我们研究了Miyazaki { \it et al.}提出的一系列用半整数$j=1/2, 1, 3/2, ...$标记的一维离散时间量子行走模型，其中每一个沃克波函数具有$2j+1$分量，并且在每一个时间步长处的跳跃范围是$2j$。在长时间极限下，赝速度分布的密度函数一般由适当标度的Konno密度函数的叠加给出。由于Konno密度函数有一个有限的开支集，并且在支集的边界处发散，当$2j+1$为偶数时，$(2j+1)$分量模型中赝速度的极限分布可以有$2j+1$峰.然而，当$j$变得很大时，我们发现这些尖峰消失了，并且在极限分布的原点周围出现了一个普遍的单调凸结构。我们讨论了一个可能的路线，从量子行走到经典扩散与$j \to \infty$限制。
英文摘要：
We study a series of one-dimensional discrete-time quantum-walk models labeled by half integers $j=1/2, 1, 3/2, ...$, introduced by Miyazaki {\it et al.}, each of which the walker's wave function has $2j+1$ components and hopping range at each time step is $2j$. In long-time limit the density functions of pseudovelocity-distributions are generally given by superposition of appropriately scaled Konno's density function. Since Konno's density function has a finite open support and it diverges at the boundaries of support, limit distribution of pseudovelocities in the $(2j+1)$-component model can have $2j+1$ pikes, when $2j+1$ is even. When $j$ becomes very large, however, we found that these pikes vanish and a universal and monotone convex structure appears around the origin in limit distributions. We discuss a possible route from quantum walks to classical diffusion associated with the $j \to \infty$ limit.
Quantum measurements play a fundamental role in quantum mechanics and quantum information processing, but it is not easy to implement generalized measurements, the most powerful measurements allowed by quantum mechanics. Here we propose a simple recipe for implementing generalized measurements on a qudit via quantum walks. With this recipe, any discrete quantum measurement can be implemented via a one-dimensional discrete quantum walk; the number of steps is only two times the number of measurement outcomes. As an illustration, we present a unified solution for implementing arbitrary symmetric…
In this work the quantum random walk search algorithm with walk coin constructed by generalized Householder reflection and phase multiplier has been studied. The coin register is one qudit with arbitrary dimension. Monte Carlo simulations, in combination with supervised machine learning, are used to find walk coins making the quantum algorithm more robust to deviations in the coin's parameters. By applying deep neural network we make prediction for the parameters of an optimal coin with arbitrary size and estimate the stability for such coin.
The capability to generate and manipulate quantum states in high-dimensional Hilbert spaces is a crucial step for the development of quantum technologies, from quantum communication to quantum computation. One-dimensional quantum walk dynamics represents a valid tool in the task of engineering arbitrary quantum states. Here we affirm such potential in a linear-optics platform that realizes discrete-time quantum walks in the orbital angular momentum degree of freedom of photons. Different classes of relevant qudit states in a six-dimensional space are prepared and measured, confirming the feasi…
The generation and control of quantum correlations in high-dimensional systems is a major challenge in the present landscape of quantum technologies. Achieving such non-classical high-dimensional resources will potentially unlock enhanced capabilities for quantum cryptography, communication and computation. We propose a protocol that is able to attain entangled states of $d$-dimensional systems through a quantum-walk-based {\it transfer \& accumulate} mechanism involving coin and walker degrees of freedom. The choice of investigating quantum walks is motivated by their generality and versatili…
Generation of entangled state is of paramount importance both from quantum theoretical foundation and technology applications. Entanglement swapping provides an efficient method to generate entanglement in quantum communication protocols. However, perfect Bell measurements for qudits, the key to entanglement swapping, have been proven impossible to achieve by using only linear elements and particle detectors. To avoid this bottleneck, we propose a novel scheme to generate entangled state including two-qubit entangled state, two-qudit entangled state, three-qubit GHZ state and three-qudit GHZ s…
High-dimensional quantum systems can offer extended possibilities and multiple advantages while developing advanced quantum technologies. In this paper, we propose a class of quantum-walk architecture networks that admit the efficient routing of high-dimensional quantum states. Perfect state transfer of an arbitrary unknown qudit state can be achieved between two arbitrary nodes via a one-dimensional lackadaisical discrete-time quantum walk. In addition, this method can be generalized to the high-dimensional lattices, where it allows distillable entanglement to be shared between arbitrary inpu…
