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Quantum Computation with Topological Codes

Part of the SpringerBriefs in Mathematical Physics Book Series (volume 8)

DOI: 10.1007/978-981-287-996-7

ISBN: 978-981-287-995-0

Publisher: Springer Singapore - Springer Journals

Dec 16, 2015

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Chapter 1Introduction to Quantum Computation

Fujii, Keisuke

Pages: 1 –23

[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...
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Chapter 2Stabilizer Formalism and Its Applications

Fujii, Keisuke

Pages: 24 –55

[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...
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Chapter 3Topological Stabilizer Codes

Fujii, Keisuke

Pages: 56 –85

[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,...
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Chapter 4Topological Quantum Computation with Surface Codes

Fujii, Keisuke

Pages: 86 –106

[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...
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Chapter 5Topologically Protected Measurement-Based Quantum Computation

Fujii, Keisuke

Pages: 107 –121

[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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