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This paper discusses a restriction of quantum theory, in which very complex states would be excluded. The toy theory is phrased in the language of the circuit model for quantum computing, its key ingredient being a limitation on the number of interactions that textit{each} qubit may undergo. As long as one stays in the circuit model, the toy theory is consistent and may even match what we shall be ever able to do in a controlled laboratory experiment. The direct extension of the restriction beyond the circuit model conflicts with observed facts: the possibility of restricting the complexity of quantum state, while saving phenomena, remains an open question.
We analyze relationships between quantum computation and a family of generalizations of the Jones polynomial. Extending recent work by Aharonov et al., we give efficient quantum circuits for implementing the unitary Jones-Wenzl representations of the
QMA (Quantum Merlin-Arthur) is the quantum analogue of the class NP. There are a few QMA-complete problems, most notably the ``Local Hamiltonian problem introduced by Kitaev. In this dissertation we show some new QMA-complete problems. The first on
Topological entanglement entropy has been extensively used as an indicator of topologically ordered phases. We study the conditions needed for two-dimensional topologically trivial states to exhibit spurious contributions that contaminates topologica
We consider a toy model for emergence of chaos in a quantum many-body short-range-interacting system: two one-dimensional hard-core particles in a box, with a small mass defect as a perturbation over an integrable system, the latter represented by tw
The negative weight adversary method, $mathrm{ADV}^pm(g)$, is known to characterize the bounded-error quantum query complexity of any Boolean function $g$, and also obeys a perfect composition theorem $mathrm{ADV}^pm(f circ g^n) = mathrm{ADV}^pm(f) m