General Upper Bounds for Gate Complexity and Depth of Reversible Circuits Consisting of NOT, CNOT and 2-CNOT Gates

On Synthesis of Reversible Circuits with Small Number of Additional Inputs Consisting of NOT, CNOT and 2-CNOT Gates

The paper discusses the gate complexity of reversible circuits with the small number of additional inputs consisting of NOT, CNOT and 2-CNOT gates. We study Shannon's gate complexity function $L(n, q)$ for a reversible circuit implementing a Boolean transformation $f\colon \mathbb Z_2^n \to \mathbb Z_2^n$ with $q \leqslant O(n^2)$ additional inputs. The general bound $L(n,q) \asymp n2^n \mathop / \log_2 n$ is proved for this case.

On Asymptotic Gate Complexity and Depth of Reversible Circuits With Additional Memory

The reversible logic can be used in various research areas, e.g. quantum computation, cryptography and signal processing. In the paper we study reversible logic circuits with additional inputs, which consist of NOT, CNOT and C\textsuperscript{2}NOT gates. We consider a set $F(n,q)$ of all transformations $\mathbb B^n \to \mathbb B^n$ that can be realized by reversible circuits with $(n+q)$ inputs. An analogue of Lupanov's method for the synthesis of reversible logic circuits with additional inputs is described. We prove upper asymptotic bounds for the Shannon gate complexity function $L(n,q)$ …

稳定器电路仿真的改进

Improved Simulation of Stabilizer Circuits

Gottesman-Knill定理表明，稳定器电路-即仅由CNOT、Hadamard和相位门组成的量子线路-可以在经典计算机上有效地模拟。本文从几个方面改进了该定理。首先，通过消除对高斯消除的需要，我们使模拟算法更快，代价是表示状态所需的位数增加了2倍。我们已经在一个名为CHP（hocT-Hadamard-Phase）的免费程序中实现了改进的算法，该程序可以轻松处理数千个量子比特。第二，我们证明了模拟稳定器电路的问题是完全的经典复杂性类ParityL，这意味着稳定器电路可能甚至不通用的经典计算。第三，我们给出了计算两个稳定器状态之间的内积的有效算法，将任何n量子位稳定器电路转换为“规范形式”，最多需要O（n^2/log n）门，以及其他有用的任务。第四，我们扩展我们的模拟算法的电路作用于混合状态，电路包含有限数量的非稳定器门，和电路一般张量积初始状态，但只包含有限数量的测量。

由随机可逆电路生成的伪随机置换

Pseudorandom Permutations from Random Reversible Circuits

研究可逆3比特门构成的随机电路生成的置换的伪随机性，证明深度为n·O~(k²)的随机电路可生成近乎k元独立置换，改进了谱隙结果，还在分组密码构造及MRCSP复杂度上取得进展。

优化量子电路通常是困难的

Optimising quantum circuits is generally hard

本文证明了多种量子电路门优化问题（包括Clifford+T电路中的T-count、T-depth、CNOT门和Hadamard门数量，以及可逆经典电路中的Toffoli门数量）均为NP困难，并给出了T-count和Toffoli-count问题的上界。

The Classification of Clifford Gates over Qubits

We examine the following problem: given a collection of Clifford gates, describe the set of unitaries generated by circuits composed of those gates. Specifically, we allow the standard circuit operations of composition and tensor product, as well as ancillary workspace qubits as long as they start and end in states uncorrelated with the input, which rule out common "magic state injection" techniques that make Clifford circuits universal. We show that there are exactly 57 classes of Clifford unitaries and present a full classification characterizing the gate sets which generate them. This is th…