MOCK MODULAR FORMS AND QUANTUM MODULAR FORMS 1
... This map Qf is well-defined by Theorem 1.1.(3) because for each rational number x there is a unique qi equivalent to x under the action of Γ0 (N ) (see section 3 for details). Motivated by a number of examples from quantum invariants of 3-manifolds, Vassiliev invariants of knots, and period function ...
... This map Qf is well-defined by Theorem 1.1.(3) because for each rational number x there is a unique qi equivalent to x under the action of Γ0 (N ) (see section 3 for details). Motivated by a number of examples from quantum invariants of 3-manifolds, Vassiliev invariants of knots, and period function ...
Two Provers in Isolation
... communicating. Therefore the assumption that the provers cannot communicate is too weak. This observation can be turned into a purely classical argument by exhibiting a black-box two-party computation, that does not allow them to communicate, but that allows them to cheat the binding condition of th ...
... communicating. Therefore the assumption that the provers cannot communicate is too weak. This observation can be turned into a purely classical argument by exhibiting a black-box two-party computation, that does not allow them to communicate, but that allows them to cheat the binding condition of th ...
Demonstration of Entanglement of Electrostatically Coupled Singlet-Triplet Qubits M. D. Shulman
... splitting, J , between |S〉 and |T0 〉, and rotations around the x-axis are driven by a magnetic field gradient, ∆B z between the electrons. We implement the S-T0 qubit by confining two electrons to a double quantum dot (QD) in a two dimensional electron gas (2DEG) located 91nm below the surface of a ...
... splitting, J , between |S〉 and |T0 〉, and rotations around the x-axis are driven by a magnetic field gradient, ∆B z between the electrons. We implement the S-T0 qubit by confining two electrons to a double quantum dot (QD) in a two dimensional electron gas (2DEG) located 91nm below the surface of a ...
Quantum Field Theory: Underdetermination, Inconsistency, and
... empirically indistinguishable. In QFT, the quantities which are subject to experimental test are scattering matrix elements. Scattering matrix elements encode the outcomes of scattering experiments. The three variants of QFT are empirically indistinguishable in the sense that the sets of scattering ...
... empirically indistinguishable. In QFT, the quantities which are subject to experimental test are scattering matrix elements. Scattering matrix elements encode the outcomes of scattering experiments. The three variants of QFT are empirically indistinguishable in the sense that the sets of scattering ...
Nonclassical states of light propagating in Kerr media
... or to be more precise the effect of self-phase modulation of the optical field propagating in a nonlinear, isotropic medium. If the intensity of light propagating through the nonlinear medium is sufficiently high the refractive index of the medium depends on the intensity causing a nonlinear change ...
... or to be more precise the effect of self-phase modulation of the optical field propagating in a nonlinear, isotropic medium. If the intensity of light propagating through the nonlinear medium is sufficiently high the refractive index of the medium depends on the intensity causing a nonlinear change ...
Quantum Associative Memory
... • The second state rotation operator rotates the phases of the desired states and also rotates the phases of all the stored patterns as well – Will force the 2 different kinds of undesired states to have the same phase (rather ...
... • The second state rotation operator rotates the phases of the desired states and also rotates the phases of all the stored patterns as well – Will force the 2 different kinds of undesired states to have the same phase (rather ...
When is an area law not an area law?
... be independent of the size of B. However, this is not always true. Rather the putative [length]0 scaling of S for d = 1 is sometimes replaced by a logarithm, as happens for example if we are dealing with a massless field. Although strictly speaking, a logarithmic scaling is not an area law, it is co ...
... be independent of the size of B. However, this is not always true. Rather the putative [length]0 scaling of S for d = 1 is sometimes replaced by a logarithm, as happens for example if we are dealing with a massless field. Although strictly speaking, a logarithmic scaling is not an area law, it is co ...
Reliable quantum computers
... we have learned how to resist and reverse the effects of decoherence. This discovery has important consequences for quantum computation, but it will also have broader ramifications. Some of the milestones that have been reached this year are as follows. That quantum error correcting codes exist was ...
... we have learned how to resist and reverse the effects of decoherence. This discovery has important consequences for quantum computation, but it will also have broader ramifications. Some of the milestones that have been reached this year are as follows. That quantum error correcting codes exist was ...
Spin-based quantum computers made by chemistry: hows and whys†
... This journal is ª The Royal Society of Chemistry 2009 ...
... This journal is ª The Royal Society of Chemistry 2009 ...
slides
... A QFT on which spacetime? a QFT of gravitons on some background doesn’t work QG should explain origin and properties of spacetime itself (geometry and topology?) background independence! it can be only be a QFT on some auxiliary or internal space (local symmetry group is natural choice) a QFT of wha ...
... A QFT on which spacetime? a QFT of gravitons on some background doesn’t work QG should explain origin and properties of spacetime itself (geometry and topology?) background independence! it can be only be a QFT on some auxiliary or internal space (local symmetry group is natural choice) a QFT of wha ...
Neutral Atom Quantum Computing with Rydberg Blockade
... ensures that quantum noise does not pose a fundamental barrier to the practical realization of a quantum computer. Thus, the threshold theorem states that provided the noise in individual quantum gates is below a certain constant threshold it is possible to efficiently perform an arbitrarily large q ...
... ensures that quantum noise does not pose a fundamental barrier to the practical realization of a quantum computer. Thus, the threshold theorem states that provided the noise in individual quantum gates is below a certain constant threshold it is possible to efficiently perform an arbitrarily large q ...
Quantum imaging technologies
... independently know where to land in order to create an interference pattern usually associated with waves? The answer lies in interpreting each electron as being in a probabilistic mixture of going through both slits at the same time. To paraphrase Dirac, “each electron only interferes with itself”. ...
... independently know where to land in order to create an interference pattern usually associated with waves? The answer lies in interpreting each electron as being in a probabilistic mixture of going through both slits at the same time. To paraphrase Dirac, “each electron only interferes with itself”. ...
Observations on Hyperplane: II. Dynamical Variables and
... To firm up the definition, let’s reserve ‘quanton’ for any particle-like quanta of a quantized field or any bound state of such quanta due to interactions which have, themselves, no macroscopic classical field manifestation, i.e., so far as we know, interactions other than electromagnetism or gravit ...
... To firm up the definition, let’s reserve ‘quanton’ for any particle-like quanta of a quantized field or any bound state of such quanta due to interactions which have, themselves, no macroscopic classical field manifestation, i.e., so far as we know, interactions other than electromagnetism or gravit ...
Collapse of Probability Distributions in Relativistic Spacetime
... occurs along an equal-time hypersurface, say, t 0 , in whatever reference frame is being used. However, such a naïve instantaneous collapse process is inconsistent with relativity, because the equal-time hypersurfaces of different inertial reference frames are different. The attempts at implementa ...
... occurs along an equal-time hypersurface, say, t 0 , in whatever reference frame is being used. However, such a naïve instantaneous collapse process is inconsistent with relativity, because the equal-time hypersurfaces of different inertial reference frames are different. The attempts at implementa ...
Achieving quantum supremacy with sparse and noisy commuting
... 1.2 Related work and perspective Circuit depth and optimal sparse IQP sampling. Below we improve on the results of [11] to extend the hardness results of IQP sampling introduced in [11] to sparsely connected circuits. The motivation for this is both theoretical and practical. We want to both improve ...
... 1.2 Related work and perspective Circuit depth and optimal sparse IQP sampling. Below we improve on the results of [11] to extend the hardness results of IQP sampling introduced in [11] to sparsely connected circuits. The motivation for this is both theoretical and practical. We want to both improve ...