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首页> 外文会议>Transactions on computational science XXXI : Special issue on singal processing and security in distributed systems >Algebraic and Logical Emulations of Quantum Circuits
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Algebraic and Logical Emulations of Quantum Circuits

机译：量子电路的代数和逻辑仿真

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Quantum circuits exhibit several features of large-scale distributed systems. They have a concise design formalism but behavior that is challenging to represent let alone predict. Issues of scalability-both in the yet-to-be-engineered quantum hardware and in classical simulators-are paramount. They require sparse representations for efficient modeling. Whereas simulators represent both the system's current state and its operations directly, emulators manipulate the images of system states under a mapping to a different formalism. We describe three such formalisms for quantum circuits. The first two extend the polynomial construction of Dawson et al. [1] to (i) work for any set of quantum gates obeying a certain "balance" condition and (ii) produce a single polynomial over any sufficiently structured field or ring. The third appears novel and employs only simple Boolean formulas, optionally limited to a form we call "parity-of-AND" equations. Especially the third can combine with off-the-shelf state-of-the-art third-party software, namely model counters and #SAT solvers, that we show capable of vast improvements in the emulation time in natural instances. We have programmed all three constructions to proof-of-concept level and report some preliminary tests and applications. These include algebraic analysis of special quantum circuits and the possibility of a new classical attack on the factoring problem. Preliminary comparisons are made with the libquantum simulator [2-4].
机译：量子电路具有大规模分布式系统的几个特征。它们具有简洁的设计形式主义，但是很难代表更容易预测的行为。尚未解决的量子硬件和经典仿真器中的可伸缩性问题至关重要。他们需要稀疏表示才能进行有效建模。模拟器直接代表系统的当前状态及其操作，而模拟器则在映射到不同形式主义的情况下操纵系统状态的图像。我们描述了量子电路的三种形式主义。前两个扩展了Dawson等人的多项式构造。 [1]至（i）对遵循一定“平衡”条件的任何一组量子门进行工作，并且（ii）在任何结构充分的场或环上生成一个多项式。第三个看起来很新颖，并且仅使用简单的布尔公式，可以选择将其限制为我们称为“ AND奇偶校验”方程的形式。尤其是第三个可以与现成的最新第三方软件（即模型计数器和#SAT求解器）结合使用，我们证明了它们能够在自然情况下极大地改善仿真时间。我们已将所有三种结构编程为概念验证级别，并报告了一些初步测试和应用。这些包括特殊量子电路的代数分析，以及对因式分解问题进行新的经典攻击的可能性。使用libquantum仿真器进行了初步比较[2-4]。

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