Furthermore, for certain classes of subsystem codes and noise processes, we prove the efficacy of the transpose channel as a simple-to-construct recovery map that works nearly as well as the optimal recovery channel. Here, we demonstrate easily checkable sufficient conditions for the existence of approximate subsystem codes. Subsystem codes extend the standard formalism of subspace QEC to codes in which only a subsystem within a subspace of states is used to store information in a noise-resilient fashion. Motivated by this, we investigate the problem of approximate subsystem codes. Similar to the RG, the composition of the error map followed by the. Recent work on approximate quantum error correction (QEC) has opened up the possibility of constructing subspace codes that protect information with high fidelity in scenarios where perfect error correction is impossible. Using a recovery map we only need the encoding map once at the beginning of computation and a decoding map at the end. We show that the recovery map is an isometric embedding of the correctable subalgebra. Short data packets sporadically transmitted by a multitude of low-cost low-power terminals require a radical change in relevant aspects of the protocol stack. Pauli X-type errors can be thought of as quantum bit-flips that map X0. The blooming of internet of things (IoT) services calls for a paradigm shift in the design of communications systems.
Physical Review A - Atomic, Molecular, and Optical Physics 86 (1) : -. To make error-correction and recovery, we need the parity check matrix P,which is an. Implements the Knill magic state distillation algorithm. Rotates a single qubit by /4 about the Y-axis.
#Recovery map quantum error correction code#
Private operation used to implement both the 5 qubit encoder and decoder. Encoding into the 3-qubits repetition code (left) leads to a logical heavy square lattice (right). Towards a unified framework for approximate quantum error correction. An encoding operation that maps an unencoded quantum register to an encoded quantum register under the 7, 1, 3 Steane quantum code. recovery map that works nearly as well as the optimal recovery channel. Towards a unified framework for approximate quantum error correction Recent work on approximate quantum error correction (QEC) has opened up the.
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