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Classical Simulation of Quantum Systems

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dc.contributor.author Van den Nest, Maarten
dc.contributor.author Verstraete, Frank
dc.date.accessioned 2010-12-01T00:17:58Z
dc.date.available 2010-12-01T00:17:58Z
dc.date.issued 2010-07-20
dc.identifier.uri http://hdl.handle.net/2429/30253
dc.description.abstract The study of quantum computations that can be simulated efficiently classically is of interest for numerous reasons. On a fundamental level, such an investigation sheds light on the intrinsic computational power that is harnessed in quantum mechanics as compared to classical physics. More practically, understanding which quantum computations do not offer any speed-ups over classical computation provides insights in where (not) to look for novel quantum algorithmic primitives. On the other hand, classical simulation of many-body systems is a challenging task, as the dimension of the Hilbert space scales with the number of particles. Therefore, to understand the properties of the systems, suitable approximation methods need to be employed. The lectures will be divided into two parts. In the first part we discuss classical simulation of quantum computation from several perspectives. We review a number of well-known examples of classically simulatable quantum computations, such as the Gottesman-Knill theorem, matchgate simulation and tensor contraction methods. We further discuss simulation methods that are centred on classical sampling methods (‘weak simulation’), and illustrate how these techniques outperform methods that rely on the exact computation of measurement probabilities (‘strong simulation’). The second part focuses on "Entanglement and variational wavefunctions in quantum many body physics". We review the idea of entanglement in quantum many-body systems and how it helps us to understand the success of numerical renormalization group methods. In particular we will discuss a few variational wave-function based methods for simulating strongly correlated quantum systems, which include (1) matrix product states (2) multiscale entanglement renormalization ansatz (3) projected entangled pair states and (4) continuous matrix product states for quantum field theories. en
dc.language.iso eng en
dc.subject classical simulation methods, quantum systems, quantum computation en
dc.title Classical Simulation of Quantum Systems en
dc.title.alternative Simulation of quantum many body systems en
dc.type text en
dc.type moving image en
dc.description.affiliation Non UBC en
dc.description.reviewstatus Unreviewed en
dc.description.scholarlevel Faculty en


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Simulation 1.mp4 197.3Mb video/mp4 Video View in browser View/Open
Simulation 2.mp4 225.5Mb video/mp4 Video View in browser View/Open
Simulation 3.mp4 203.8Mb video/mp4 Video View in browser View/Open
Simulation 4.mp4 205.4Mb video/mp4 Video View in browser View/Open
Simulation 5.mp4 206.4Mb video/mp4 Video View in browser View/Open
Simulation 6.mp4 204.1Mb video/mp4 Video View in browser View/Open
classical_simulation.pdf 5.219Mb Adobe Portable Document Format Slides   View/Open
classical_simulation2.pdf 544.5Kb Adobe Portable Document Format Slides   View/Open
classical_simulation3.pdf 601.1Kb Adobe Portable Document Format Slides   View/Open
 

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