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Quantum Computation, Complexity, and Many-Body Physics
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Recently developed quantum algorithms suggest that quantum computers can solve certain problems and perform certain tasks more efficiently than conventional computers. Among other reasons, this is due to the possibility of creating non-classical correlations, or quantum entanglement, which is a phenomena hard or impossible to reproduce by classical-information methods. In this thesis I first investigate the simulation of quantum systems on a quantum computer constructed of two-level quantum elements or qubits. For this purpose, I present algebra mappings that allow one to obtain physical properties and compute correlation functions of fermionic, anyonic, and bosonic systems with such a computer. The results obtained show that the complexity of preparing a quantum state which contains the desired information for the computation is crucial. Second, I present a wide class of quantum computations, which could involve entangled states, that can be simulated with the same efficiency on both types of computers. The notion of generalized quantum entanglement then naturally emerges. This generalization of entanglement is based on the idea that entanglement is an observer-dependent concept, that is, relative to a set of preferred observables.
Forward citations
Cited by 5 Pith papers
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Enabling Lie-Algebraic Classical Simulation beyond Free Fermions
Symmetry-adapted Pauli-orbit and modified Gell-Mann bases make polynomial-dimensional dynamical Lie algebras practically simulable beyond free fermions.
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The Lie Algebra of XY-mixer Topologies and Warm Starting QAOA for Constrained Optimization
The paper decomposes dynamical Lie algebras of XY-mixer topologies and demonstrates warm-starting QAOA via pre-training on restricted generators to improve convergence on constrained optimization problems.
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Euclidean-Monte-Carlo-informed ground-state preparation for quantum simulation of scalar field theory
A classical pipeline turns Euclidean Monte Carlo correlation data into a variational ansatz and an efficient quantum circuit for the (1+1)D phi^4 ground state.
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Demonstration of Efficient Predictive Surrogates for Large-scale Quantum Processors
Classical surrogates using truncated trigonometric expansions emulate noisy quantum processors and cut measurement overhead in VQE pre-training and Floquet phase identification.
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Implicit solvent sample-based quantum diagonalization
SQD with IEF-PCM solvation reproduces CASCI IEF-PCM energies for four small molecules on IBM quantum hardware.
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