Non-Resonant Effects in Implementation of Quantum Shor Algorithm
G. P. Berman, G. D. Doolen, G. V. Lopez, V. I. Tsifrinovich
我们在伊辛自旋量子计算机上模拟了Shor的算法。详细分析了非共振效应的影响。结果表明，我们的“$2πk$”-方法成功地抑制非共振效应，即使相对较大的值的拉比频率。
We simulate Shor's algorithm on an Ising spin quantum computer. The influence of non-resonant effects is analyzed in detail. It is shown that our ``$2πk$''-method successfully suppresses non-resonant effects even for relatively large values of the Rabi frequency.
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Implementation of quantum algorithms with resonant interactions
我们提出了一个方案，实现量子算法与共振相互作用。我们的方案只需要两个原子和一个腔模之间的共振相互作用，这是简单可行的。此外，该实现将是在腔QED系统中制造量子计算机的重要一步。
The optical scheme is proposed for realization of controlled phase quantum gate based on the off-resonant interaction of photon with three-level atom in single mode QED-cavity. Possible physical implementation of this scheme is discussed.
Multi-Qubit Gate with Trapped Ions for Microwave and Laser-Based Implementation
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Non-resonant dot-cavity coupling and its applications in resonant quantum dot spectroscopy
我们目前的实验研究的非共振点腔耦合的一个单一的量子点内的微柱的点已被共振激发的s-壳层，从而避免了在量子点及其周围产生额外的电荷。作为纯单点-腔系统的直接证据，在量子点和模式发射的自相关函数以及点和模式信号之间的交叉关联函数中一致地观察到强光子反聚束。强斯托克斯和反斯托克斯类发射被观察到的能量高达100倍的量子点线宽的量子点模式失谐。此外，我们证明，非共振点腔耦合可以用来直接监测和研究相关的量子点的s-壳层性质，如精细结构分裂，发射饱和和功率展宽，以及光子统计与可忽略的背景贡献。我们的研究结果打开了一个新的视角的理解和实施的点腔系统的单光子源，单和多个量子点激光器，半导体腔量子电动力学，以及它们的实施，例如在量子信息技术。
One-step implementation of the Fredkin gate via quantum Zeno dynamics
基于量子Zeno动力学，研究了共振和大失谐条件下双模腔中Fredkin门的一步实现，降低了实验操作的复杂性.通过数值计算讨论了腔衰减和原子自发发射的影响。结果表明，两种模型的保真度和成功概率均对腔衰减具有鲁棒性，而在大失谐模型中，保真度和成功概率对原子自发发射不敏感.此外，相互作用的时间是相当短的共振模型相比，大失谐模型。
The Influence of Superpositional Wave Function Oscillations on Shor's Quantum Algorithm
我们研究了叠加波函数振荡对整数因式分解的Shor量子算法性能的影响。结果表明，波函数振荡可以破坏所需的量子干涉。这种不期望的效应可以使用量子计算的共振脉冲实现来常规地消除，但是需要对非共振实现进行特殊分析。
We consider a quantum processor based on five qutrits represented by spins S=1, which is driven by radio fre-quency (RF) pulses selective in transitions between adjacent levels. Numerical simulation of the implementation of the quantum-adiabatic clustering algorithm was performed on the example of partitioning a set of six points into three groups. We find the amplitudes and durations of rectangular RF pulses, as well as the durations of free evolu-tion intervals in the control pulse sequence, which made it possible to engineer a time-dependent effective Hamilto-nian in the discrete-time appro…
Third order parametric down-conversion describes a class of nonlinear processes in which a pump photon can be down-converted into triplets of photons. It has been identified as a source of non-classical light, with capabilities beyond those offered by better-established processes such as spontaneous four-wave mixing. Here we discuss the implementation of TOPDC in integrated photonic systems. We derive equations for the rates of TOPDC in a non-resonant (waveguide) and resonant (microring) platform, such that the scaling with experimental parameters can be plainly seen. We find that generally no…
Cavity implementation of quantum interference in a $Λ$-type atom
提出了一种在有限温度下实现$Λ$型原子与频率可调、具有预选偏振态的单模腔场耦合的量子干涉的方案。干涉辅助的人口捕获，人口反转和探测增益在一边带的Autler-Townes光谱预测某些腔谐振频率。
Logical operations with single x-ray photons via dynamically-controlled nuclear resonances
从理论上研究了利用共振光核相互作用实现偏振编码x射线的逻辑运算。我们表明，通过共振散射核和快速旋转的核超精细磁场来控制输出光子的偏振，单量子比特逻辑门可以模拟。可以采用第二控制量子位来触发磁场旋转，从而允许用于X射线光子的受控非门的若干实现选择。
The goal of this paper is to outline a general-purpose scalable implementation of Shor's period finding algorithm using fundamental quantum gates, and to act as a blueprint for linear optical implementations of Shor's algorithm for both general and specific values of N. This offers a broader view of a problem often overlooked in favour of compiled versions of the algorithm.
