Optimization of Quantum Circuits for Stabilizer Codes
Optimization of Quantum Circuits for Stabilizer Codes
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DOI：
10.1109/tcsi.2024.3384436
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发表时间：
2023-09
期刊：
影响因子：
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通讯作者：
Arijit Mondal;K. Parhi
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文献类型：
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作者：
Arijit Mondal;K. Parhi
量子计算是一项新兴技术，有可能实现与经典同行相比的指数级加速。为了实现量子优势，量子原理正被应用于通信、信息处理和人工智能等领域。然而，量子计算机面临着一个根本问题，因为量子比特噪音极大，容易退相干。保持量子比特没有错误是迈向可靠量子计算的最重要的步骤之一。在过去的几十年里，已经提出了不同的用于量子纠错的稳定子码，并且已经提出了几种将经典纠错码引入量子域的方法。然而，到目前为止，还没有提出用于这些量子编码器和解码器的电路设计和优化的正式方法。本文提出了一种用于系统构造一般稳定子码的编码电路的形式化算法。该算法被用来设计八量子比特码的编解码电路。接下来，我们提出了一种对所设计的编码器电路进行优化的系统方法。利用所提出的方法，我们根据所使用的两个量子比特门的数量来优化编码电路。所提出的优化八量子位编码器使用18个CNOT门和4个Hadamard门，而以前的工作是使用14个单量子位门、33个2量子位门和6个CCNOT门。编解码器电路使用IBM Qiskit进行了验证。我们还给出了Steane码和13量子比特码的优化编码电路。
Quantum computing is an emerging technology that has the potential to achieve exponential speedups over their classical counterparts. To achieve quantum advantage, quantum principles are being applied to fields such as communications, information processing, and artificial intelligence. However, quantum computers face a fundamental issue since quantum bits are extremely noisy and prone to decoherence. Keeping qubits error free is one of the most important steps towards reliable quantum computing. Different stabilizer codes for quantum error correction have been proposed in past decades and several methods have been proposed to import classical error correcting codes to the quantum domain. However, formal approaches towards the design and optimization of circuits for these quantum encoders and decoders have so far not been proposed. In this paper, we propose a formal algorithm for systematic construction of encoding circuits for general stabilizer codes. This algorithm is used to design encoding and decoding circuits for an eight-qubit code. Next, we propose a systematic method for the optimization of the encoder circuit thus designed. Using the proposed method, we optimize the encoding circuit in terms of the number of 2-qubit gates used. The proposed optimized eight-qubit encoder uses 18 CNOT gates and 4 Hadamard gates, as compared to 14 single qubit gates, 33 2-qubit gates, and 6 CCNOT gates in a prior work. The encoder and decoder circuits are verified using IBM Qiskit. We also present optimized encoder circuits for Steane code and a 13-qubit code in terms of the number of gates used.