We introduce some new perfect state transfer and teleportation schemes by quantum walks with two coins. Encoding the transferred information in coin 1 state and alternatively using two coin operators, we can perfectly recover the information on coin 1 state at target position only by at most two times of flipping operation. Based on quantum walks with two coins either on the line or on the $N$-circle, we can perfectly transfer any qubit state. In addition, using quantum walks with two coins either on complete graphs or regular graphs, we can first implement perfect qudit state transfer by quan…
A potential quantum internet would open up the possibility of realizing numerous new applications, including provably secure communication. Since losses of photons limit long-distance, direct quantum communication and widespread quantum networks, quantum repeaters are needed. The so-called PLOB-repeaterless bound [Pirandola et al., Nat. Commun. 8, 15043 (2017)] is a fundamental limit on the quantum capacity of direct quantum communication. Here, we analytically derive the quantum-repeater gain for error-corrected, one-way quantum repeaters based on higher-dimensional qudits for two different p…
Comparing Schemes for Creating Qudit Graph States from 16- & 128-dimensional Hilbert Space using Donors in Silicon
School of Electrical Engineering and Telecommunications, UNSW Sydney（新南威尔士大学电气工程和电信学院）；ARC Centre of Excellence for Quantum Computation and Communication Technology（量子计算与通信技术卓越研究中心）；Centre for Quantum Software and Information, University of Technology Sydney（悉尼科技大学量子软件与信息研究中心）；InstituteQ, Aalto University（阿尔托大学量子研究所）
The conditional version of sandwiched Tsallis relative entropy (CSTRE) is employed to study the bipartite separability of one parameter family of N-qudit Werner- Popescu states in their 1 : N-1 partition. For all N, the strongest limitation on bipartite separability is realized in the limit q tending to infinity and is found to match exactly with the separability range obtained using an algebraic method which is both necessary and sufficient. The theoretical superiority of using CSTRE criterion to find the bipartite separability range over the one using Abe- Rajagopal (AR) q-conditional entrop…
The notion of universal quantum computation can be generalized to multi-level qudits, which offer advantages in resource usage and algorithmic efficiencies. Trapped ions, which are pristine and well-controlled quantum systems, offer an ideal platform to develop qudit-based quantum information processing. Previous work has not fully explored the practicality of implementing trapped-ion qudits accounting for known experimental error sources. Here, we describe a universal set of protocols for state preparation, single-qudit gates, a new generalization of the Mølmer-Sørensen gate for two-qudit gat…
Quantum tomography makes it possible to obtain comprehensive information about certain logical elements of a quantum computer. In this regard, it is a promising tool for debugging quantum computers. The practical application of tomography, however, is still limited by systematic measurement errors. Their main source are errors in the quantum state preparation and measurement procedures. In this work, we investigate the possibility of suppressing these errors in the case of ion-based qudits. First, we will show that one can construct a quantum measurement protocol that contains no more than a s…
Stimulated Raman adiabatic passage (STIRAP) is a widely used protocol to realize high-fidelity and robust quantum control in various quantum systems. However, further application of this protocol in superconducting qubits is limited by population leakage caused by the only weak anharmonicity. Here we introduce an optimally controlled shortcut-to-adiabatic (STA) technique to speed up the STIRAP protocol in a superconducting qudit. By modifying the shapes of the STIRAP pulses, we experimentally realize a fast (32 ns) and high-fidelity quantum state transfer. In addition, we demonstrate that our …
Classical turbo codes efficiently approach the Shannon limit, and so bringing these over to the quantum scenario would allow for rapid transmission of quantum information. Early on in the work of defining the quantum analogue, it was shown that an efficient recursive subroutine (quantum convolutional codes) would always be catastrophic. This result may have stunted the further research into this coding scheme. In this document, we prove that this previously proven no-go theorem is no longer always true if we extend the coding scheme into qudit space with dimension some prime larger than 2. Thi…
HPE Quantum, Emergent Machine Intelligence, HPE Labs（惠普企业量子计算、新兴机器学习实验室）；Quantum Artificial Intelligence Laboratory, NASA Ames Research Center（美国国家航空航天局艾姆斯研究中心量子人工智能实验室）；KBR, Inc.（KBR公司）；USRA Research Institute for Advanced Computer Science（大学空间研究协会先进计算机科学研究所）；School of Electrical Engineering and Telecommunications, UNSW Sydney（新南威尔士大学悉尼分校电气与电信工程学院）；ARC Centre of Excellence for Quantum Computation and Communication Technology（ARC量子计算与通信技术卓越中心）