Toolbox of resonant quantum gates in Circuit QED
我们提出了在电路量子电动力学中实现快速共振门用于量子信息处理。我们展示了如何在谐振器内适当利用三能级超导量子位构成了执行不同的两量子位谐振门的关键工具，与较慢的色散技术相比，提高了操作速度。为了说明谐振双量子比特门在电路QED中的好处，我们考虑通过使用谐振控制相位（CPHASE）和单量子比特门在N × N超导量子比特阵列中实现二维团簇态，其中产生时间随N线性增长。对于N = 3，并考虑到退相干机制，保真度超过60%的产生这种集群状态。
One-step implementation of the genuine Fredkin gate in high-$Q$ coupled three-cavity arrays
我们提出了两种有效的方法来实现Fredkin门与原子分别被困在一个阵列的三个高- $Q$耦合腔。第一种方案是基于共振动力学，在保持其他子空间不变的情况下，在特定子空间中产生快速共振相互作用;第二种方案利用色散相互作用，通过虚拟激发过程实现两个分布式目标量子比特之间的有效长距离偶极-偶极相互作用。这两种方案都可以在一个步骤中实现Fredkin门的标准形式，而无需任何后续的单量子位操作。利用主方程分析了退相干效应对门性能的影响，严格的数值模拟表明该量子门具有较高的平均保真度。
Quantum Computation as a Dynamical Process
本文讨论了量子计算的动力学问题。我们证明，快速波函数振荡可以通过破坏所需的量子干涉来影响Shor量子算法的性能。我们还表明，这种破坏性的影响，可以避免使用共振脉冲技术。讨论了伊辛自旋系统中量子逻辑门的共振脉冲实现动力学。我们还讨论了非共振激发的影响。我们计算的参数范围内，可以最大限度地减少不良的非共振效应。最后，我们描述了“$2πk$ -方法”，它避免了非共振量子比特的有害偏转。
Resonant purification of mixed states for closed and open quantum systems
纯态是实现量子技术的基础，并且在过去几年中已经开发了几种用于纯化量子系统S的状态的方法。在这封信中，我们提出了一种新的方法，基于S与辅助系统P的相互作用，具有广泛的适用性。考虑到两个能级系统S和P，并假设它们之间的特定相互作用，我们证明了在适当的条件下，可以得到完整的纯化的参数表征P.使用分析和数值工具，我们表明，纯化过程中表现出的共振行为，在这两种情况下的系统与外部环境隔离或不。
Nonadiabatic holonomic quantum computation has attracted increasing interest because of its robustness. In this paper, based on the shortcuts to adiabaticity (STA), we propose a scheme to construct a three-qubit nonadiabatic holonomic gate in a cavity quantum electrodynamics system. In the scheme, the three-qubit holonomic gate is implemented in a single step. Besides, numerical simulations show that the constructed holonomic quantum gate holds the characteristics of high-fidelity, decoherence-resistance and error-immunity.
