Quantum communication complexity of establishing a shared reference frame

We discuss the aligning of spatial reference frames from a quantum communication complexity perspective. This enables us to analyze multiple rounds of communication and give several simple examples demonstrating tradeoffs between the number of rounds and the type of communication. Using a distributed variant of a quantum computational algorithm, we give an explicit protocol for aligning spatial axes via the exchange of spin-1/2 particles which makes no use of either exchanged entangled states, or of joint measurements. This protocol achieves a worst-case fidelity for the problem of "direction finding" that is asymptotically equivalent to the optimal average case fidelity achievable via a single forward communication of entangled states.     

Optimal block-tridiagonalization of matrices for coherent charge transport

Numerical quantum transport calculations are commonly based on a tight-binding formulation. A wide class of quantum transport algorithms require the tight-binding Hamiltonian to be in the form of a block-tridiagonal matrix. Here, we develop a matrix reordering algorithm based on graph partitioning techniques that yields the optimal block-tridiagonal form for quantum transport. The reordered Hamiltonian can lead to significant performance gains in transport calculations, and allows to apply conventional two-terminal algorithms to arbitrarily complex geometries, including multi-terminal structures. The block-tridiagonalization algorithm can thus be the foundation for a generic quantum transport code, applicable to arbitrary tight-binding systems. We demonstrate the power of this approach by applying the block-tridiagonalization algorithm together with the recursive Green’s function algorithm to various examples of mesoscopic transport in two-dimensional electron gases in semiconductors and graphene.     

Quantum speedup in adaptive boosting of binary classification

In classical machine learning,a set of weak classifiers can be adaptively combined for improving the overall performance,a technique called adaptive boosting(or AdaBoost).However,constructing a combined classifier for a large data set is typically resource consuming.Here we propose a quantum extension of AdaBoost,demonstrating a quantum algorithm that can output the optimal strong classifier with a quadratic speedup in the number of queries of the weak classifiers.Our results also include a generalization of the standard AdaBoost to the cases where the output of each classifier may be probabilistic.We prove that the query complexity of the non-deterministic classifiers is the same as those of deterministic classifiers,which may be of independent interest to the classical machine-learning community.Additionally,once the optimal classifier is determined by our quantum algorithm,no quantum resources are further required.This fact may lead to applications on near term quantum devices.     

Optimal identification of Hamiltonian information by closed-loop laser control of quantum systems

A closed loop learning control concept is introduced for teaching lasers to manipulate quantum systems for the purpose of optimally identifying Hamiltonian information. The closed loop optimal identification algorithm operates by revealing the distribution of Hamiltonians consistent with the data. The control laser is guided to perform additional experiments, based on minimizing the dispersion of the distribution. Operation of such an apparatus is simulated for two model finite dimensional quantum systems.     

Optimal measurements for general quantum systems

We give a general formulation of the theory of optimal quantum measurements, based on Gudder's [8] convex structure approaches to axiomatic quantum mechanics, which includes the case of Holevo's formulation [14] and operational quantum mechanics [3]. Simple and general conditions for existence of Bayes optimal measurements are obtained by a method without operator valued measure techniques. For this purpose, a representation of convex prestructures and a characterization of a class of loss functions are obtained. Finally, an application of the results to Wald's theory of statistical decision functions is shown.     

Quantum M-P Neural Network

Quantum Neural Network (QNN) is a young and outlying science built upon the combination of classical neural network and quantum computing. Making use of quantum linear superposition, this paper presents a quantum M-P neural network based on the analysis of the conventional M-P neural network. Moreover, the working principle of this proposed network and its corresponding weight updating algorithm are expatiated in the two cases of input state being in the orthogonal and non-orthogonal basic set, respectively. In addition, this paper not only validates that this quantum M-P network can realize some network functions, such as “XOR”, but also verifies the feasibility and validity of its weight learning algorithm by some simple examples.     

