Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 8 of 8 for “"local Hamiltonians"”.
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Improved Tools for Local Hamiltonians
… systems with a structured energy operator, a local Hamiltonian. We begin with the most structured setting where the Hamiltonian has a spectral gap and spatial locality. This setting is widely studied using approximate ground space projectors (AGSPs). In chapter 1 we give an improved analysis …
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Local Hamiltonians in quantum computation
In this thesis, I investigate aspects of local Hamiltonians in quantum computing. First, I focus on the Adiabatic Quantum Computing model, based on evolution with a time- dependent Hamiltonian. I show that to succeed using AQC, the Hamiltonian involved must have local structure, which leads to a …
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Complexity of Basis-Restricted Local Hamiltonians
… problems that ask about properties of local Hamiltonians, which are of critical importance in quantum complexity because they can be viewed as quantum generalizations of classical constraint satisfaction problems. In this work, we study the complexity of certain restricted variants of …
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Algorithms for quantum simulation: design, analysis, implementation, and application
… develop a classical sampler for time-dependent Hamiltonians, using which we give a simulation algorithm that substantially improves over previous approaches when the Hamiltonian varies significantly with time. We propose a general theory to analyzing product formulas, an approach to quantum …
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Control, gates, and error suppression with Hamiltonians in quantum computation
… in the limit of infinitely large penalties, local errors are completely suppressed. We further derive bounds for the finite-penalty case and present numerical simulations suggesting that the method achieves even greater protection than these bounds indicate. We next consider the task of …
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Random partitions and the quantum Benjamin-Ono hierarchy
… of L to construct a generating function y(u) of local Hamiltonians commuting with y3. This explicit y(u) is a special case of the y-operator defined implicitly by functional calculus in Nekrasov (2016).
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Efficiently Learning, Testing, and Simulating Quantum Many-Body Systems
… an area law in the ground state of any gapped local Hamiltonian with an arbitrary geometry. This new feature of ground-state entanglement is obtained using a connection to the seemingly different problem of finding the communication complexity of testing bipartite states. 3. We devise an …
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Quantum Stochastic Processes and Quantum Many-Body Physics
… condition renders the problem NP-hard. In the local Hamiltonian part, we study computation embedded into the ground state of a many-body quantum system, going beyond "history state" constructions with a linear clock. We first develop a series of mathematical techniques which allow us to study …