2022/02/24 by Chi-Kwong Li, Cordelia Li, Li, Chi-Kwong +5 · 1 citation
Computer Science · #81-05 #81Q99 #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum-Dot Cellular Automata
paper · pdf · doi:10.48550/arxiv.2202.12408
openalex publication_date 2022/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 σx⊗ n, σy⊗ n and σz⊗ n, where σx, σy, σz 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.