Quantum computation by teleportation and symmetry

A preliminary overview of measurement-based quantum computation in the setting of symmetry and topological phases of quantum matter is given. The underlying mechanism for universal quantum computation by teleportation or symmetry are analyzed, with the emphasis on the relation with tensor-network states in the presence of various symmetries. Perspectives are also given for the role of symmetry and phases of quantum matter in measurement-based quantum computation and fault tolerance.Comment: Comments are welcome

Spinless Quantum Field Theory and Interpretation

Quantum field theory is mostly known as the most advanced and well-developed theory in physics, which combines quantum mechanics and special relativity consistently. In this work, we study the spinless quantum field theory, namely the Klein-Gordon equation, and we find that there exists a Dirac form of this equation which predicts the existence of spinless fermion. For its understanding, we start from the interpretation of quantum field based on the concept of quantum scope, we also extract new meanings of wave-particle duality and quantum statistics. The existence of spinless fermion is consistent with spin-statistics theorem and also supersymmetry, and it leads to several new kinds of interactions among elementary particles. Our work contributes to the study of spinless quantum field theory and could have implications for the case of higher spin.Comment: 15 page

Convex decomposition of dimension-altering quantum channels

Quantum channels, which are completely positive and trace preserving mappings, can alter the dimension of a system; e.g., a quantum channel from a qubit to a qutrit. We study the convex set properties of dimension-altering quantum channels, and particularly the channel decomposition problem in terms of convex sum of extreme channels. We provide various quantum circuit representations of extreme and generalized extreme channels, which can be employed in an optimization to approximately decompose an arbitrary channel. Numerical simulations of low-dimensional channels are performed to demonstrate our channel decomposition scheme

Strong analog classical simulation of coherent quantum dynamics

A strong analog classical simulation of general quantum evolution is proposed, which serves as a novel scheme in quantum computation and simulation. The scheme employs the approach of geometric quantum mechanics and quantum informational technique of quantum tomography, which applies broadly to cases of mixed states, nonunitary evolution, and infinite dimensional systems. The simulation provides an intriguing classical picture to probe quantum phenomena, namely, a coherent quantum dynamics can be viewed as a globally constrained classical Hamiltonian dynamics of a collection of coupled particles or strings. Efficiency analysis reveals a fundamental difference between the locality in real space and locality in Hilbert space, the latter enables efficient strong analog classical simulations. Examples are also studied to highlight the differences and gaps among various simulation methods.Comment: 11 pages, 5 figure

Quantum Computing with sine-Gordon Qubits

A universal quantum computing scheme, with a universal set of logical gates, is proposed based on networks of 1D quantum systems. The encoding of information is in terms of universal features of gapped phases, for which effective field theories such as sine-Gordon field theory can be employed to describe a qubit. Primary logical gates are from twist, pump, glue, and shuffle operations that can be realized in principle by tuning parameters of the systems. Our scheme demonstrates the power of 1D quantum systems for robust quantum computing.Comment: Please also refer to the journal versio

Choi states, symmetry-based quantum gate teleportation, and stored-program quantum computing

The stored-program architecture is canonical in classical computing, while its power has not been fully recognized for the quantum case. We study quantum information processing with stored quantum program states, i.e., using qubits instead of bits to encode quantum operations. We develop a stored-program model based on Choi states, following from channel-state duality, and a symmetry-based generalization of deterministic gate teleportation. Our model enriches the family of universal models for quantum computing, and can also be employed for tasks including quantum simulation and communication

Robust Object Tracking Based on Self-adaptive Search Area

Discriminative correlation filter (DCF) based trackers have recently achieved excellent performance with great computational efficiency. However, DCF based trackers suffer boundary effects, which result in the unstable performance in challenging situations exhibiting fast motion. In this paper, we propose a novel method to mitigate this side-effect in DCF based trackers. We change the search area according to the prediction of target motion. When the object moves fast, broad search area could alleviate boundary effects and reserve the probability of locating object. When the object moves slowly, narrow search area could prevent effect of useless background information and improve computational efficiency to attain real-time performance. This strategy can impressively soothe boundary effects in situations exhibiting fast motion and motion blur, and it can be used in almost all DCF based trackers. The experiments on OTB benchmark show that the proposed framework improves the performance compared with the baseline trackers.Comment: 10 pages, 4 figures, 3 tables, SPIE 10th International Symposium on Multispectral Image Processing and Pattern Recognitio

Quantum circuit design for accurate simulation of qudit channels

We construct a classical algorithm that designs quantum circuits for algorithmic quantum simulation of arbitrary qudit channels on fault-tolerant quantum computers within a pre-specified error tolerance with respect to diamond-norm distance. The classical algorithm is constructed by decomposing a quantum channel into a convex combination of generalized extreme channels by optimization of a set of nonlinear coupled algebraic equations. The resultant circuit is a randomly chosen generalized extreme channel circuit whose run-time is logarithmic with respect to the error tolerance and quadratic with respect to Hilbert space dimension, which requires only a single ancillary qudit plus classical dits.Comment: Revised: withdrawn claim that the optimization is conve

The one loop renormalization of the effective Higgs sector and its implications

We study the one-loop renormalization the standard model with anomalous Higgs couplings ($O(p^2)$) by using the background field method, and provide the whole divergence structure at one loop level. The one-loop divergence structure indicates that, under the quantum corrections, only after taking into account the mass terms of Z bosons ($O(p^2)$) and the whole bosonic sector of the electroweak chiral Lagrangian ($O(p^4)$), can the effective Lagrangian be complete up to $O(p^4)$.Comment: ReVTeX, 18 pages; in the sequel to hep-ph/0211258, hep-ph/0211301, and hep-ph/021236

Mixed random walks with a trap in scale-free networks including nearest-neighbor and next-nearest-neighbor jumps

Random walks including non-nearest-neighbor jumps appear in many real situations such as the diffusion of adatoms and have found numerous applications including PageRank search algorithm, however, related theoretical results are much less for this dynamical process. In this paper, we present a study of mixed random walks in a family of fractal scale-free networks, where both nearest-neighbor and next-nearest-neighbor jumps are included. We focus on trapping problem in the network family, which is a particular case of random walks with a perfect trap fixed at the central high-degree node. We derive analytical expressions for the average trapping time (ATT), a quantitative indicator measuring the efficiency of the trapping process, by using two different methods, the results of which are consistent with each other. Furthermore, we analytically determine all the eigenvalues and their multiplicities for the fundamental matrix characterizing the dynamical process. Our results show that although next-nearest-neighbor jumps have no effect on the leading sacling of the trapping efficiency, they can strongly affect the prefactor of ATT, providing insight into better understanding of random-walk process in complex systems.Comment: Definitive version accepted for publication in The Journal of Chemical Physic