The review does not focus on a particular technology but discusses topics that will be relevant for various quantum technologies. (Color online) (a) Schematic of various approaches for controlling a quantum system: (i) unitary control on the system alone or both the system and an ancilla (ii) quantum feedback control based on measurement of the ancilla (iii) driven-dissipative control with either engineered dissipation or Hamiltonian engineering (iv) holonomic quantum control based on only engineered dissipation. The complexity of decoding and the notion of passive or self-correcting quantum memories are discussed. The second part of the review is focused on providing an overview of quantum error correction using two-dimensional (topological) codes, in particular, the surface code architecture. Quantum error correction is a hybrid between quantum mechanics and the classical theory of error-correcting codes that are concerned with the fundamental. The theory of fault tolerance and quantum error correction is reviewed, and examples of various codes and code constructions, the general quantum error-correction conditions, the noise threshold, the special role played by Clifford gates, and the route toward fault-tolerant universal quantum computation are discussed. A quantum error correction code for the approximated channel is also a correctable code for the original channel, and its performance can be obtained by Monte. In this review the formalism of qubit stabilizer and subsystem stabilizer codes and their possible use in protecting quantum information in a quantum memory are considered. Active quantum error correction using qubit stabilizer codes has emerged as a promising, but experimentally challenging, engineering program for building a universal quantum computer. The second part of the review is focused on providing an overview of quantum error correction using two-dimensional (topological) codes, in particular.
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