Accelerating computational tasks with quantum resources is a widely-pursued goal that is presently limited by the challenges associated with high-fidelity control of many-body quantum systems. The paradigm of reservoir computing presents an attractive alternative, especially in the noisy intermediate-scale quantum era, since control over the internal system state and knowledge of its dynamics are not required. Instead, complex, unsupervised internal trajectories through a large state space are leveraged as a computational resource. Quantum systems offer a unique venue for reservoir computing, …
Autonomous quantum error correction utilizes the engineered coupling of a quantum system to a dissipative ancilla to protect quantum logical states from decoherence. We show that the Knill-Laflamme condition, stating that the environmental error operators should act trivially on a subspace, which then becomes the code subspace, is sufficient for logical qudits to be protected against Markovian noise. It is proven that the error caused by the total Lindbladian evolution in the code subspace can be suppressed up to very long times in the limit of large engineered dissipation, by explicitly deriv…
Quantum computation can be achieved by preparing an appropriate initial product state of qudits and then letting it evolve under a fixed Hamiltonian. The readout is made by measurement on individual qudits at some later time. This approach is called the Hamiltonian quantum computation and it includes, for example, the continuous-time quantum cellular automata and the universal quantum walk. We consider one spatial dimension and study the compromise between the locality $k$ and the local Hilbert space dimension $d$. For geometrically 2-local (i.e., $k=2$), it is known that $d=8$ is already suff…
Dynamical Decoupling of Nonclassical States in a Biased-Noise Spin Qudit
School of Electrical Engineering and Telecommunications, UNSW Sydney（新南威尔士大学电气与电信工程学院）；HPE Quantum, Emergent Machine Intelligence, Hewlett Packard Labs（惠普实验室）；Quantum Artificial Intelligence Laboratory (QuAIL), NASA Ames Research Center（NASA艾姆斯研究中心量子人工智能实验室）；KBR, Inc.（KBR公司）；ARC Centre of Excellence for Quantum Computer Performance & Integration (QPI)（量子计算机性能与集成卓越中心）；School of Engineering, RMIT University（皇家墨尔本理工大学工程学院）；USRA Research Institute for Advanced Computer Science（美国大学空间研究协会高级计算机科学研究所）
Qudit extension of parameterized IQP circuits: A generative quantum machine learning approach to integer data
Parity Quantum Computing Germany GmbH（Parity量子计算德国有限公司）；Parity Quantum Computing GmbH（Parity量子计算有限公司）；Institute for Theoretical Physics, University of Innsbruck（因斯布鲁克大学理论物理研究所）
We study the correlation clustering problem using the quantum approximate optimization algorithm (QAOA) and qudits, which constitute a natural platform for such non-binary problems. Specifically, we consider a neutral atom quantum computer and propose a full stack approach for correlation clustering, including Hamiltonian formulation of the algorithm, analysis of its performance, identification of a suitable level structure for ${}^{87}{\rm Sr}$ and specific gate design. We show the qudit implementation is superior to the qubit encoding as quantified by the gate count. For single layer QAOA, w…
Dimensional advantage in network cooling with hybrid oscillator-qudit systems
Harish-Chandra Research Institute, a CI of HBNI（哈里希-昌德拉研究所）；Dipartimento di Fisica “Aldo Pontremoli,” Università degli Studi di Milano（米兰大学阿尔多·庞特莫利物理系）
Nearly all modern solid-state quantum processors approach quantum computation with a set of discrete qubit operations (gates) that can achieve universal quantum control with only a handful of primitive gates. In principle, this approach is highly flexible, allowing full control over the qubits' Hilbert space without necessitating the development of specific control protocols for each application. However, current error rates on quantum hardware place harsh limits on the number of primitive gates that can be concatenated together (with compounding error rates) and remain viable. Here, we report…
Reinforcement Learning for Robust Calibration of Multi-Qudit Quantum Gates
LyRIDS, ECE Engineering School, OMNES Education（OMNES教育旗下ECE工程学院）；Advanced ICT Research Institute, National Institute of Information and Communications Technology（信息通信技术研究所先进ICT研究部）；Research Institute for Science and Technology, Tokyo University of Science（东京理科大学科学技术研究院）
Optimal Control of Spin Qudits Subject to Decoherence Using Amplitude-and-Frequency-Constrained Pulses
Universidad de Zaragoza（萨拉戈萨大学）；Instituto de Nanociencia y Materiales de Aragón (INMA), CSIC-Universidad de Zaragoza（阿拉贡纳米科学与材料研究所（INMA），西班牙国家研究委员会-萨拉戈萨大学）；ETH Zurich（苏黎世联邦理工学院）；Universidad de Valladolid（巴利亚多利德大学）；Institute for Biocomputation and Physics of Complex Systems (BIFI) of the University of Zaragoza（萨拉戈萨大学生物计算与复杂系统物理研究所（BIFI））
