Quantum Proofs for Classical Theorems
... is to go to complex numbers: using the identity eix = cos x + i sin x we have ei(x+y) = eix eiy = (cos x + i sin x)(cos y + i sin y) = cos x cos y − sin x sin y + i(cos x sin y + sin x cos y) . Taking the real parts of the two sides gives our identity. Another example is the probabilistic method, as ...
... is to go to complex numbers: using the identity eix = cos x + i sin x we have ei(x+y) = eix eiy = (cos x + i sin x)(cos y + i sin y) = cos x cos y − sin x sin y + i(cos x sin y + sin x cos y) . Taking the real parts of the two sides gives our identity. Another example is the probabilistic method, as ...
Entanglement and its Role in Shor`s Algorithm
... number c. Now c/22n is closely approximated by the fraction j/r and so r can be obtained classically using continued fractions. Choosing the larger register to be 2n qubits provides a high enough accuracy for c such that r can be determined from a single measurement on all 2n qubits. It is possible ...
... number c. Now c/22n is closely approximated by the fraction j/r and so r can be obtained classically using continued fractions. Choosing the larger register to be 2n qubits provides a high enough accuracy for c such that r can be determined from a single measurement on all 2n qubits. It is possible ...
An introduction to Quantum Complexity
... BQP is closed under complement BQP is closed under intersection (and union) ...
... BQP is closed under complement BQP is closed under intersection (and union) ...
Application of Quantum Computing principles to Natural Language Processing
... one state to another is achieved by using a pulse of energy, such as from a laser let’s say that we use 1 unit of laser energy. But what if we only use half a unit of laser energy and completely isolate the particle from all external influences? According to quantum law, the particle then enters a s ...
... one state to another is achieved by using a pulse of energy, such as from a laser let’s say that we use 1 unit of laser energy. But what if we only use half a unit of laser energy and completely isolate the particle from all external influences? According to quantum law, the particle then enters a s ...
Time-asymptotic wave propagation in collisionless plasmas
... finite amplitude smaller 共in the case of initial damping兲 than its initial value but different from zero. The decrease of the amplitude oscillations occurs because, as the trapped particles oscillate on orbits of different frequencies, they lose phase coherence until there is no net density flux in ...
... finite amplitude smaller 共in the case of initial damping兲 than its initial value but different from zero. The decrease of the amplitude oscillations occurs because, as the trapped particles oscillate on orbits of different frequencies, they lose phase coherence until there is no net density flux in ...
From Quantum Gates to Quantum Learning: recent research and
... – Circuit behavior is governed explicitly by quantum mechanics – Signal states are vectors interpreted as a superposition of binary ...
... – Circuit behavior is governed explicitly by quantum mechanics – Signal states are vectors interpreted as a superposition of binary ...
Entanglement and its Role in Shor`s Algorithm
... amount of classical resources. In recent work, Jozsa and Linden [4] have proven that, if a quantum algorithm cannot be simulated classically using resources only polynomial in the size of the input data, then it must have multipartite entanglement involving unboundedly many of its qubits – if it is ...
... amount of classical resources. In recent work, Jozsa and Linden [4] have proven that, if a quantum algorithm cannot be simulated classically using resources only polynomial in the size of the input data, then it must have multipartite entanglement involving unboundedly many of its qubits – if it is ...
Braid Topologies for Quantum Computation
... unlikely at low enough temperature. This built in protection from error and decoherence is an appealing feature of TQC which may compensate for the extreme technical challenges that will have to be overcome to realize it. It has been shown that several different kinds of nonabelian quasiparticles ca ...
... unlikely at low enough temperature. This built in protection from error and decoherence is an appealing feature of TQC which may compensate for the extreme technical challenges that will have to be overcome to realize it. It has been shown that several different kinds of nonabelian quasiparticles ca ...
Free Energies of Cavity and Noncavity Hydrated Electrons at the
... are packed within the electron’s wave function (possibly even to a higher density than in bulk liquid water),1,7 or as a hybrid of these two pictures, with strong overlap between the electron’s wave function and the first-shell water molecules that surround a small central cavity.8,12 However, as of ...
... are packed within the electron’s wave function (possibly even to a higher density than in bulk liquid water),1,7 or as a hybrid of these two pictures, with strong overlap between the electron’s wave function and the first-shell water molecules that surround a small central cavity.8,12 However, as of ...
Quantum Symmetric States - UCLA Department of Mathematics
... The tail σ-algebra is the intersection of the σ-algebras generated by {xN , xN +1 , . . .} as N goes to ∞. Thus, the expectation E can be seen as an integral (w.r.t. a probability measure on the tail algebra) — that is, as a sort of convex combination — of expectations with respect to which the rand ...
... The tail σ-algebra is the intersection of the σ-algebras generated by {xN , xN +1 , . . .} as N goes to ∞. Thus, the expectation E can be seen as an integral (w.r.t. a probability measure on the tail algebra) — that is, as a sort of convex combination — of expectations with respect to which the rand ...
Classical canonical transformation theory as a tool to describe
... even for the simplest chemical objects which allow an exact quantum mechanical treatment. For more complicated polyatomic systems, the only computationally a†ordable tool in reaction dynamics has been so far classical trajectory simulations. These are known to provide good average results for reacti ...
... even for the simplest chemical objects which allow an exact quantum mechanical treatment. For more complicated polyatomic systems, the only computationally a†ordable tool in reaction dynamics has been so far classical trajectory simulations. These are known to provide good average results for reacti ...
Resonances, dissipation and decoherence in exotic and artificial atoms
... to compute quantum dot spectra. Among the most common examples, one can mention density functional theory [29–31], configuration interaction [32–34], Hartree-Fock calculations [35–37], quantum Monte Carlo methods [38–40], variational techniques [41–43] or many-body perturbation theory [44]. The nece ...
... to compute quantum dot spectra. Among the most common examples, one can mention density functional theory [29–31], configuration interaction [32–34], Hartree-Fock calculations [35–37], quantum Monte Carlo methods [38–40], variational techniques [41–43] or many-body perturbation theory [44]. The nece ...
