Quantum Hamming (sphere-packing) bound. Setup: a non-degenerate [[n,k,d]] stabiliser code able to correct t = ⌊(d−1)/2⌋ arbitrary single-qubit errors. Theorem: 2^k·V_q(n,t) ≤ 2^n where the quantum error-sphere volume V_q(n,t) = Σ_{j=0}^t…
Quantum Hamming (sphere-packing) bound. Setup: a non-degenerate [[n,k,d]] stabiliser code able to correct t = ⌊(d−1)/2⌋ arbitrary single-qubit errors. Theorem: 2^k·V_q(n,t) ≤ 2^n where the quantum error-sphere volume V_q(n,t) = Σ_{j=0}^t…