Three proposed nondegenerate quantum codes

PHYSICS · Subjective · Fermi University Physics · Quantum Information & Technology · Open quantum systems, decoherence and error correction · Open quantum systems, decoherence and error correction

Quantum Information and Technology, Ch Quantum error correction

Problem

Three proposed nondegenerate quantum codes, each meant to correct any single-qubit error (

t=1

), are

[[6,1,3]]

[[5,2,3]]

and

[[8,3,3]]

. For each code, test the quantum Hamming bound

2^k\sum_{j=0}^t\binom nj3^j\le2^n

and the quantum Singleton bound

n-k\ge2(d-1)

, and state whether the proposed parameters are ruled out by either bound.

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