Implementation of Shor's Algorithm with a Single Photon in 32 Dimensions
本文实验展示了在单光子的32维时间仓中编码信息，并实现编译版Shor算法，证明高维量子系统具备强大的复杂量子信息处理能力。
Cavity QED implementation of the multi-qubit refined Deutsch-Jozsa algorithm
从理论上研究了利用多个里德伯原子与单模微波腔的共振相互作用实现多量子比特的精化Deutsch-Jozsa（DJ）算法，该算法可以有效地实现多量子比特控制的相位门.我们展示了如何在高保真度下实现多量子位精化DJ算法，即使在弱腔衰减和一些缺陷的情况下。我们认为，在我们的计划所需的操作几乎是在目前的实验可能性。
A scheme to encode arbitrarily long integer pairs on degenerate optical parametric oscillations multiplexed in time is proposed. The classical entanglement between the polarization directions and the phases of the oscillating pulses, regarded as two computational registers, furnishes the integer correlations within each pair. We show the major algorithmic steps, modular exponentiation and discrete Fourier transform, of Shor's quantum factoring algorithm can be executed in the registers as pulse interferences under the assistance of external logics. The factoring algorithm is thus rendered equi…
Shor's quantum algorithm is very important for cryptography, since it can factor large numbers much faster than classical algorithms. In this study, we implement a simulator for Shor's quantum algorithm on graphic processor units (GPU) and compare our results with Liquid -which is Microsoft quantum simulation platform- and two classical CPU-implementations. We evaluate 10 benchmarks for comparing our GPU implementation with Liquid and single-core implementation. The analysis shows that GPU vector operations is more suitable for Shor's quantum algorithm. Our GPU kernel function is compute-bound…
Implementation of three-qubit Grover search in cavity QED
利用三个里德伯原子与单模微波腔的共振相互作用，基于三量子比特量子门的思想[Phys.Rev.A73，064304（2006）]，考虑了弱腔衰减条件下三量子比特Grover搜索算法的实现.我们模拟了在腔衰减影响下的搜索过程，并表明我们的方案可以有效地实现高保真度地找到标记态。所需的操作是非常接近的达到与当前的腔QED技术。
Impact of qubit anharmonicity on near-resonant Rabi oscillations
本研究探讨了量子比特非谐性对弱近共振微波驱动下 Rabi 振荡的影响，揭示了 Rabi 频率平方与驱动幅度平方的线性关系，并分析了 fluxonium 量子比特 CZ 门实现中的泄漏与相位误差。
We investigate a hybrid quantum system consisting of spatially separated resonant exchange qubits, defined in three-electron semiconductor triple quantum dots, that are coupled via a superconducting transmission line resonator. Drawing on methods from circuit quantum electrodynamics and Hartmann-Hahn double resonance techniques, we analyze three specific approaches for implementing resonator-mediated two-qubit entangling gates in both dispersive and resonant regimes of interaction. We calculate entangling gate fidelities as well as the rate of relaxation via phonons for resonant exchange qubit…
Resonant Adiabatic Passage with Three Qubits
我们研究了绝热量子隐形传态的非绝热实现，发现通过共振可以达到完美的保真度。我们阐明了隐形传态的物理机制，为三个量子比特，通过映射到两个平行的和相互相干的绝热通道的动力学。通过转换到绝热框架中，我们用自旋为1/2的粒子的磁共振来解释这种共振。我们的结果建立了一个快速和鲁棒的方法来转移量子态，并提出了一种替代路线向高精度量子门。
Light propagation in disordered media is a fundamental and important problem in optics and photonics. In particular, engineering light-matter interaction in disordered cold atomic ensembles is one of the central topics in modern quantum and atomic optics. The collective response of dense atomic gases under light excitation, which crucially depends on the spatial distribution of atoms and the geometry of the ensemble, has important impacts on quantum technologies like quantum sensors, atomic clocks and quantum information storage. Here we analyze near-resonant light transmission in two-dimensio…
Characterisation of an exchange-based two-qubit gate for resonant exchange qubits
共振交换量子位是一个有前途的家庭除了实验实现的编码的单量子位使用半导体量子点。我们之前已经表明，用单个交换脉冲在两个共振交换量子位之间执行CPHASE门应该是简单的。这种方法使用能隙来抑制泄漏，而不是传统的脉冲序列。在本文中，我们提出的分析和模拟我们提出的两个量子比特门的电荷和Overhauser场噪声在目前的实验中观察到的水平。我们的主要结果是，我们期望实现我们的双量子位门，以实现高精度，在百分比水平的错误和门时间可比的单量子位操作。因此，交换耦合共振交换量子比特仍然是量子计算的有吸引力的方法。
Implementation of a Quantum Metamaterial
