Jingfu Zhang, Zhiheng Lu
By studying the attribute of the inversion about average operation in quantum searching algorithm, we find the similarity between the quantum searching and the course of two rigid bodies'collision. Some related questions are discussed from this similarity.
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The landmark Grover algorithm for amplitude amplification serves as an essential subroutine in various type of quantum algorithms, with guaranteed quantum speedup in query complexity. However, there have been no proposal to realize the original motivating application of the algorithm, i.e., the database search or more broadly the pattern matching in a practical setting, mainly due to the technical difficulty in efficiently implementing the data loading and amplitude amplification processes. In this paper, we propose a quantum algorithm that approximately executes the entire Grover database sea…
Efficient Quantum Counting and Quantum Content-Addressable Memory for DNA similarity
提出量子内容寻址存储器QCAM及量子计数算法硬件高效实现HEQC，利用Grover算法与并行均匀控制旋转门优化电路，实现DNA序列k-mer集合Jaccard相似性计算。
Grover's algorithm for quantum search can also be applied to classical energy transfer. The procedure takes a system in which the total energy is equally distributed among $N$ subsystems and transfers most of the it to one marked subsystem. We show that in a relativistic setting the efficiency of this procedure can be improved. We will consider the transfer of relativistic kinetic energy in a series of elastic collisions. In this case, the number of steps of the energy transfer procedure approaches 1 as the initial velocities of the objects become closer to the speed of light. This is a conseq…
In the recent years, we have seen that Grover search algorithm (Proceedings, 28th annual ACM symposium on the theory of computing, pp. 212-219, 1996) by using quantum parallelism has revolutionized the field of solving huge class of NP problems in comparisons to classical systems. In this work, we explore the idea of extending Grover search algorithm to approximate algorithms. Here we try to analyze the applicability of Grover search to process an unstructured database with a dynamic selection function in contrast to the static selection function used in the original work (Grover in Proceeding…
We propose a scheme to implement two-qubit Grover's quantum search algorithm using Cavity Quantum Electrodynamics. Circular Rydberg atoms are used as quantum bits (qubits). They interact with the electromagnetic field of a non-resonant cavity . The quantum gate dynamics is provided by a cavity-assisted collision, robust against decoherence processes. We present the detailed procedure and analyze the experimental feasibility.
In a fundamental paper [Phys. Rev. Lett. 78, 325 (1997)] Grover showed how a quantum computer can find a single marked object in a database of size N by using only O(N^{1/2}) queries of the oracle that identifies the object. His result was generalized to the case of finding one object in a subset of marked elements. We consider the following computational problem: A subset of marked elements is given whose number of elements is either M or K, M<K, our task is to determine which is the case. We show how to solve this problem with a high probability of success using only iterations of Grover's b…
In this note, we give a quantum algorithm that finds collisions in arbitrary r-to-one functions after only O((N/r)^(1/3)) expected evaluations of the function. Assuming the function is given by a black box, this is more efficient than the best possible classical algorithm, even allowing probabilism. We also give a similar algorithm for finding claws in pairs of functions. Furthermore, we exhibit a space-time tradeoff for our technique. Our approach uses Grover's quantum searching algorithm in a novel way.
Toward Secure Multitenant Quantum Computing: Circuit Affinity, Crosstalk Patterns, and Grouping Strategies
研究通过分析七台IBM超导处理器的串扰模式，识别出三种电路类型，提出基于硬件特性的调度策略以提升系统利用率并保障计算完整性。
In "Playing Pool with $π$", Galperin invented an extraordinary method to learn the digits of $π$ by counting the collisions of billiard balls. Here I demonstrate an exact isomorphism between Galperin's bouncing billiards and Grover's algorithm for quantum search. This provides an illuminating way to visualize Grover's algorithm.
