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- Title
Error correction schemes for fully correlated quantum channels protecting both quantum and classical information.
- Authors
Li, Chi-Kwong; Lyles, Seth; Poon, Yiu-Tung
- Abstract
We study efficient quantum error correction schemes for the fully correlated channel on an n-qubit system with error operators that assume the form σ x ⊗ n , σ y ⊗ n , σ z ⊗ n . Previous schemes are improved to facilitate implementation. In particular, when n is odd and equals 2 k + 1 , we describe a quantum error correction scheme using one arbitrary qubit σ to protect the data state ρ in a 2k-qubit system. The encoding operation σ ⊗ ρ ↦ Φ (σ ⊗ ρ) only requires 3k CNOT gates (each with one control bit and one target bit). After the encoded state Φ (σ ⊗ ρ) goes through the channel, we can apply the inverse operation Φ - 1 to produce σ ~ ⊗ ρ so that a partial trace operation can recover ρ . When n is even and equals 2 k + 2 , we describe a hybrid quantum error correction scheme using any one of the two classical bits σ ∈ { | i j ⟩ ⟨ i j | : i , j ∈ { 0 , 1 } } to protect a 2k-qubit state ρ and two classical bits. The encoding operation σ ⊗ ρ ↦ Φ (σ ⊗ ρ) can be done by 3 k + 2 CNOT gates and a single-qubit Hadamard gate. After the encoded state Φ (σ ⊗ ρ) goes through the channel, we can apply the inverse operation Φ - 1 to produce σ ⊗ ρ so that a perfect protection of the two classical bits σ and the 2k-qubit state is achieved. If one uses an arbitrary two-qubit state σ , the same scheme will protect 2k-qubit states. The scheme was implemented using MATLAB, Mathematica, Python and the IBM's quantum computing framework qiskit.
- Subjects
INTERNATIONAL Business Machines Corp.; ERROR correction (Information theory); QUANTUM computing; QUANTUM gates; PYTHON programming language
- Publication
Quantum Information Processing, 2020, Vol 19, Issue 5, p1
- ISSN
1570-0755
- Publication type
Article
- DOI
10.1007/s11128-020-02639-z