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Fast naviation with icosahedral golden gates 快速导航与二十面体金门
4区 物理与天体物理 Q2 Mathematics Pub Date : 2023-09-01 DOI: 10.26421/qic23.11-12-1
Terrence R Blackman, Zachary Stier
An algorithm of Ross and Selinger for the factorization of diagonal elements of PU(2) to within distance $varepsilon$ was adapted by Parzanchevski and Sarnak into an efficient probabilistic algorithm for any element of PU(2) using at most effective $3log_pfrac{1}{varepsilon^{3}}$ factors from certain well-chosen sets associated to a number field and a prime $p$. The icosahedral super golden gates are one such set associated to $mathbb{Q}(sqrt{5})$. We leverage recent work of Carvalho Pinto, Petit, and Stier to reduce this bound to $frac{7}{3}log_{59}frac{1}{varepsilon^3}$, and we implement the algorithm in Python. This represents an improvement by a multiplicative factor of $log_259approx5.9$ over the analogous result for the Clifford+$T$ gates. This is of interest because the icosahedral gates have shortest factorization lengths among all super golden gates.
Ross和Selinger将PU(2)的对角线元素分解到距离$varepsilon$内的算法被Parzanchevski和Sarnak采用为PU(2)的任何元素的有效概率算法,该算法使用与数字域和素数$p$相关的某些精心选择的集合中的最有效$3log_pfrac{1}{varepsilon^{3}}$因子。二十面体超级金门就是与$mathbb{Q}(sqrt{5})$相关的一组。我们利用Carvalho Pinto, Petit和Stier最近的工作将这个界限降低到$frac{7}{3}log_{59}frac{1}{varepsilon^3}$,并在Python中实现该算法。这表示与Clifford+ $T$门的类似结果相比,有了$log_259approx5.9$倍的改进。这是有趣的,因为二十面体门是所有超级金门中分解长度最短的。
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引用次数: 0
Dynamics of one two-level-atom interacting with a multiple cavity modes 一个两能级原子与多腔模式相互作用的动力学
4区 物理与天体物理 Q2 Mathematics Pub Date : 2023-09-01 DOI: 10.26421/qic23.11-12-2
Taoufik Said, Abdelhaq Chouikh, Zoubida Sakhi, Mohamed Bennai
We discuss how to implement quantum logic gates by considering a two-level-atom driven by a strong microwave field and successively interacting with m+1 cavity modes. The scheme is insensitive to the initial state of the atom, and the operation time is independent of the number of cavity modes involved in the system operations. This scheme is used to realize two quantum logic gates (m-target-qubit controlled-global-phase gate and Multi-qubit phase shift gate) in a time much shorter than the photonic lifetime. We also studied the influence of decoherence on the fidelity. In general, our system is reasonably less sensitive to the photonic and atomic decay rates and therefore it can be experimentally realized.
我们讨论了如何通过考虑由强微波场驱动的两能级原子与m+1腔模式的连续相互作用来实现量子逻辑门。该方案对原子的初始状态不敏感,并且操作时间与系统操作中涉及的腔模式的数量无关。该方案在短于光子寿命的时间内实现了两个量子逻辑门(m-目标量子位控制的全局相位门和多量子位相移门)。我们还研究了退相干对保真度的影响。总的来说,我们的系统对光子和原子衰变率的敏感性较低,因此可以通过实验实现。
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引用次数: 0
Closed-form analytic expressions for shadow estimation with brickwork circuits 砖砌电路阴影估计的封闭解析表达式
4区 物理与天体物理 Q2 Mathematics Pub Date : 2023-09-01 DOI: 10.26421/qic23.11-12-5
Mirko Arienzo, Markus Heinrich, Ingo Roth, Martin Kliesch
Properties of quantum systems can be estimated using classical shadows, which implement measurements based on random ensembles of unitaries. Originally derived for global Clifford unitaries and products of single-qubit Clifford gates, practical implementations are limited to the latter scheme for moderate numbers of qubits. Beyond local gates, the accurate implementation of very short random circuits with two-local gates is still experimentally feasible and, therefore, interesting for implementing measurements in near-term applications. In this work, we derive closed-form analytical expressions for shadow estimation using brickwork circuits with two layers of parallel two-local Haar-random (or Clifford) unitaries. Besides the construction of the classical shadow, our results give rise to sample-complexity guarantees for estimating Pauli observables.We then compare the performance of shadow estimation with brickwork circuits to the established approach using local Clifford unitaries and find improved sample complexity in the estimation of observables supported on sufficiently many qubits.
