quantum set intersection and its application to associative memory we describe a quantum algorithm for computing the intersection of two sets and its application to associative memory the algorithm is based on a modification of grover s quantum search algorithm grover 1996 we present algorithms for pattern retrieval pattern completion and pattern correction we show that the quantum associative memory can store an exponential number of memories and retrieve them in sub exponential time we prove that this model has advantages over known classical associative memories as well as previously proposed quantum models

trading quantum for classical resources in quantum data compression we study the visible compression of a source script e phii pi of pure quantum signal states or more formally the minimal resources per signal required to represent arbitrarily long strings of signals with arbitrarily high fidelity when the compressor is given the identity of the input state sequence as classical information according to the quantum source coding theorem the optimal quantum rate is the von neumann entropy s script e qubits per signal we develop a refinement of this theorem in order to analyze the situation in which the states are coded into classical and quantum bits that are quantified separately this leads to a trade off curve q r where q r qubits per signal is the optimal quantum rate for a given classical rate of r bits per signal our main result is an explicit characterization of this trade off function by a simple formula in terms of only single signal perfect fidelity encodings of the source we give a thorough discussion of many further mathematical properties of our formula including an analysis of its behavior for group covariant sources and a generalization to sources with continuously parametrized states we also show that our result leads to a number of corollaries characterizing the trade off between information gain and state disturbance for quantum sources in addition we indicate how our techniques also provide a solution to the so called remote state preparation problem finally we develop a probability free version of our main result which may be interpreted as an answer to the question how many classical bits does a qubit cost this theorem provides a type of dual to holevo s theorem insofar as the latter characterizes the cost of coding classical bits into qubits

computation in finitary stochastic and quantum processes abstract we introduce stochastic and quantum finite state transducers as computation theoretic models of classical stochastic and quantum finitary processes formal process languages representing the distribution over a process behaviors are recognized and generated by suitable specializations we characterize and compare deterministic and nondeterministic versions summarizing their relative computational power in a hierarchy of finitary process languages quantum finite state transducers and generators are a first step toward a computation theoretic analysis of individual repeatedly measured quantum dynamical systems they are explored via several physical systems including an iterated beam splitter an atom in a magnetic field and atoms in an ion trap a special case of which implements the deutsch quantum algorithm we show that these systems behaviors and so their information processing capacity depends sensitively on the measurement protocol

a quantum computing primer for operator theorists this is an exposition of some of the aspects of quantum computation and quantum information that have connections with operator theory after a brief introduction we discuss quantum algorithms we outline basic properties of quantum channels or equivalently completely positive trace preserving maps the main theorems for quantum error detection and correction are presented and we conclude with a description of a particular passive method of quantum error correction

continuous time quantum algorithms for unstructured problems we consider a family of unstructured optimization problems for which we propose a method for constructing analogue continuous time not necessarily adiabatic quantum algorithms that are faster than their classical counterparts in this family of problems which we refer to as scrambled input problems one has to find a minimum cost configuration of a given integer valued n bit black box function whose input values have been scrambled in some unknown way special cases within this set of problems are grover s search problem of finding a marked item in an unstructured database certain random energy models and the functions of the deutsch josza problem we consider a couple of examples in detail in the first we provide an o 1 deterministic analogue quantum algorithm to solve the seminal problem of deutsch and josza in which one has to determine whether an n bit boolean function is constant gives 0 on all inputs or 1 on all inputs or balanced returns 0 on half the input states and 1 on the other half we also study one variant of the random energy model and show that as one might expect its minimum energy configuration can be found quadratically faster with a quantum adiabatic algorithm than with classical algorithms

tensor norms and the classical communication complexity of nonlocal quantum measurement we initiate the study of quantifying nonlocality of a bipartite measurement by the minimum amount of classical communication required to simulate the measurement we derive general upper bounds in terms of some tensor norms of the measurement operator as applications we show that a if the amount of communication is a constant then quantum and classical communication protocols with an unlimited amount of shared entanglement or shared randomness compute the same class of functions and b it requires only a constant amount of communication to classically generate an approximation of the output distribution resulting from local measurements on an entangled quantum state as long as the number of measurement outcomes is a constant

partial correlations in multipartite quantum systems abstract quantum correlations are more general than entanglement a problem on how to characterize and quantify quantum correlations has attracted substantial attention quantum correlations in bipartite systems have been researched extensively in this paper partial correlations in a multipartite quantum system a 1 a 2 a n are discussed in detail in order to reveal correlations of a given state with respect to some subsystems for a nonempty subset of the index set 1 2 n classical correlations cc quantum correlations qc partially classical correlations pcc and genuinely quantum correlations gqc are introduced in a multipartite system subsequently characterizations of cc are obtained secondly a measure function g of partial correlations of a state is defined and called the quantum discord it is proved that g is nonnegative independent of the choice of basis and invariant under local unitary transformations it is also proved that a state is cc if and only if g 0 and then it is qc if and only if g 0 moreover some relationships among partial correlations with respect to different are discussed in light of the measure function finally an illustrative example with 6 qubit ghz state is given

