Shyamal S. Somaroo, David G. Cory, Timothy F. Havel
We show how the basic operations of quantum computing can be expressed and manipulated in a clear and concise fashion using a multiparticle version of geometric (aka Clifford) algebra. This algebra encompasses the product operator formalism of NMR spectroscopy, and hence its notation leads directly to implementations of these operations via NMR pulse sequences.
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Using the concept of crossing state and the formalism of second quantization, we propose a prescription for computing the density of arrivals of particles for multiparticle states, both in the free and the interacting case. The densities thus computed are positive, covariant in time for time independent hamiltonians, normalized to the total number of arrivals, and related to the flux. We investigate the behaviour of this prescriptions for bosons and fermions, finding boson enhancement and fermion depletion of arrivals.
Multiparticle entanglement leads to richer correlations than two-particle entanglement and gives rise to striking contradictions with local realism, inequivalent classes of entanglement, and applications such as one-way or topological quantum computing. When exposed to decohering or dissipative environments, multiparticle entanglement yields subtle dynamical features and access to new classes of states and applications. Here, using a string of trapped ions, we experimentally characterize the dynamics of entanglement of a multiparticle state under the influence of decoherence. By embedding an e…
Multiparticle entangled quantum states, a key resource in quantum-enhanced metrology and computing, are usually generated by coherent operations exclusively. However, unusual forms of quantum dynamics can be obtained when environment coupling is used as part of the state generation. In this work, we used quantum Zeno dynamics (QZD), based on nondestructive measurement with an optical microcavity, to deterministically generate different multiparticle entangled states in an ensemble of 36 qubit atoms in less than 5 microseconds. We characterized the resulting states by performing quantum tomogra…
Entangled many-body states are an essential resource for quantum computing and interferometry. Determining the type of entanglement present in a system usually requires access to an exponential number of parameters. We show that in the case of pure multi-particle quantum states, features of the global entanglement can already be extracted from local information alone. This is achieved by associating with any given class of entanglement an entanglement polytope---a geometric object which characterizes the single-particle states compatible with that class. Our results, applicable to systems of a…
From Entanglement to Universality: A Multiparticle Spacetime Algebra Approach to Quantum Computational Gates Revisited
本文重访几何代数在量子计算中的应用，利用 MSTA 刻画量子态与门并重新分析普适门证明，揭示态与算符的概念统一及转子方法优势。
Aaronson and Arkhipov recently used computational complexity theory to argue that classical computers very likely cannot efficiently simulate linear, multimode, quantum-optical interferometers with arbitrary Fock-state inputs [Aaronson and Arkhipov, Theory Comput. 9, 143 (2013)]. Here we present an elementary argument that utilizes only techniques from quantum optics. We explicitly construct the Hilbert space for such an interferometer and show that its dimension scales exponentially with all the physical resources. We also show in a simple example just how the Schrödinger and Heisenberg pictu…
Given a multiparticle quantum state, one may ask whether it can be represented as a thermal state of some Hamiltonian with k-particle interactions only. The distance from the exponential family defined by these thermal states can be considered as a measure of complexity of a given state. We investigate the resulting optimization problem and show how symmetries can be exploited to simplify the task of finding the nearest thermal state in a given exponential family. We also present an algorithm for the computation of the complexity measure and consider specific examples to demonstrate its applic…