量子系统的性质可以使用经典阴影来估计,它实现了基于酉元的随机系综的测量。最初是为全局Clifford单一性和单量子位Clifford门的产物推导的,实际实现仅限于后者的中等数量的量子位。除了局部门之外,用双局部门精确实现非常短的随机电路在实验上仍然是可行的,因此,在近期应用中实现测量很有趣。在这项工作中,我们推导了使用具有两层平行双局部Haar-random(或Clifford)酉元的砖砌电路的阴影估计的封闭形式解析表达式。除了构造经典阴影外,我们的结果还为估计泡利观测值提供了样本复杂度保证。然后,我们将砖砌电路的阴影估计性能与使用局部Clifford一元的既定方法进行比较,并发现在足够多的量子位支持的可观察值估计中改进了样本复杂性。
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引用次数: 13
A simpler security proof for 6-state quantum key distribution 一个更简单的六态量子密钥分发安全性证明
4区 物理与天体物理 Q2 Mathematics Pub Date : 2023-09-01 DOI: 10.26421/qic23.11-12-4
Kaan Akyuz, Boris Skoric
Six-state Quantum Key Distribution (QKD) achieves the highest key rate in the class of qubit-based QKD schemes. The standard security proof, which has been developed since 2005, invokes complicated theorems involving smooth R'{e}nyi entropies. In this paper we present a simpler security proof for 6-state QKD that entirely avoids R'{e}nyi entropies. This is achieved by applying state smoothing directly in the Bell basis. We obtain the well known asymptotic rate, but with slightly more favorable finite-size terms. We furthermore show that the same proof technique can be used for 6-state quantum key recycling.
在基于量子比特的量子密钥分发方案中,六态量子密钥分发(QKD)实现了最高的密钥速率。自2005年以来开发的标准安全性证明调用了涉及光滑R {e}nyi熵的复杂定理。在本文中,我们提出了一个更简单的六态QKD安全性证明,它完全避免了R {e}nyi熵。这是通过在贝尔基中直接应用状态平滑来实现的。我们得到了众所周知的渐近速率,但有稍微有利的有限大小项。我们进一步证明了同样的证明技术可以用于六态量子密钥的回收。
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引用次数: 0
Many-body quantum state control in the presence of environmental noise 环境噪声下的多体量子态控制
4区 物理与天体物理 Q2 Mathematics Pub Date : 2023-09-01 DOI: 10.26421/qic23.11-12-3
Zara Yu, Da-Wei Luo
We consider the quantum state control of a multi-state system which evolves an initial state into a target state. We explicitly demonstrate the control method in an interesting case involving the transfer and rotation of a Schr"{o}dinger cat state through a coupled harmonic oscillator chain at a predetermined time $T$. We use the gradient-based Krotov's method to design the time-dependent parameters of the coupled chain to find an optimal control shape that will evolve the system into a target state. We show that the prescribed quantum state control can be achieved with high fidelity, and the robustness of the control against generic environment noises is explored. Our findings will be of interest for the optimal control of a many-body open quantum system in the presence of environmental noise.
我们考虑多态系统的量子态控制,该系统由初始态演化为目标态。我们在一个有趣的例子中明确地证明了这种控制方法,这个例子涉及到薛定谔猫态在预定时间通过耦合谐振子链的转移和旋转。我们使用基于梯度的Krotov方法来设计耦合链的时间相关参数,以找到将系统进化到目标状态的最优控制形状。我们证明了规定的量子态控制可以以高保真度实现,并探讨了控制对一般环境噪声的鲁棒性。我们的发现将对存在环境噪声的多体开放量子系统的最优控制感兴趣。
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引用次数: 0
Mermin polytopes quantum computation and foundations 人鱼多面体量子计算与基础
4区 物理与天体物理 Q2 Mathematics Pub Date : 2023-07-01 DOI: 10.26421/qic23.9-10-2
Cihan Okay, Ho Yiu Chung, Selman Ipek
Mermin square scenario provides a simple proof for state-independent contextuality. In this paper, we study polytopes $MP_beta$ obtained from the Mermin scenario, parametrized by a function $beta$ on the set of contexts. Up to combinatorial isomorphism, there are two types of polytopes $MP_0$ and $MP_1$ depending on the parity of $beta$. Our main result is the classification of the vertices of these two polytopes. In addition, we describe the graph associated with the polytopes. All the vertices of $MP_0$ turn out to be deterministic. This result provides a new topological proof of a celebrated result of Fine characterizing noncontextual distributions on the CHSH scenario. $MP_1$ can be seen as a nonlocal toy version of $Lambda$-polytopes, a class of polytopes introduced for the simulation of universal quantum computation. In the $2$-qubit case, we provide a decomposition of the $Lambda$-polytope using $MP_1$, whose vertices are classified, and the nonsignaling polytope of the $(2,3,2)$ Bell scenario, whose vertices are well-known.