We analyze the performance of classical and quantum search algorithms from a thermodynamic perspective, focusing on resources such as time, energy, and memory size. We consider two examples that are relevant to post-quantum cryptography: Grover's search algorithm, and the quantum algorithm for collision-finding. Using Bennett's "Brownian" model of low-power reversible computation, we show classical algorithms that have the same asymptotic energy consumption as these quantum algorithms. Thus, the quantum advantage in query complexity does not imply a reduction in these thermodynamic resource co…
Motivated by the similarity between adiabatic quantum algorithms and quantum phase transitions, we study the impact of decoherence on the sweep through a second-order quantum phase transition for the prototypical example of the Ising chain in a transverse field and compare it to the adiabatic version of Grovers search algorithm, which displays a first order quantum phase transition. For site-independent and site-dependent coupling strengths as well as different operator couplings, the results show that (in contrast to first-order transitions) the impact of decoherence caused by a weak coupling…
In the continuum limit (large number of qubits), adiabatic quantum algorithms display a remarkable similarity to sweeps through quantum phase transitions. We find that transitions of second or higher order are advantageous in comparison to those of first order. With this insight, we propose a novel adiabatic quantum algorithm for the solution of 3-satisfiability (3-SAT) problems (exact cover), which is significantly faster than previous proposals according to numerical simulations (up to 20 qubits). These findings suggest that adiabatic quantum algorithms can solve NP-complete problems such as…
We demonstrate a novel method for applying a scientific quantum algorithm - the Grover Algorithm (GA) - to search for rare events in proton-proton collisions at 13 TeV collision energy using CERN's Large Hadron Collider. The search is of an unsorted database from the ATLAS detector in the form of ATLAS Open Data. As indicated by the Higgs boson decay channel $H\rightarrow ZZ^*\rightarrow 4l$, the detection of four leptons in one event may be used to reconstruct the Higgs boson and, more importantly, evince Higgs boson decay to some new phenomena, such as $H\rightarrow ZZ_d \rightarrow 4l$. In …
In this paper we present an efficiently scaling quantum algorithm which finds the size of the maximum common edge subgraph for a pair of arbitrary graphs and thus provides a meaningful measure of graph similarity. The algorithm makes use of a two-part quantum dynamic process: in the first part we obtain information crucial for the comparison of two graphs through linear quantum computation. However, this information is hidden in the quantum system with vanishingly small amplitude that even quantum algorithms such as Grover's search are not fast enough to distill the information efficiently. In…
Exploiting the similarity between adiabatic quantum algorithms and quantum phase transitions, we argue that second-order transitions -- typically associated with broken or restored symmetries -- should be advantageous in comparison to first-order transitions. Guided by simple examples we construct an alternative adiabatic algorithm for the NP-complete problem {\em Exact Cover 3}. We show numerically that its average performance (for the considered cases up to ${\cal O}\{20\}$ qubits) is better than that of the conventional scheme. The run-time of adiabatic algorithms is not just determined by …
In symmetric cryptanalysis, the model of superposition queries has led to surprising results, with many constructions being broken in polynomial time thanks to Simon's period-finding algorithm. But the practical implications of these attacks remain blurry. In contrast, the results obtained so far for a quantum adversary making classical queries only are less impressive. In this paper, we introduce a new quantum algorithm which uses Simon's subroutines in a novel way. We manage to leverage the algebraic structure of cryptosystems in the context of a quantum attacker limited to classical queries…
Identifying jets formed in high-energy particle collisions requires solving optimization problems over potentially large numbers of final-state particles. In this work, we consider the possibility of using quantum computers to speed up jet clustering algorithms. Focusing on the case of electron-positron collisions, we consider a well-known event shape called thrust whose optimum corresponds to the most jet-like separating plane among a set of particles, thereby defining two hemisphere jets. We show how to formulate thrust both as a quantum annealing problem and as a Grover search problem. A ke…
This MS thesis explores the effects and origins of a 'noise with memory' in the dynamics of an open quantum system. The system considered here is a multi-qubit register performing the Grover's quantum search algorithm. We show that a Markovian-correlated noise can enhance the efficiency of the algorithm over a time correlation-less noise. We also analytically find the set of necessary and sufficient conditions for the algorithm's success probability to remain invariant with respect to the number of noisy sites in the register and point out that these conditions hold irrespective of the presenc…
Quantum Algorithms for Approximate Graph Isomorphism Testing
本文提出量子算法用于近似图同构性测试，通过量子行走搜索和局部一致性传播实现高效检测，证明查询复杂度为O(n^{3/2} log n/ε)，并建立经典下界，展示量子加速。
Quantum Algorithms for Finding Vacua in the ADK Landscape
本研究提出量子算法在ADK弦论景观玩具模型中寻找小宇宙学常数真空，利用线性结构将问题简化为碰撞问题，实现查询复杂度从$2^{N/2}$降至$2^{N/3}$，大幅降低计算成本。
Quantum similarity learning for anomaly detection
本文提出一种基于经典-量子混合网络的量子相似性学习方法，用于LHC超出标准模型新物理的异常检测，通过聚类算法降低噪声使性能提升9%，展现了量子算法在高能物理数据分析中的潜力。
Tight Time-Space Lower Bounds for Collision Finding and Element Distinctness under Label Symmetry
针对碰撞寻找与元素区分性问题，在标签对称算法类内证明了最优的查询-空间权衡下界，并开发了空间敏感的压缩预言机技术。
Pseudo-deterministic Quantum Algorithms
研究提出伪确定性量子算法，展示其在查询复杂度上的分离结果，并识别可实现伪确定性的量子搜索问题类。
Rotational dynamics induced by low energy binary collisions of quantum droplets
本文理论研究了超冷原子量子液滴离轴二体碰撞的旋转动力学，发现异核混合物中序参量相位演化显著不同，并验证了碰撞过程中总角动量和线性动量守恒，同时建立了韦伯数、碰撞参数与动力学变量分布的关联。
Quantum-Based Feature Selection for Multi-classification Problem in Complex Systems with Edge Computing
本文提出量子特征选择算法 QReliefF，通过量子态编码、振幅估计和 Grover-Long 最近邻搜索降低多分类复杂度，并经 Rigetti 仿真验证可行性。
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