Quantum Error Correction Scheme for Fully Correlated Noise

• URL: http://arxiv.org/abs/2202.12408v2
• Date: Wed, 29 Mar 2023 00:07:37 GMT
• Title: Quantum Error Correction Scheme for Fully Correlated Noise
• Authors: Chi-Kwong Li, Yuqiao Li, Diane Christine Pelejo and Sage Stanish
• Abstract summary: This paper investigates quantum error correction schemes for fully-correlated noise channels on an $n$-qubit system. We implement a hybrid quantum error correction scheme that protects both quantum and classical information using IBM's quantum computers.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper investigates quantum error correction schemes for fully-correlated noise channels on an $n$-qubit system, where error operators take the form $W^{\otimes n}$, with $W$ being an arbitrary $2\times 2$ 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 \texttt{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 $\sigma_x^{\otimes n}, \sigma_y^{\otimes n}$ and $\sigma_z^{\otimes n}$, where $\sigma_x, \sigma_y, \sigma_z$ 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.

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