操纵电磁波通过亚波长尺寸的人工结构的传播是超材料的核心功能。共振结构，如开口环共振器，扮演人造“原子”的角色，并塑造磁响应。超导超材料因其极低的欧姆损耗和通过利用约瑟夫森电感调谐其谐振频率的可能性而成为人们关注的焦点。此外，约瑟夫森电感的非线性性质使得能够制造真正的人造原子。这种超导量子二能级系统（量子比特）的阵列可以用于实现量子超材料。在这里，我们进行了一个实验，其中20个超导通量量子比特嵌入到一个微波谐振器。通过谐振器传输的信号的相位揭示了高达8个量子比特的集体谐振耦合。基于这个原理验证实验的许多人造原子的量子线路提供了广泛的前景，从检测单个微波光子到相位开关，量子双折射和超辐射相变。
The three-qubit Toffoli gate plays an important role in quantum error correction and complex quantum algorithms such as Shor's factoring algorithm, motivating the search for efficient implementations of this gate. Here we introduce a Toffoli gate suitable for exchange-coupled electron spin qubits in silicon quantum dot arrays. Our protocol is a natural extension of a previously demonstrated resonantly driven CNOT gate for silicon spin qubits. It is based on a single exchange pulse combined with a resonant microwave drive, with an operation time on the order of 100 ns and fidelity exceeding 99%…
Enhancing photoassociation rates by non-resonant light control of shape resonances
光缔合，使用激光从原子组装分子，受到原子对在足够短的原子间间隔下的低密度的限制。在这里，我们发现强度为10^10 W/cm ^2量级的非共振光改变了原子的热云，增强了形状共振的玻尔兹曼权重，并将散射态推到离解极限以下。这导致光缔合速率增强了几个数量级，并为热系综中的基态分子数量比迄今为止所达到的数量大得多开辟了道路。
Three qubit Grover's algorithm using superconducting quantum interference devices in cavity QED
提出了一种利用四能级超导量子干涉器件（SQUID）耦合到超导谐振腔实现三量子比特Grover算法的方案。该方案是基于谐振，非谐振腔场与SQUID的相互作用和经典微波脉冲的应用。我们表明，SQUID水平间距的调整过程中的门操作，绝热通道，和二阶失谐是不需要的，导致更快的实施。我们还表明，即使在存在能级衰减和腔耗散的情况下，也可以高保真地搜索标记态。
Asymptotic model for shape resonance control of diatomics by intense non-resonant light
基于原子与非共振光场的长程散射特性，推导了原子与非共振光场通过极化率各向异性相互作用的普适模型。相应的动力学可以使用节线技术来求解渐近薛定谔方程。它包括在长范围内施加物理边界条件和在分离内区和渐近区的位置处使波函数消失。结果表明，依赖于非共振光强度的节线可以满意地解释短程极化率的影响。该方法允许确定共振结构，能量，宽度，通道混合和杂交，即使是窄共振。
Inspired by a recent experiment [Phys. Rev. Letts. \textbf{122}, 253201(2019)] that an unprecedented quantum interference was observed in the way of Stimulated Raman adiabatic passage (STIRAP) due to the coexisting resonant- and detuned-STIRAPs, we comprehensively study this effect for uncovering its robustness towards the external-field fluctuations of laser noise, imperfect resonance condition as well as the excited-state decaying. We verify that, an auxiliary dynamical phase accumulated in hold time caused by the quasi-dark state can sensitively manipulate the visibility and frequency of th…
The non-adiabatic geometric quantum computation (NGQC) has attracted a lot of attention for noise-resilient quantum control. However, previous implementations of NGQC require long evolution paths that make them more vulnerable to incoherent errors than their dynamical counterparts.In this work, we experimentally realize a universal short-path non-adiabatic geometric gate set (SPNGQC) with a 2-times shorter evolution path on a superconducting quantum processor. Characterizing with both quantum process tomography and randomized benchmarking methods, we report an average single-qubit gate fidelit…
The implementation of holonomic quantum computation on superconducting quantum circuits is challenging due to the general requirement of controllable complicated coupling between multilevel systems. Here we solve this problem by proposing a scalable circuit QED lattice with simple realization of a universal set of nonadiabatic holonomic quantum gates. Compared with the existing proposals, we can achieve both the single and two logical qubit gates in an tunable and all-resonant way through a hybrid transmon-transmission-line encoding of the logical qubits in the decoherence-free subspaces. This…
Implementation of Shor Algorithm: Factoring a 4096-Bit Integer Under Specific Constraints
针对量子计算实用化需求，研究聚焦Shor算法实现，通过提升模运算效率，在特定约束下完成4096位整数分解，相比SOTA方法效率显著提升且支持更长整数分解。
Dipole spectrum structure of non-resonant non-pertubative driven two-level atoms
在电偶极近似和旋波近似下，分析了非共振强单色光场激发二能级原子的偶极谱。我们发现，显然复杂的光谱结构可以完全描述为两个家庭：谐波频率的驱动场和场致非线性荧光。我们制定的问题提供了定量的法律最相关的光谱特征：谐波比和相位，非微扰斯塔克位移，谐波高原的频率限制。特别是，我们证明了锁定的谐波相位在翅膀的平台打开的可能性，通过谐波滤波产生超短脉冲。
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