密度矩阵表示的量子计算的图形模拟
Graph-based simulation of quantum computation in the density matrix representation
摘要：
随着晶体管尺寸接近纳米级，量子线路和数据编码方法出现在最方便的通信形式中，量子力学现象在信息处理中发挥着越来越重要的作用。由于所涉及的量子态空间的巨大尺寸，有效地模拟这种现象是极其困难的。一个主要的复杂性是由于量子态和环境之间不必要的相互作用引起的误差（噪声）。因此，使用密度矩阵表示来模拟量子线路及其相关联的误差在许多应用中是潜在重要的，但是在时间和存储器资源两者上都远远超出了大多数经典模拟技术的计算能力。密度矩阵的大小随着模拟的量子比特的数量呈指数增长，使得显式存储密度矩阵的基于阵列的模拟技术难以处理。在这项工作中，我们提出了一种新的技术，旨在有效地模拟量子线路的错误。特别是，我们描述了新的基于图形的算法在模拟器QuIDDPro/D中实现。虽然以前报道的基于图形的模拟器操作的状态矢量表示，这些新的算法使用的密度矩阵表示。为了衡量QuIDDPro/D提供的改进，我们将其模拟性能与优化的基于阵列的模拟器QCSim进行了比较。两个模拟器在一组涉及纠错、可逆逻辑、通信和量子搜索的量子线路基准上生成的经验结果表明，基于图形的方法远远优于基于阵列的方法。
英文摘要：
Quantum-mechanical phenomena are playing an increasing role in information processing, as transistor sizes approach the nanometer level, and quantum circuits and data encoding methods appear in the securest forms of communication. Simulating such phenomena efficiently is exceedingly difficult because of the vast size of the quantum state space involved. A major complication is caused by errors (noise) due to unwanted interactions between the quantum states and the environment. Consequently, simulating quantum circuits and their associated errors using the density matrix representation is potentially significant in many applications, but is well beyond the computational abilities of most classical simulation techniques in both time and memory resources. The size of a density matrix grows exponentially with the number of qubits simulated, rendering array-based simulation techniques that explicitly store the density matrix intractable. In this work, we propose a new technique aimed at efficiently simulating quantum circuits that are subject to errors. In particular, we describe new graph-based algorithms implemented in the simulator QuIDDPro/D. While previously reported graph-based simulators operate in terms of the state-vector representation, these new algorithms use the density matrix representation. To gauge the improvements offered by QuIDDPro/D, we compare its simulation performance with an optimized array-based simulator called QCSim. Empirical results, generated by both simulators on a set of quantum circuit benchmarks involving error correction, reversible logic, communication, and quantum search, show that the graph-based approach far outperforms the array-based approach.
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