Advancements in quantum image filtering:Exponential speedup on a subset of images

The pursuit of quantum supremacy in computational tasks has driven the exploration of quantum algorithms capable of surpassing classical counterparts.In the realm of image processing,a notable advancement towards this objective is highlighted in the study by Cui et al.[1].Their work proposes a quantum image filtering(QImF)algorithm that exhibits exponential acceleration for a specific subset of images,offering a glimpse into the potential of quantum computing in image processing.

Characterization of Exact One-Query Quantum Algorithms for Partial Boolean Functions

The query model(or black-box model)has attracted much attention from the communities of both classical and quantum computing.Usually,quantum advantages are revealed by presenting a quantum algorithm that has a better query complexity than its classical counterpart.In the history of quantum algorithms,the Deutsch algorithm and the Deutsch-Jozsa algorithm play a fundamental role and both are exact one-query quantum algorithms.This leads us to con-sider the problem:what functions can be computed by exact one-query quantum algorithms?This problem has been ad-dressed in the literature for total Boolean functions and symmetric partial Boolean functions,but is still open for general partial Boolean functions.Thus,in this paper,we continue to characterize the computational power of exact one-query quantum algorithms for general partial Boolean functions.First,we present several necessary and sufficient conditions for a partial Boolean function to be computed by exact one-query quantum algorithms.Second,inspired by these conditions,we discover some new representative functions that can be computed by exact one-query quantum algorithms but have an essential difference from the already known ones.Specially,it is worth pointing out that before our work,the known func-tions that can be computed by exact one-query quantum algorithms are all symmetric functions and the quantum algo-rithm used is essentially the Deutsch-Jozsa algorithm,whereas the functions discovered in this paper are generally asym-metric and new algorithms to compute these functions are required.Thus,this expands the class of functions that can be computed by exact one-query quantum algorithms.

Quantum speedup and limitations on matroid property problems

Matroid theory has been developed to be a mature branch of mathematics and has extensive applications in combinatorial optimization,algorithm design and so on.On the other hand,quantum computing has attracted much attention and has been shown to surpass classical computing on solving some computational problems.Surprisingly,crossover studies of the two fields seem to be missing in the literature.This paper initiates the study of quantum algorithms for matroid property problems.It is shown that quadratic quantum speedup is possible for the calculation problem of finding the girth or the number of circuits(bases,flats,hyperplanes)of a matroid,and for the decision problem of deciding whether a matroid is uniform or Eulerian,by giving a uniform lower boundΩ■on the query complexity of all these problems.On the other hand,for the uniform matroid decision problem,an asymptotically optimal quantum algorithm is proposed which achieves the lower bound,and for the girth problem,an almost optimal quantum algorithm is given with query complexityO■.In addition,for the paving matroid decision problem,a lower boundΩ■on the query complexity is obtained,and an O■ quantum algorithm is presented.

Free-space optical neural network based on thermal atomic nonlinearity

As artificial neural networks(ANNs)continue to make strides in wide-ranging and diverse fields of technology,the search for more efficient hardware implementations beyond conventional electronics is gaining traction.In particular,optical implementations potentially offer extraordinary gains in terms of speed and reduced energy consumption due to the intrinsic parallelism of free-space optics.At the same time,a physical nonlinearity—a crucial ingredient of an ANN—is not easy to realize in free-space optics,which restricts the potential of this platform.This problem is further exacerbated by the need to also perform the nonlinear activation in parallel for each data point to preserve the benefit of linear free-space optics.Here,we present a free-space optical ANN with diffraction-based linear weight summation and nonlinear activation enabled by the saturable absorption of thermal atoms.We demonstrate,via both simulation and experiment,image classification of handwritten digits using only a single layer and observed 6% improvement in classification accuracy due to the optical nonlinearity compared to a linear model.Our platform preserves the massive parallelism of free-space optics even with physical nonlinearity,and thus opens the way for novel designs and wider deployment of optical ANNs.

Distributed exact Grover’s algorithm

Distributed quantum computation has gained extensive attention.In this paper,we consider a search problem that includes only one target item in the unordered database.After that,we propose a distributed exact Grover’s algorithm(DEGA),which decomposes the original search problem into■n/2■parts.Specifically,(i)our algorithm is as exact as the modified version of Grover’s algorithm by Long,which means the theoretical probability of finding the objective state is 100%;(ii)the actual depth of our circuit is 8(n mod 2)+9,which is less than the circuit depths of the original and modified Grover’s algorithms,1+8■π/4√2^(n)■and 9+8■π/4√2^(n)-1/2■,respectively.It only depends on the parity of n,and it is not deepened as n increases;(iii)we provide particular situations of the DEGA on MindQuantum(a quantum software)to demonstrate the practicality and validity of our method.Since our circuit is shallower,it will be more resistant to the depolarization channel noise.