A Theory of the Quantum Error-Correcting Codes
By Li Fang. 2001
612 citations recorded by the source corpus.
View Paper: https://www.semanticscholar.org/paper/784312dfc1c152354272e89bb054eb2eb8438579
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Citations in the corpus
- Nonbinary Stabilizer Codes Over Finite Fields (2005, background): “Recall that a quantum code Q is able to detect an error E in the unitary group U(q n ) if and only if the condition h c1|E|c2i = �Eh c1|c2i holds for all c1,c2 ∈ Q, see [ 61 ].”
- Decoherence-Free Subspaces and Subsystems (2003, background): “[73] gives two equivalent criteria for the general condition for QECC.”
- Reversing quantum dynamics with near-optimal quantum and classical fidelity (2000, unknown): “Perfectly reversible operations have a decomposition A i for which A i P C = √ p i W i for some probabilities p i , where the W i are isometries from C into orthogonal subspaces, which means that W † i W j = δ ij P C [4, 5].”
- Quantum error correction for quantum memories (2013, unknown): “The quantum error-correction conditions (Bennett et al. , 1996; Knill and Laflamme, 1997) say that there exists such an error-correcting reversal operation R if and only if the following conditions are obeyed for all errors E i ; E j ∈ E : Here c ij is a constant independent of the code word j x i…”
- Widely Tunable On-Chip Microwave Circulator for Superconducting Quantum Circuits (2017, background): “One approach to error-correction involves the use of stabilizer codes [50, 51, 52], in which a logical qubit is formed by redundantly encoding information in a register of entangled physical qubits.”
- Quantum accuracy threshold for concatenated distance-3 codes (2005, background): “t corrects terrors is said to have distance 2t+1, because (at least roughly speaking) Pauli operators that preserve the code space and act nontrivially within the code space have weight at least 2t+1 [21]. Thus we will say “distance-3 code” to indicate a quantum code that can correct one error, and ”