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- Title
Quantum error correction scheme for fully-correlated noise.
- Authors
Li, Chi-Kwong; Li, Yuqiao; Pelejo, Diane Christine; Stanish, Sage
- Abstract
This paper investigates quantum error correction schemes for fully-correlated noise channels on an n-qubit system, where error operators take the form W ⊗ n , with W being an arbitrary 2 × 2 unitary operator. In previous literature, a recursive quantum error correction scheme can be used to protect k qubits using (k + 1) -qubit ancilla. We implement this scheme on 3-qubit and 5-qubit channels using the IBM quantum computers, where we uncover an error in the previous paper related to the decomposition of the encoding/decoding operator into elementary quantum gates. Here, we present a modified encoding/decoding operator that can be efficiently decomposed into (a) standard gates available in the qiskit library and (b) basic gates comprised of single-qubit gates and CNOT gates. Since IBM quantum computers perform relatively better with fewer basic gates, a more efficient decomposition gives more accurate results. Our experiments highlight the importance of an efficient decomposition for the encoding/decoding operators and demonstrate the effectiveness of our proposed schemes in correcting quantum errors. Furthermore, we explore a special type of channel with error operators of the form σ x ⊗ n , σ y ⊗ n and σ z ⊗ n , where σ x , σ y , σ z are the Pauli matrices. For these channels, we implement a hybrid quantum error correction scheme that protects both quantum and classical information using IBM's quantum computers. We conduct experiments for n = 3 , 4 , 5 and show significant improvements compared to recent work.
- Subjects
INTERNATIONAL Business Machines Corp.; QUANTUM computers; QUANTUM gates; UNITARY operators; PAULI matrices; QUANTUM operators; NOISE
- Publication
Quantum Information Processing, 2023, Vol 22, Issue 8, p1
- ISSN
1570-0755
- Publication type
Article
- DOI
10.1007/s11128-023-04009-x