elementary gates for cartoon computation the basic one bit gates x y z hadamard phase 8 as well as the controlled cnot and toffoli gates are reformulated in the language of geometric algebra quantum like computation thus all the quantum algorithms can be reformulated in purely geometric terms without any need of tensor products

quasiclassical computation abstract the chemical kinetic description of time evolution where the phase is random but the states are discrete is discussed as a basis for a computational approach this proposed scheme uses numbers in the entire range of 0 to 1 to represent boolean propositions in the implementation by chemical kinetics these numbers are the mole fractions of different species vibrational relaxation in a mixture of hcl and dci is the physical system that is used to illustrate the approach energy exchange in such a mixture corresponds to two strongly coupled two level systems a search problem previously discussed in the quantum computing literature is solved as an example the solution requires the same number of function evaluations as in the quantal case the action of the oracle is described in detail

from quantum cellular automata to quantum lattice gases a natural architecture for nanoscale quantum computation is that of a quantum cellular automaton motivated by this observation we begin an investigation of exactly unitary cellular automata after proving that there can be no nontrivial homogeneous local unitary scalar cellular automaton in one dimension we weaken the homogeneity condition and show that there are nontrivial exactly unitary partitioning cellular automata we find a one parameter family of evolution rules which are best interpreted as those for a one particle quantum automaton this model is naturally reformulated as a two component cellular automaton which we demonstrate to limit to the dirac equation we describe two generalizations of this automaton the second of which to multiple interacting particles is the correct definition of a quantum lattice gas

novel quantum image encryption using one dimensional quantum cellular automata we investigate the application of quantum cellular automata in image encryption and propose a novel quantum gray scale image encryption algorithm based on one dimensional quantum cellular automata the quantum image encryption algorithm can be realized by subtly constructing the evolution rules of one dimensional quantum cellular automata because all quantum operations are invertible the quantum image decryption algorithm is the inverse of the encryption algorithm the proposed quantum image encryption algorithm has an algorithm complexity of n lower than the algorithm complexity n2 of existing quantum image encryption schemes based on quantum fourier transform supported by detailed numerical simulation and theoretical analysis our proposal has outperformed its classical counterpart and other image encryption schemes in terms of the security computational complexity and robustness and it also provides a clue of introducing quantum cellular automata into image encryption

fault tolerant quantum computation with constant error rate this paper shows that quantum computation can be made fault tolerant against errors and inaccuracies when eta the probability for an error in a qubit or a gate is smaller than a constant threshold eta c this result improves on shor s result proceedings of the 37th symposium on the foundations of computer science ieee los alamitos ca 1996 pp 56 65 which shows how to perform fault tolerant quantum computation when the error rate eta decays polylogarithmically with the size of the computation an assumption which is physically unreasonable the cost of making the quantum circuit fault tolerant in our construction is polylogarithmic in time and space our result holds for a very general local noise model which includes probabilistic errors decoherence amplitude damping depolarization and systematic inaccuracies in the gates moreover we allow exponentially decaying correlations between the errors both in space and in time fault tolerant computation can be performed with any universal set of gates the result also holds for quantum particles with p 2 states namely p qudits and is also generalized to one dimensional quantum computers with only nearest neighbor interactions no measurements or classical operations are required during the quantum computation we estimate the threshold of our construction to be eta c simeq 10 6 in the best case by this we show that local noise is in principle not an obstacle for scalable quantum computation the main ingredient of our proof is the computation on states encoded by a quantum error correcting code qecc to this end we introduce a special class of calderbank shor steane css codes called polynomial codes the quantum analogue of reed solomon codes their nice algebraic structure allows all of the encoded gates to be transversal we also provide another version of the proof which uses more general css codes but its encoded gates are slightly less elegant to achieve fault tolerance we encode the quantum circuit by another circuit by using one of these qeccs this step is repeated polyloglog many times each step slightly improving the effective error rate to achieve the desired reliability the resulting circuit exhibits a hierarchical structure and for the analysis of its robustness we borrow terminology from khalfin and tsirelson found phys 22 1992 pp 879 948 and gacs advances in computing research a research annual randomness and computation jai press greenwich ct 1989 the paper is to a large extent self contained in particular we provide simpler proofs for many of the known results we use such as the fact that it suffices to correct for bit flips and phase flips the correctness of css codes and the fact that two qubit gates are universal together with their extensions to higher dimensional particles we also provide full proofs of the universality of the sets of gates we use the proof of universality was missing in shor s paper this paper thus provides a self contained and complete proof of universal fault tolerant quantum computation in the presence of local noise

