. Essentially, a quantum modular form of weight k is a complex-valued function f on Q whose modular obstructions, or cocycles, f |k (1 ...
... on R\{γ −1 ∞}. This provides one of the first examples of the burgeoning new theory of quantum modular forms, laid out by Zagier [22], which we review in Section 2.2. Essentially, a quantum modular form of weight k is a complex-valued function f on Q whose modular obstructions, or cocycles, f |k (1 ...
Quantum Optics - Department of Physics and Astronomy
... that electrons behaved like waves. This wave-particle duality was at the heart of quantum mechanics, which would support a mathematical model to explain both properties. ...
... that electrons behaved like waves. This wave-particle duality was at the heart of quantum mechanics, which would support a mathematical model to explain both properties. ...
Schroedinger`s cat states generated by the environment
... one of the two equivalent scenarios, obtained from each other by π/2 rotation of the spins in the ensemble (Lx ↔ Lz ). (i) Lx coupling to the bath (cooperative population exchange): We prepare the system in a Lz -eigenstate with ωz = 0. (ii) Lz -coupling to the bath (pure cooperative dephasing): we ...
... one of the two equivalent scenarios, obtained from each other by π/2 rotation of the spins in the ensemble (Lx ↔ Lz ). (i) Lx coupling to the bath (cooperative population exchange): We prepare the system in a Lz -eigenstate with ωz = 0. (ii) Lz -coupling to the bath (pure cooperative dephasing): we ...
Maritime Applications of Quantum Computation
... models, like the RGB (Red, Green and Blue) and HSI (Hue, Saturation and Intensity) models, are used to specify colors in a standard way that makes sense under the theoretical and technological assumptions of classical computers and/or printing systems. The mathematical definition of a qubit presente ...
... models, like the RGB (Red, Green and Blue) and HSI (Hue, Saturation and Intensity) models, are used to specify colors in a standard way that makes sense under the theoretical and technological assumptions of classical computers and/or printing systems. The mathematical definition of a qubit presente ...
Path integral for the quantum harmonic oscillator using elementary
... allowing us to obtain a final result which is exact for arbitrary N ~the number of intervals chosen for the discretization—see below!. These results are thus directly transferable to the case of a polymer chain with nonvanish537 ...
... allowing us to obtain a final result which is exact for arbitrary N ~the number of intervals chosen for the discretization—see below!. These results are thus directly transferable to the case of a polymer chain with nonvanish537 ...
Physics 139B Solutions to Homework Set 4 Fall 2009 1. Liboff
... In case (b), there are no first-order transitions from the ground state to excited states of the oscillator with quantum number k ≥ 2. This is a consequence of eq. (19), which indicates that h0| x |ki = 0 for k ≥ 2. However, when higher orders of perturbation theory are taken into account, one does ...
... In case (b), there are no first-order transitions from the ground state to excited states of the oscillator with quantum number k ≥ 2. This is a consequence of eq. (19), which indicates that h0| x |ki = 0 for k ≥ 2. However, when higher orders of perturbation theory are taken into account, one does ...
Circuit QED: Superconducting Qubits Coupled to
... A quantum machine is a device whose degrees of freedom are intrinsically quantum mechanical. While we do not yet fully understand the properties of such devices, there is great hope (and some mathematical proof) that such machines will have novel capabilities that are impossible to realize on classi ...
... A quantum machine is a device whose degrees of freedom are intrinsically quantum mechanical. While we do not yet fully understand the properties of such devices, there is great hope (and some mathematical proof) that such machines will have novel capabilities that are impossible to realize on classi ...
The Basics of Quantum Physics: Introducing State Vectors
... In this case, you can say that the total of the two dice is the quantum number and that each quantum number represents a different state. Each system can be represented by a state vector — a one-dimensional matrix — that indicates the relative probability amplitude of being in each state. Here’s how ...
... In this case, you can say that the total of the two dice is the quantum number and that each quantum number represents a different state. Each system can be represented by a state vector — a one-dimensional matrix — that indicates the relative probability amplitude of being in each state. Here’s how ...
Communications: Entanglement switch for dipole arrays
... around 1, and cooling the dipoles to temperatures 共T兲 corresponding to a fraction of the dipole-dipole interaction energy 共⍀兲.30 For a dipole moment 共p兲 of few debyes, and a typical experimental electric field 共⬃105 V / m, required for the dipole moment to actually manifest itself12,31兲, dipoledipol ...
... around 1, and cooling the dipoles to temperatures 共T兲 corresponding to a fraction of the dipole-dipole interaction energy 共⍀兲.30 For a dipole moment 共p兲 of few debyes, and a typical experimental electric field 共⬃105 V / m, required for the dipole moment to actually manifest itself12,31兲, dipoledipol ...
Quantum Physical Symbol Systems
... interpretation. Symbol structures can designate objects in the world external to the system, thus allowing the system to affect and/or be affected by the designated object. Symbol structures designating a sequence of actions can be interpreted, thus allowing the system either to act in the world or ...
... interpretation. Symbol structures can designate objects in the world external to the system, thus allowing the system to affect and/or be affected by the designated object. Symbol structures designating a sequence of actions can be interpreted, thus allowing the system either to act in the world or ...