As information carriers in quantum computing, photonic qubits have the advantage of undergoing negligible decoherence. However, the absence of any significant photon-photon interaction is problematic for the realization of non-trivial two-qubit gates. One solution is to introduce an effective nonlinearity by measurements resulting in probabilistic gate operations. In one-way quantum computation, the random quantum measurement error can be overcome by applying a feed-forward technique, such that the future measurement basis depends on earlier measurement results. This technique is crucial for a…
Expressing and Analyzing Quantum Algorithms with Qualtran
本文介绍开源库 Qualtran，通过抽象、数据结构和标准构建模块支持量子算法的表示、模拟、图示生成与资源估算，并在多类关键算法上展示可复现分析能力。
A Gate-Based Quantum Computing Framework for Codon Optimization
本研究提出基于门控量子计算的密码子优化框架，利用VQE、SVQE和QAOA算法，在三氨基酸基准上成功复现精确基态解，并在IBM量子硬件上验证了可复现性能，为未来更大蛋白质序列的量子优化奠定基础。
We demonstrate how machine learning is able to model experiments in quantum physics. Quantum entanglement is a cornerstone for upcoming quantum technologies such as quantum computation and quantum cryptography. Of particular interest are complex quantum states with more than two particles and a large number of entangled quantum levels. Given such a multiparticle high-dimensional quantum state, it is usually impossible to reconstruct an experimental setup that produces it. To search for interesting experiments, one thus has to randomly create millions of setups on a computer and calculate the r…
Quantum computing in spin-adapted representations for efficient simulations of spin systems
本文提出了一种直接在总自旋算符本征基中设计量子算法的新形式体系，结合对称群方法与内部自由度截断方案，为反铁磁Heisenberg模型构建了自旋适应的Hamiltonian层级，并开发了浅层量子电路状态准备方案以实现高效量子模拟。
Cutting Medusa's Path -- Tackling Kill-Chains with Quantum Computing
本文提出利用量子计算和漏洞图解决网络安全问题，通过QUBO和量子退火确定补丁优先级以消除所有杀伤链，证明了量子求解时间相比经典算法的指数增长几乎保持恒定。
Graph states are the main computational building blocks of measurement-based computation and a useful tool for error correction in the gate model architecture. The graph states form a class of quantum states which are eigenvectors for the abelian group of stabilizer operators. They own topological properties, arising from their graph structure, including the presence of highly connected nodes, called hubs. Starting from hub nodes, we demonstrate how to efficiently express a graph state through the generators of the stabilizer group. We provide examples by expressing the ring and the star topol…
Hybridlane: A Software Development Kit for Hybrid Continuous-Discrete Variable Quantum Computing
Hybridlane是一种开源软件工具包，提供混合连续-离散变量量子计算的统一前端，通过自动导线类型推断和解耦门语义，实现高效且无需模拟的电路验证与操作。
Quantum-classical neurons upgraded with optical spin qubits for advanced computing and networking architectures
研究用光学自旋量子比特升级量子-经典神经元，通过实验测量集成后的神经元，推导考虑其与量子比特自旋相互作用的量子模型并计算，以预测量子计算操作在该系统状态空间的扩展，对实现有量子光学能力的硬件神经元至关重要。
Quantum devices may overcome limitations of classical computers in studies of nuclear structure functions and parton Wigner distributions of protons and nuclei. In this talk, we discuss a worldline approach to compute nuclear structure functions in the high energy Regge limit of QCD using a hybrid quantum computer, by expressing the fermion determinant in the QCD path integral as a quantum mechanical path integral over $0+1$-dimensional fermionic and bosonic world-lines in background gauge fields. Our simplest example of computing the well-known dipole model result for the structure function $…
Hamiltonian simulation with explicit formulas for Digital-Analog Quantum Computing
提出一种数字-模拟量子计算方案，通过将任意两体哈密顿量表示为伊辛哈密顿量的局部酉变换之和（项数最多为系统大小的二次方），避免了预处理阶段的大规模数值优化，实现了多项式时间内的次优解。
Quantum Physics using Weighted Model Counting
本文提出用加权模型计数解决线性代数问题，特别是物理和量子计算中的问题，通过将狄拉克符号转换为WMC问题，展示了其在计算各物理模型配分函数中的有效性。
Photons are natural carriers of quantum information due to their ease of distribution and long lifetime. This thesis concerns various related aspects of quantum information processing with single photons. Firstly, we demonstrate N-photon entanglement generation through a generalised N X N symmetric beam splitter known as the Bell multiport. A wide variety of 4-photon entangled states as well as the N-photon W-state can be generated with an unexpected non-monotonic decreasing probability of success with N. We also show how the same setup can be used to generate multiatom entanglement. A further…
Inequivalent $Z_2^n$-graded brackets, $n$-bit parastatistics and statistical transmutations of supersymmetric quantum mechanics
该研究推导了Z₂ⁿ分次算子环中不等价李型括号的数量公式，构建了对应仲统计的量子哈密顿量，并证明N扩展一维超对称量子力学存在多种由不等价分次李代数描述的统计嬗变形式。
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