a chaos based symmetric image encryption scheme using a bit level permutation in recent years a variety of chaos based digital image encryption algorithms have been suggested most of these algorithms implement permutations and diffusions at the pixel level by considering the pixel as the smallest atomic element of an image in fact a permutation at the bit level not only changes the position of the pixel but also alters its value here we propose an image cryptosystem employing the arnold cat map for bit level permutation and the logistic map for diffusion simulations have been carried out and analyzed in detail demonstrating the superior security and high efficiency of our cryptosystem

eliminating the texture features in visually meaningful cipher images generally most image encryption algorithms transform original images into texture like or noise like ones unfortunately the feature like texture or noise is just a hint of the existence of encryption for attackers to solve this problem bao et al inf sci 324 2015 197 207 proposed a new image encryption algorithm which can transform original images into visually meaningful ones however the resulting cipher images have some texture features which may be a hint of the existence of encryption to some extent to overcome this flaw we present a new visually meaningful image encryption algorithm based on discrete wavelet transform and discrete quantum walks numerical simulation security analysis and performance comparison demonstrate that our proposal is superior to bao et al s scheme it promotes the combination of image encryption and quantum computation

multipartite nonlocality as a resource and quantum correlations having indefinite causal order the characterization of quantum correlations in terms of information theoretic resource has been a fruitful approach to understand the power of quantum correlations as a resource while bipartite entanglement and bell inequality violation in this setting have been extensively studied relatively little is known about their multipartite counterpart in this paper we apply and adapt the recently proposed definitions of multipartite nonlocality bancal et al 2013 phys rev a 88 014102 to the three and four partite scenarios to gain new insight on the resource aspect of multipartite nonlocal quantum correlations specifically we show that reproducing certain tripartite quantum correlations requires mixtures of classical resources be it the ability to change the groupings or the time orderings of measurements thus when seen from the perspective of biseparable one way classical signaling resources certain tripartite quantum correlations do not admit a definite causal order in the four partite scenario we obtain a superset description of the set of biseparable correlations which can be produced by allowing two groups of bipartite non signaling resources quantum violation of the resulting bell like inequalities is investigated as a byproduct we obtain some new examples of device independent witnesses for genuine four partite entanglement and also device independent witnesses that allow one to infer the structure of the underlying multipartite entanglement this article is part of a special issue of journal of physics a mathematical and theoretical devoted to 50 years of bell s theorem

quantum entanglement and the communication complexity of the inner product function we consider the communication complexity of the binary inner product function in a variation of the two party scenario where the parties have an a priori supply of particles in an entangled quantum state we prove linear lower bounds for both exact protocols as well as for protocols that determine the answer with bounded error probability our proofs employ a novel kind of quantum reduction from a quantum information theory problem to the problem of computing the inner product the communication required for the former problem can then be bounded by an application of holevo s theorem we also give a specific example of a probabilistic scenario where entanglement reduces the communication complexity of the inner product function by one bit

on the distributional complexity of disjointness we prove that the distributional communication complexity of the predicate disjointness with respect to a very simple measure on inputs is n

quantum communication complexity advantage implies violation of a bell inequality we obtain a general connection between a large quantum advantage in communication complexity and bell nonlocality we show that given any protocol offering a sufficiently large quantum advantage in communication complexity there exists a way of obtaining measurement statistics that violate some bell inequality our main tool is port based teleportation if the gap between quantum and classical communication complexity can grow arbitrarily large the ratio of the quantum value to the classical value of the bell quantity becomes unbounded with the increase in the number of inputs and outputs

smoothing low snr molecular images via anisotropic median diffusion we propose a new anisotropic diffusion filter for denoising low signal to noise molecular images this filter which incorporates a median filter into the diffusion steps is called an anisotropic median diffusion filter this hybrid filter achieved much better noise suppression with minimum edge blurring compared with the original anisotropic diffusion filter when it was tested on an image created based on a molecular image model the universal quality index proposed in this paper to measure the effectiveness of denoising suggests that the anisotropic median diffusion filter can retain adherence to the original image intensities and contrasts better than other filters in addition the performance of the filter is less sensitive to the selection of the image gradient threshold during diffusion thus making automatic image denoising easier than with the original anisotropic diffusion filter the anisotropic median diffusion filter also achieved good denoising results on a piecewise smooth natural image and real raman molecular images

