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Journal of the Physical Society of Japan

How to Combat Quantum Bursts of Errors Efficiently

Ying Guo, Guihua Zeng

Published Mar 14, 2006• 3 citations
Publisher

Abstract

To construct a quantum code with much error-correcting ability, the philosophy of the quantum interleaving is illustrated by introducing the block interleaving techniques. Quantum interleaving is a process to rearrange the qubits of several states of the same code so as to spread the same quantum errors over multiple states. Utilizing the interleaving technique, the concatenated k n -qubit code is constructed in this paper with more error-correcting ability than utilizing only one n -qubit quantum error-correcting code (QECC) without introducing the redundant qubits. It hence suggests an important way to design an quantum convolution code as the classical convolutional code has been constructed. For the application, the proposed quantum interleaving technique becomes an effective means to combat quantum bursts of errors by converting quantum bursts of errors into quantum random errors.

DOI
10.1143/jpsj.75.034402

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To construct a quantum code with much error-correcting ability, the philosophy of the quantum interleaving is illustrated by introducing the block interleaving techniques. Quantum interleaving is a process to rearrange the qubits of several states of the same code so as to spread the same quantum errors over multiple states. Utilizing the interleaving technique, the concatenated k n -qubit code is constructed in this paper with more error-correcting ability than utilizing only one n -qubit quantum error-correcting code (QECC) without introducing the redundant qubits. It hence suggests an important way to design an quantum convolution code as the classical convolutional code has been constructed. For the application, the proposed quantum interleaving technique becomes an effective means to combat quantum bursts of errors by converting quantum bursts of errors into quantum random errors.
In a noisy quantum channel, burst errors usually causes multiple bit-phase flips that are adjacent to each other (Vatan, Raichowdry and Anantram, 1999; Grassl and Beth, 2000). This effectively makes some quantum error-correcting codes to be unusable. In this paper, the concept of interleaving qubit transmission is proposed. By using the interleaving method in a quantum information transmission process, burst errors in a quantum channel are re-arranged into different time slots. This relocation makes the error bits non-adjacent and hence increases the probability of information recovery. Note that although this scheme enhances the error-correcting capability of the encoded quantum information, it does not increase the redundancy of the code, because only the qubit sequences are relocated. In addition to the interleaving scheme, implementation of the proposed scheme at the circuit level is also discussed in this paper.
Quantum memory is essential for the development of many devices in quantum information processing, including a synchronization tool that can match the various processes in a quantum computer, a quantum gate that maintains the identity of any state, and a mechanism for converting predetermined photons into on-demand photons. Quantum memory can be used in many aspects, such as quantum computing and quantum communication. Continuous research and experiments have enabled quantum memory to realize the storage of qubits. On the other hand, interleaving techniques are used to deal with burst of errors. Many works from literature provide effective interleaving techniques for combating burst of errors by using classical error-correcting codes. However, to the best of our knowledge, little is known regarding interleaving techniques for combating cluster of errors in topological quantum error-correcting codes. Thenceforward, it is proposed in this work a new interleaving technique by using good toric quantum codes, namely Bombin and Martin-Delgado toric codes and another class of toric codes from literature which is described in this work. As a consequence, by applying this new interleaving method to such toric quantum codes, new quantum burst-error correcting codes are obtained which improve the coding gain. In addition to the proposed quantum interleaving technique improves such parameter, it can be used for burst-error correction in errors which are located, quantum data stored and quantum channels with memory.
Quantum error-correcting codes (QECCs) and decoherence-free subspace (DFS) codes provide active and passive means, respectively, to address certain types of errors that arise during quantum computation. The latter technique is suitable to correct correlated errors with certain symmetries and the former to correct independent errors. The concatenation of a QECC and a DFS code results in a degenerate code that splits into actively and passively correcting parts, with the degeneracy impacting either part, leading to degenerate errors as well as degenerate stabilizer operators. The concatenation of the two types of code can aid universal fault-tolerant quantum computation when a mix of correlated and independent errors is encountered. In particular, we show that for sufficiently strongly correlated errors, the concatenation with the DFS as the inner code provides better entanglement fidelity, whereas for sufficiently independent errors, the concatenation with the QECC as the inner code is preferable. As illustrative examples, we examine in detail the concatenation of a two-qubit DFS code and a three-qubit repetition code or five-qubit Knill-Laflamme code, under independent and correlated errors.