Backpropagation Training in Adaptive Quantum Networks

We introduce a robust, error-tolerant adaptive training algorithm for generalized learning paradigms in high-dimensional superposed quantum networks, or adaptive quantum networks. The formalized procedure applies standard backpropagation training across a coherent ensemble of discrete topological configurations of individual neural networks, each of which is formally merged into appropriate linear superposition within a predefined, decoherence-free subspace. Quantum parallelism facilitates simultaneous training and revision of the system within this coherent state space, resulting in accelerated convergence to a stable network attractor under consequent iteration of the implemented backpropagation algorithm. Parallel evolution of linear superposed networks incorporating backpropagation training provides quantitative, numerical indications for optimization of both single-neuron activation functions and optimal reconfiguration of whole-network quantum structure.     

Exponential speedup of quantum newton optimization algorithm for general polynomials

Quantum optimization algorithms can outperform their classical counterpart and are key in modern technology. The second-order optimization algorithm(the Newton algorithm) is a critical optimization method, speeding up the convergence by employing the second-order derivative of loss functions in addition to their first derivative. Here, we propose a new quantum second-order optimization algorithm for general polynomials with a computational complexity of O(poly(log d)). We use this algorithm to solve the nonlinear equation and learning parameter problems in factorization machines. Numerical simulations show that our new algorithm is faster than its classical counterpart and the first-order quantum gradient descent algorithm. While existing quantum Newton optimization algorithms apply only to homogeneous polynomials, our new algorithm can be used in the case of general polynomials, which are more widely present in real applications.     

The Measurement-Disturbance Relation and the Disturbance Trade-off Relation in Terms of Relative Entropy

We employ quantum relative entropy to establish the relation between the measurement uncertainty and its disturbance on a state in the presence (and absence) of quantum memory. For two incompatible observables, we present the measurement-disturbance relation and the disturbance trade-off relation. We find that without quantum memory the disturbance induced by the measurement is never less than the measurement uncertainty and with quantum memory they depend on the conditional entropy of the measured state. We also generalize these relations to the case with multiple measurements. These relations are demonstrated by two examples.     

Characterizing the dynamics of quantum discord under phase damping with POVM measurements

In the analysis of quantum discord, the minimization of average entropy traditionally involved over orthogonal projective measurements may be attained at more optimal decompositions by using the positive-operator-valued measure(POVM)measurements. Taking advantage of the quantum steering ellipsoid in combination with three-element POVM optimization,we show that, for a family of two-qubit X states locally interacting with Markovian non-dissipative environments, the decay rates of quantum discord show smooth dynamical evolutions without any sudden change. This is in contrast to two-element orthogonal projective measurements, in which case the sudden change of the decay rates of quantum and classical decoherences may be a common phenomenon. Notwithstanding this, we find that a subset of X states(including the Bell diagonal states) involving POVM optimization can still preserve the sudden change character as usual.     

The reservoir learning power across quantum many-body localization transition

Harnessing the quantum computation power of the present noisy-intermediate-size-quantum devices has received tremendous interest in the last few years. Here we study the learning power of a one-dimensional long-range randomly-coupled quantum spin chain, within the framework of reservoir computing. In time sequence learning tasks, we find the system in the quantum many-body localized (MBL) phase holds long-term memory, which can be attributed to the emergent local integrals of motion. On the other hand, MBL phase does not provide sufficient nonlinearity in learning highly-nonlinear time sequences, which we show in a parity check task. This is reversed in the quantum ergodic phase, which provides sufficient nonlinearity but compromises memory capacity. In a complex learning task of Mackey–Glass prediction that requires both sufficient memory capacity and nonlinearity, we find optimal learning performance near the MBL-to-ergodic transition. This leads to a guiding principle of quantum reservoir engineering at the edge of quantum ergodicity reaching optimal learning power for generic complex reservoir learning tasks. Our theoretical finding can be tested with near-term NISQ quantum devices.     

Template matching of mixed quantum states

We consider the problem of optimal classification of an unknown input mixed quantum state with respect to a set of predefined patterns C_i, each represented by a known mixed quantum template . The performance of the matching strategy is addressed within a Bayesian formulation where the cost function, as suggested by the theory of monotone distances between quantum states, is chosen to be the fidelity or the relative entropy between the input and the templates. We investigate various examples of quantum template matching for the case of a finite number of copies of a two-level input state and for a generic, group covariant, set of two-level template states.     

