ToddBrun 量子通信、量子纠错、LDPC、Altera FPGA时序分析.pptVIP

General Entanglement-Assisted Quantum Error-Correcting Codes Todd A. Brun, Igor Devetak and Min-Hsiu Hsieh Communication Sciences Institute Classical symplectic codes Quantum stabilizer codes Properties of Stabilizer Codes We can see that stabilizer codes have the following properties: The code corresponds to an isotropic (that is, dual-containing) classical code over a symplectic space. The error correcting conditions are almost the same as classical (except for the existence of degenerate quantum codes, in which distinct errors share the same error syndrome). Correction consists of measuring an error syndrome and performing an appropriate correcting action (a unitary). Entanglement-assisted error correction Entanglement-assisted stabilizer formalism It turns out that we can establish a simple extension of the usual stabilizer formalism to describe entanglement-assisted codes. We again establish a “stabilizer” which is a subgroup of the Pauli group on n q-bits; but we no longer require this subgroup to be Abelian. For such a subgroup, we can find a set of generators which fall into two groups: Isotropic generators, which commute with all other generators; and Symplectic generators, which come in anticommuting pairs; each pair commutes with all other generators. Entanglement-assisted stabilizer formalism Properties of the entanglement-assisted stabilizer formalism We can now compare the properties of an EAQECC to those of an ordinary QECC: The code corresponds to a classical code over a symplectic space. (No longer needs to be dual-containing!) The error correcting conditions are almost the same as classical (except for the existence of degenerate quantum codes, in which distinct errors share the same error syndrome). Correction consists of measuring an error syndrome and performing an appropriate correcting action (a unitary). The GF(4) Construction Operator QECCs OQECC Stabilizer Formalism Entanglement-assisted operator quantum error-correct