Quantum Gates and Simon`s Algorithm
... A register of two coupled qubits can hold any of the states |Ψi = α |↑↑i + β |↓↑i + γ |↑↓i + δ |↓↓i in the state space H2 ⊗ H2 = C2 ⊗ C2 . Two separate qubits Two separate qubits can hold any of the product states |Ψ1 i ⊗ |Ψ2 i = (α1 |↑i + β1 |↓i)⊗(α2 |↑i + β2 |↓i) in the state space H2 ⊕ H2 ⊂ C2 ⊕ ...
... A register of two coupled qubits can hold any of the states |Ψi = α |↑↑i + β |↓↑i + γ |↑↓i + δ |↓↓i in the state space H2 ⊗ H2 = C2 ⊗ C2 . Two separate qubits Two separate qubits can hold any of the product states |Ψ1 i ⊗ |Ψ2 i = (α1 |↑i + β1 |↓i)⊗(α2 |↑i + β2 |↓i) in the state space H2 ⊕ H2 ⊂ C2 ⊕ ...
Exotic spheres and curvature - American Mathematical Society
... the structure of these objects as smooth manifolds. Second, to outline the basics of curvature for Riemannian manifolds which we will need later on. In subsequent sections, we will explore the interaction between topology and geometry for exotic spheres. We will use the term differentiable to mean di ...
... the structure of these objects as smooth manifolds. Second, to outline the basics of curvature for Riemannian manifolds which we will need later on. In subsequent sections, we will explore the interaction between topology and geometry for exotic spheres. We will use the term differentiable to mean di ...
Quantum Information with Fermionic Gaussian States - Max
... Theoretical and Mathematical Physics ...
... Theoretical and Mathematical Physics ...
Lecture Notes for Physics 229: Quantum Information and Computation
... Furthermore, in quantum theory, noncommuting observables cannot simultaneously have precisely de ned values (the uncertainty principle), and in fact performing a measurement of one observable A will necessarily in uence the outcome of a subsequent measurement of an observable B , if A and B do not c ...
... Furthermore, in quantum theory, noncommuting observables cannot simultaneously have precisely de ned values (the uncertainty principle), and in fact performing a measurement of one observable A will necessarily in uence the outcome of a subsequent measurement of an observable B , if A and B do not c ...
t+1
... 1. Project onto ground state of Ht+1 2. t = t + 1 For (suitable representation of) trivial group G = 1, G-isometric PEPS = maximally entangled pairs ...
... 1. Project onto ground state of Ht+1 2. t = t + 1 For (suitable representation of) trivial group G = 1, G-isometric PEPS = maximally entangled pairs ...
Resource Theory of Coherence
... on a d-dimensional system; we show that a maximally coherent state of rank d is always sufficient as a resource if incoherent operations are allowed, and rank d2 for “strictly incoherent” operations. We also show lower bounds on the simulation cost of channels that allow us to conclude that there ex ...
... on a d-dimensional system; we show that a maximally coherent state of rank d is always sufficient as a resource if incoherent operations are allowed, and rank d2 for “strictly incoherent” operations. We also show lower bounds on the simulation cost of channels that allow us to conclude that there ex ...
Emulating Quantum Computation
... infancy of the field has resulted in research covering a huge number of often very specific ideas which are spread across numerous architectures and approaches. Very little of this relates to the simulation or emulation of quantum computation on classical computers. Any development in new techniques ...
... infancy of the field has resulted in research covering a huge number of often very specific ideas which are spread across numerous architectures and approaches. Very little of this relates to the simulation or emulation of quantum computation on classical computers. Any development in new techniques ...
Hyperbolic Geometry and 3-Manifold Topology
... Example 2.2. (Thurston [T1]) Let X be a closed hyperbolic 3-manifold that fibers over the circle with fiber S. Let N be the infinite cyclic covering space corresponding to S. Topologically, N ≈ S × R but area(S × t) is uniformly bounded. Further, since π1 (N ) is normal in π1 (X), they both have the sa ...
... Example 2.2. (Thurston [T1]) Let X be a closed hyperbolic 3-manifold that fibers over the circle with fiber S. Let N be the infinite cyclic covering space corresponding to S. Topologically, N ≈ S × R but area(S × t) is uniformly bounded. Further, since π1 (N ) is normal in π1 (X), they both have the sa ...
Springer Tracts in Modern Physics
... Mesoscopic physics has emerged as a new, interdisciplinary field combining concepts of atomic, molecular, cluster, and condensed-matter physics. On the one hand mesoscopic systems represent an important class of electronic devices in the rapidly growing fields of micro- and nano-physics. Quantum int ...
... Mesoscopic physics has emerged as a new, interdisciplinary field combining concepts of atomic, molecular, cluster, and condensed-matter physics. On the one hand mesoscopic systems represent an important class of electronic devices in the rapidly growing fields of micro- and nano-physics. Quantum int ...
![arXiv:math/0601458v1 [math.QA] 19 Jan 2006](http://s1.studyres.com/store/data/016933886_1-4589dd82cd2aa488abf2eaccb6d6b836-300x300.png)
arXiv:math/0601458v1 [math.QA] 19 Jan 2006
... Categorification is best understood as the reverse of “decategorification”. This is a process which begins with some category, and produces a structure for which isomorphisms in the original category appear as equations between objects instead. Categorification is the reverse process, replacing equa ...
... Categorification is best understood as the reverse of “decategorification”. This is a process which begins with some category, and produces a structure for which isomorphisms in the original category appear as equations between objects instead. Categorification is the reverse process, replacing equa ...
Prog. Theor. Phys. Suppl. 176, 384 (2008).
... a complex phase eiθ , where θ = 0, π correspond to the statistics of bosons and fermions, respectively, and θ = 0, π is referred to as the statistics of Abelian anyons. The statistics of non-Abelian anyons are described by k × k unitary matrices acting on a degenerate ground-state manifold with k > ...
... a complex phase eiθ , where θ = 0, π correspond to the statistics of bosons and fermions, respectively, and θ = 0, π is referred to as the statistics of Abelian anyons. The statistics of non-Abelian anyons are described by k × k unitary matrices acting on a degenerate ground-state manifold with k > ...
Quantum Physics of Nature QuPoN 2015 Book of Abstracts
... with high spatial resolution, which, e.g., can be used to project complex holograms. Modern LC-SLMs additionally allow to modulate the reflected phase front by several multiples of a wavelength. These "thick" phase patterns have similar properties as volume holograms, showing wavelength and angular ...
... with high spatial resolution, which, e.g., can be used to project complex holograms. Modern LC-SLMs additionally allow to modulate the reflected phase front by several multiples of a wavelength. These "thick" phase patterns have similar properties as volume holograms, showing wavelength and angular ...