人鱼广场场景为独立于状态的上下文性提供了一个简单的证明。在本文中,我们研究了从Mermin场景中得到的多面体$MP_beta$,在上下文集合上用一个函数$beta$参数化。直到组合同构为止,根据$beta$的宇称,有两种类型的多面体$MP_0$和$MP_1$。我们的主要结果是这两个多面体的顶点的分类。此外,我们还描述了与多面体相关的图。$MP_0$的所有顶点都是确定性的。这个结果为Fine在CHSH场景中描述非上下文分布的著名结果提供了一个新的拓扑证明。$MP_1$可以看作是$Lambda$ -多面体的非局部玩具版本,这是一类为模拟通用量子计算而引入的多面体。在$2$ -qubit情况下,我们使用$MP_1$(其顶点是分类的)和$(2,3,2)$ Bell场景的非信号多角体(其顶点是众所周知的)对$Lambda$ -多角体进行分解。
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引用次数: 0
Partition GHZ SLOCC class of three qubits into ten families under LU 将三量子位的GHZ SLOCC类在LU下划分为十族
4区 物理与天体物理 Q2 Mathematics Pub Date : 2023-04-01 DOI: 10.26421/qic23.5-6-3
Dafa Li
In [Science 340:1205, (2013)], via entanglement polytopes Michael Walter et al. obtained a finite yet systematic classification of multi-particle entanglement. It is well known that under SLOCC, pure states of three (four) qubits are partitioned into six (nine) families. Ac'{i}n et al. proposed the generalized Schmidt decomposition for three qubits and partitioned pure states of three qubits into five types. In this paper,we present a LU invariant and an entanglement measures for the GHZ SLOCC class of three qubits, and partition states of the GHZ SLOCC class of three qubits into ten families and each family into two subfamilies under LU. We give a necessary and sufficient condition for the uniqueness of the generalized Schmidt decomposition for the GHZ SLOCC class.
在[Science 340:1205,(2013)]中,Michael Walter等人通过纠缠多面体获得了多粒子纠缠的有限而系统的分类。众所周知,在SLOCC下,三(四个)量子比特的纯态被划分为六(九个)族。Ac {i}n等人提出了三个量子比特的广义Schmidt分解,并将三个量子比特的纯态划分为五种类型。本文给出了三个量子比特的GHZ SLOCC类的LU不变量和纠缠度量,并在LU下将三个量子比特的GHZ SLOCC类的状态划分为十个族,每个族又划分为两个子族。给出了GHZ SLOCC类广义Schmidt分解唯一性的一个充分必要条件。
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引用次数: 0
The Connes embedding problem cones嵌入问题
IF 1 4区 物理与天体物理 Q2 Mathematics Pub Date : 2020-01-01 DOI: 10.1017/9781108782081.013
Travis B. Russell
We show that Connes’ embedding problem is equivalent to the weak Tsirelson problem in the setting of two-outcome synchronous correlation sets. We further show that the extreme points of two-outcome synchronous correlation sets can be realized using a certain class of universal C*-algebras. We examine these algebras in the three-experiment case and verify that the strong and weak Tsirelson problems have affirmative answers in that setting.
我们证明了在双结果同步相关集的情况下,Connes的嵌入问题等价于弱Tsirelson问题。进一步证明了双结果同步相关集的极值点可以用一类泛C*-代数来实现。我们在三个实验的情况下检验这些代数,并验证强和弱Tsirelson问题在这种情况下有肯定的答案。
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引用次数: 2
Quantum speedup of training radial basis function networks 训练径向基函数网络的量子加速
IF 1 4区 物理与天体物理 Q2 Mathematics Pub Date : 2019-06-01 DOI: 10.5555/3370207.3370213
ShaoChangpeng
Radial basis function (RBF) network is a simple but useful neural network model that contains wide applications in machine learning. The training of an RBF network reduces to solve a linear system,...
径向基函数(RBF)网络是一种简单而实用的神经网络模型,在机器学习中有着广泛的应用。RBF网络的训练简化为求解一个线性系统。
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引用次数: 1
Periodicity for the fourier quantum walk on regular graphs 正则图上傅立叶量子行走的周期性
IF 1 4区 物理与天体物理 Q2 Mathematics Pub Date : 2019-02-01 DOI: 10.5555/3370239.3370242
SaitoKei
Quantum walks determined by the coin operator on graphs have been intensively studied. The typical examples of coin operator are the Grover and Fourier matrices. The periodicity of the Grover walk ...
由图上的硬币算子确定的量子行走已经得到了深入的研究。硬币算子的典型例子是Grover矩阵和傅立叶矩阵。格罗弗步行的周期性。。。
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引用次数: 1
期刊
Quantum Information & Computation
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