Strategies to measure a quantum state

We consider the problem of determining the mixed quantum state of a large but finite number of identically prepared quantum systems from data obtained in a sequence of ideal (von Neumann) measurements, each performed on an individual copy of the system. In contrast to previous approaches, we do not average over the possible unknown states but work out a “typical” probability distribution on the set of states, as implied by the experimental data. As a consequence, any measure of knowledge about the unknown state and thus any notion of “best strategy” (i.e., the choice of observables to be measured, and the number of times they are measured) depend on the unknown state. By learning from previously obtained data, the experimentalist re-adjusts the observable to be measured in the next step, eventually approaching an optimal strategy. We consider two measures of knowledge and exhibit all “best” strategies for the case of a two-dimensional Hilbert space. Finally, we discuss some features of the problem in higher dimensions and in the infinite dimensional case.     

Modeling tools for design of type-II superlattice photodetectors

In this paper, we present a range of modeling tools that are used in the design and performance evaluation of type-II superlattice detectors. Among these is an optical and photo carrier transport model for the spectral total external QE, which takes into account carrier diffusion length. Using this model, the diffusion length is extracted from external quantum efficiency measurements. It can also be used to fine-tune an optical cavity in relation to the wavelength range of interest for optimal quantum efficiency. Furthermore, an electrical device model for band bending, dark current and doping optimization is described. The modeling tools are discussed and examples of their use are given for MWIR type-II detectors based on InAs/AlSb/GaSb superlattices.     

Weak measurements as an instance of non-ideal measurements

We introduce weak measurements (WM) as a type of non-ideal measurement (NIM) coupling the system and the measuring device in a specific manner involving a weak interaction followed by post-selection. For the particular case of a WM measurement of spin, we solve the quantum dynamics for the coupled system-meter ensemble exactly for any type of non-ideal measurement. The standard WM regime is obtained as a limiting case; eccentric ??semi-weak?? values not only appear in other cases of NIM, but can also have a larger magnitude than the usual weak values. A couple of examples comparing the merits of the WM regime and of the exact treatment in situations of potential interest to quantum information applications are considered.     

Monotonic convergent optimal control theory with strict limitations on the spectrum of optimized laser fields

We present a modified optimal control scheme based on the Krotov method, which allows for strict limitations on the spectrum of the optimized laser fields. A frequency constraint is introduced and derived mathematically correct, without losing monotonic convergence of the algorithm. The method guarantees a close link to learning loop control experiments and is demonstrated for the challenging control of nonresonant Raman transitions, which are used to implement a set of global quantum gates for molecular vibrational qubits.     

The Large Hadron Collider: A Marvel of Technology,edited by Lyndon Evans

Machine learning algorithms learn a desired input-output relation from examples in order to interpret new inputs. This is important for tasks such as image and speech recognition or strategy optimisation, with growing applications in the IT industry. In the last couple of years, researchers investigated if quantum computing can help to improve classical machine learning algorithms. Ideas range from running computationally costly algorithms or their subroutines efficiently on a quantum computer to the translation of stochastic methods into the language of quantum theory. This contribution gives a systematic overview of the emerging field of quantum machine learning. It presents the approaches as well as technical details in an accessible way, and discusses the potential of a future theory of quantum learning.     

Investigation of Commuting Hamiltonian in Quantum Markov Network

Graphical Models have various applications in science and engineering which include physics, bioinformatics, telecommunication and etc. Usage of graphical models needs complex computations in order to evaluation of marginal functions, so there are some powerful methods including mean field approximation, belief propagation algorithm and etc. Quantum graphical models have been recently developed in context of quantum information and computation, and quantum statistical physics, which is possible by generalization of classical probability theory to quantum theory. The main goal of this paper is preparing a primary generalization of Markov network, as a type of graphical models, to quantum case and applying in quantum statistical physics. We have investigated the Markov network and the role of commuting Hamiltonian terms in conditional independence with simple examples of quantum statistical physics.     

基于保真度的量子信令最佳帧长算法

为了解决量子信令的最佳帧长问题,本文提出了一种基于保真度的量子信令最佳帧长的算法.根据量子信令收发模型,定义了一个由若干量子态组成的量子信令的联合保真度,并通过计算链路的有效利用率而得出最佳帧长的算法.仿真结果与理论分析完全相符,从而表明本文提出的最佳帧长算法稳定、易行,可以应用到复杂多变的实际环境中.