PPT-Product-state approximations to quantum ground states

Fernando Brandão UCL Aram Harrow MIT arXiv 13100017 Constraint Satisfaction Problems x 1 c 1 c 2 c 3 k CSP Variables x 1 x n in Σ n Alphabet Σ Constraints . India. Bangalore. Abstract. . We will begin with definitions and examples of the notions of partial trace, partial transpose, completely positive maps and completely entangled . subspaces. . We shall display certain classes of states that can be determined by their partial traces. Entanglement is a powerful resource in Quantum information and communication. Separable states satisfy the Peres test of positivity under partial transpose (PPT) but there is an abundance of non-PPT (NPT) entangled states. Completely entangled subspaces of multipartite quantum systems viz., subspaces of the tensor product of finitely many finite-dimensional Hilbert spaces containing no non-zero product vector, have received attention by many researchers beginning with Bennett et al . Dieter Jaksch. Outline. Lecture 1: Introduction. What defines a quantum simulator? Quantum simulator criteria. Strongly correlated quantum systems.. Lecture 2: Optical lattices. Bose-Einstein condensation, adiabatic loading of an optical lattice. Hamiltonian . Dieter Jaksch. Outline. Lecture 1: Introduction. What defines a quantum simulator? Quantum simulator criteria. Strongly correlated quantum systems.. Lecture 2: Optical lattices. Bose-Einstein condensation, adiabatic loading of an optical lattice. Hamiltonian . Chapter 12. E-mail: . benzene4president@gmail.com. Web-site: http://clas.sa.ucsb.edu/staff/terri/. Quantum – . ch 12. 1. A photon has a frequency (v) of 5.45 x 10. 8. MHz. a. Calculate the photons wavelength (λ) in nm. Quantum Hamiltonian Complexity. Aram Harrow (MIT). Simons Institute. 16 Jan 2014. Entanglement. Original motivation for quantum computing. [Feynman ‘82]. Nature isn't classical, dammit, and if you want to make a simulation of Nature, you'd better make it quantum mechanical, and by golly it's a wonderful problem, because it doesn't look so easy.. and the monogamy of entanglement. Aram . Harrow (MIT). Brown SUMS. March 9, 2013. Quantum mechanics. QM has also explained:. the stability of atoms. the photoelectric effect. e. verything else we’ve looked at. Collection of two-state quantum systems (. qubits. ). Operations which manipulate isolated . qubits. or pairs of . qubits. Initialise. . qubit. to . single state. Detect . qubit. state. Large scale device:. Kyoto University, YITP, Masatoshi SATO. Mahito Kohmoto (University of Tokyo, ISSP). . Yong-Shi Wu (Utah University). In collaboration with. 2. Review paper on Topological Quantum Phenomena. Y. Tanaka, MS, N. . and the monogamy of entanglement. Aram . Harrow. MIT (UCL until Jan 2015). Quantum mechanics. QM has also explained:. the stability of atoms. the photoelectric effect. e. verything else we’ve looked at. Groundstates. Fernando . G.S.L. . Brand. ão. Imperial -> UCL. Based on joint work with . A. Harrow . . Paris, April 2013. Quantum Many-Body Systems. Quantum Hamiltonian . Principle of Superposition: . quantum states show interference and require both an amplitude and a phase for the parts. Superposition applies in time as well as space. For any observable, measured values come from a particular set of possibilities (sometimes quantised). Some states (. Quantum Hamiltonian Complexity. Aram Harrow (MIT). Simons Institute. 16 Jan 2014. Entanglement. Original motivation for quantum computing. [Feynman ‘82]. Nature isn't classical, dammit, and if you want to make a simulation of Nature, you'd better make it quantum mechanical, and by golly it's a wonderful problem, because it doesn't look so easy.. Daniel Reitzner. Research Center for Quantum Information, Slovak Academy of Sciences. 1st . eduQUTE. school on quantum technologies. Bratislava 19-22/02/2018. Recapitulation. What have we learnt yesterday.... Daniel Reitzner. Research Center for Quantum Information, Slovak Academy of Sciences. 1st . eduQUTE. school on quantum technologies. Bratislava 19-22/02/2018. Welcome notes. Do not hesitate to ask questions anytime during the talk if something will be unclear!.