Atom optics: Old ideas, current technology, and new results
... and his father W.H. Bragg went on to perform a series of experiments to measure crystal structures using X-ray diffraction [24]. The work earned them the Nobel Prize in 1915. It is interesting to note that this work also brought together the previously disparate fields of crystallography and X-ray phy ...
... and his father W.H. Bragg went on to perform a series of experiments to measure crystal structures using X-ray diffraction [24]. The work earned them the Nobel Prize in 1915. It is interesting to note that this work also brought together the previously disparate fields of crystallography and X-ray phy ...
Operator Product Expansion and Conservation Laws in Non
... same spot that lowers to zero using both C and Ki . This is similar to the case of the null operator in the previous. As an example, again we specialize to the family of the operator n (However, the same arguments can be applied in any family where these requirements are met). Consider the spot deno ...
... same spot that lowers to zero using both C and Ki . This is similar to the case of the null operator in the previous. As an example, again we specialize to the family of the operator n (However, the same arguments can be applied in any family where these requirements are met). Consider the spot deno ...
The landscape of Anderson localization in a disordered medium
... exact sense described above. These lines will be called valleys of the landscape. One yet has to stress that the values of the control landscape u have to be significantly small in the valleys (i.e. much smaller that 1/λ where λ is a typical eigenvalue of the localized eigenfunction) for the inequal ...
... exact sense described above. These lines will be called valleys of the landscape. One yet has to stress that the values of the control landscape u have to be significantly small in the valleys (i.e. much smaller that 1/λ where λ is a typical eigenvalue of the localized eigenfunction) for the inequal ...
Quantum treatment of two-stage sub
... optical lattice field at the level of tens of MW/cm2 is required, what is hardly feasible in an experiment. Therefore, much lower temperature of atomic cloud is needed. At the same time, since the transition considered has degenerate energy levels, one can anticipate activation of so-called sub-Dopp ...
... optical lattice field at the level of tens of MW/cm2 is required, what is hardly feasible in an experiment. Therefore, much lower temperature of atomic cloud is needed. At the same time, since the transition considered has degenerate energy levels, one can anticipate activation of so-called sub-Dopp ...
Evolving Quantum circuits - Portland State University
... distinguishable different states of a qudit. These states can be a photon’s polarizations or an elementary particle’s spins. After encoding these distinguishable quantities into multiple-valued constants, a notation for ternary qudit states is |0>, |1> and |2> (we discuss only ternary quantum logic ...
... distinguishable different states of a qudit. These states can be a photon’s polarizations or an elementary particle’s spins. After encoding these distinguishable quantities into multiple-valued constants, a notation for ternary qudit states is |0>, |1> and |2> (we discuss only ternary quantum logic ...
What can string theory teach us about condensed matter physics?
... Also, we have σ(ω → ∞) = σ∞ , associated with the density of states for particle-hole creation (the “optical conductivity”) in the CFT3. Tuesday, October 4, 2011 ...
... Also, we have σ(ω → ∞) = σ∞ , associated with the density of states for particle-hole creation (the “optical conductivity”) in the CFT3. Tuesday, October 4, 2011 ...
Adiabatic creation of coherent superposition states in atomic beams
... One of the techniques frequently used for robust population transfer, and potentially available for the creation of superpositions, is stimulated Raman adiabatic passage (STIRAP) [6]. This technique uses two pulses, offset from each other in time, and the Raman coupling !a ↔ !c ↔ !b. One of the cond ...
... One of the techniques frequently used for robust population transfer, and potentially available for the creation of superpositions, is stimulated Raman adiabatic passage (STIRAP) [6]. This technique uses two pulses, offset from each other in time, and the Raman coupling !a ↔ !c ↔ !b. One of the cond ...
Introduction to loop quantum gravity
... How does one think in loop quantum gravity? Loop quantum gravity is based on the assumption that quantum mechanics and general relativity are correct. It assumes background independence and does not attempt to unify forces, only to quantise gravity. Spacetime is assumed to be four-dimensional and no ...
... How does one think in loop quantum gravity? Loop quantum gravity is based on the assumption that quantum mechanics and general relativity are correct. It assumes background independence and does not attempt to unify forces, only to quantise gravity. Spacetime is assumed to be four-dimensional and no ...
Polynomial-Time Algorithms for Prime Factorization and Discrete
... For quantum computation, in addition to \space" and \time," there is also a third potential resource, \accuracy." For a quantum computer to work, at least in any currently envisioned implementation, it will need to make changes in the quantum states of objects (e.g., atoms, photons, or atomic nuclei ...
... For quantum computation, in addition to \space" and \time," there is also a third potential resource, \accuracy." For a quantum computer to work, at least in any currently envisioned implementation, it will need to make changes in the quantum states of objects (e.g., atoms, photons, or atomic nuclei ...
A quantum logical and geometrical approach to the study of
... in the lattice of closed subspaces L共H兲 that, for the finite dimensional case, is a modular lattice.20 In this frame, the pure state of the system is represented by the meet 共i.e., the lattice infimum兲 of all actual properties, more on this below. A comprehensive description of QL in present termino ...
... in the lattice of closed subspaces L共H兲 that, for the finite dimensional case, is a modular lattice.20 In this frame, the pure state of the system is represented by the meet 共i.e., the lattice infimum兲 of all actual properties, more on this below. A comprehensive description of QL in present termino ...