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[In this chapter, we introduce the basic concepts of quantum computation. We first describe the minimum unit of quantum information, the qubit, and define several gate operations for it. Then, we explain the Solovay–Kitaev algorithm, which provides a way to decompose an arbitrary single-qubit...
[In general, the description of quantum states is a difficult task because it requires exponentially many parameters in the number of qubits as shown in Eq. (1.38). To understand these complex quantum systems, it is essential to have efficient tools. The stabilizer formalism is one such powerful...
[Protecting quantum information from decoherence is of prime importance to realize quantum information processing. Several approaches have been proposed toward reliable quantum information processing, ranging from passive to active protections, such as decoherence-free subspaces (Lidar et al,...
[In this chapter, we explain how to perform topological fault-tolerant quantum computation on the surface code. All operations employed are nearest-neighbor (at most) two-qubit gates and single-qubit measurements on a 2D array of qubits. This property is quite favorable for the fabrication of...
[In this chapter, we reformulate topological fault-tolerant quantum computation explained in the previous chapter in terms of meausrement-based quantum computation.]
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