segmentation of natural images using anisotropic diffusion and linking of boundary edges we present a segmentation method of natural images that uses an anisotropic diffusion algorithm and a region growing algorithm we propose a modified version of the anisotropic diffusion algorithm as a precise edge preserving smoothing technique modified by using boundary edges we incorporate a linking algorithm for boundary edges based on a directional potential function into the anisotropic diffusion algorithm to improve the ability of edge preserving smoothing as a result unnecessary details of images are effectively smoothed before performing a region growing algorithm therefore the proposed method is suitable for an accurate segmentation of natural images several simulated examples are presented that demonstrate the effectiveness of the proposed technique

quantum query as a state decomposition abstract the quantum query model is a framework that allows us to express most known quantum algorithms algorithms represented by this model consist of a set of unitary operators acting over a finite hilbert space and a final measurement step consisting of a set of projectors in this work we prove that the application of these unitary operators before the measurement step is equivalent to decomposing a unit vector into a sum of vectors and then inverting some of their relative phases we also prove that the vectors of that sum must fulfill a list of properties and we call such vectors a block set if we define the measurement step for the block set formulation similarly to the quantum query model then we prove that both formulations give the same gram matrix of output states although the block set formulation allows a much more explicit form therefore the block set reformulation of the quantum query model gives us an alternative interpretation of how quantum algorithms work finally we apply our approach to the analysis and complexity of quantum exact algorithms

an infinite pebble game and applications we generalize the pebble game to infinite directed acyclic graphs and use this generalization to give new and shorter proofs of the following well known results 1 that unbounded memory increases the power of logics of programs and 2 that there exists a context free grammar with infinite index

quantum computing without entanglement it is generally believed that entanglement is essential for quantum computing we present here a few simple examples in which quantum computing without entanglement is better than anything classically achievable in terms of the reliability of the outcome after a fixed number of oracle calls using a separable that is unentangled state we show that the deutsch jozsa problem and the simon problem can be solved more reliably by a quantum computer than by the best possible classical algorithm even probabilistic we conclude that a entanglement is not essential for quantum computing and b some advantage of quantum algorithms over classical algorithms persists even when the quantum state contains an arbitrarily small amount of information that is even when the state is arbitrarily close to being totally mixed

splitting information securely with entanglement although many quantum security tools have been proposed many of them are quantum secret key distribution protocols however we naturally wish to construct quantum cryptosystems different from the conventional cryptosystems in this paper first we show simple methods with prior entanglement in order to split a party s message among some parties securely moreover as an application we also show that by using our splitting methods we can construct not only quantum secret key distribution protocols but also quantum cryptosystems some of our quantum cryptosystems are different from the conventional cryptosystems because they are executed interactively

on the power of non local boxes a non local box is a virtual device that has the following property given that alice inputs a bit at her end of the device and that bob does likewise it produces two bits one at alice s end and one at bob s end such that the xor of the outputs is equal to the and of the inputs this box inspired from the chsh inequality was first proposed by popescu and rohrlich to examine the question given that a maximally entangled pair of qubits is non local why is it not maximally non local we believe that understanding the power of this box will yield insight into the non locality of quantum mechanics it was shown recently by cerf gisin massar and popescu that this imaginary device is able to simulate correlations from any measurement on a singlet state here we show that the non local box can in fact do much more through the simulation of the magic square pseudo telepathy game and the mermin ghz pseudo telepathy game we show that the non local box can simulate quantum correlations that no entangled pair of qubits can in a bipartite scenario and even in a multi party scenario finally we show that a single non local box cannot simulate all quantum correlations and propose a generalization for a multi party non local box in particular we show quantum correlations whose simulation requires an exponential amount of non local boxes in the number of maximally entangled qubit pairs

period adding bifurcation in a logistic map with memory we introduce a single step memory dependence in the fully chaotic logistic map this makes it a two dimensional system in general however we show that by using composite functions to define two one dimensional maps it is possible to obtain some analytic results for the bifurcation structure numerical results support the calculated bifurcation scheme and in addition yield a further insight which allows the calculation of the convergence ratio for a new period adding scenario

functions computable in polynomial space consider nondeterministic polynomial time turing machine that on input x outputs a 3 3 matrix with entries from 1 0 1 on each of its paths define the function f where f x is the upper left entry in the product of all these matrices in an order of the paths to be made precise below we show that the class of functions f computable as just described is exactly the class fpspace of integer valued functions computable by polynomial space turing machines along the way we obtain characterizations of fpspace in terms of arithmetic circuits and straight line programs

strengths and weaknesses of quantum computing recently a great deal of attention has been focused on quantum computation following a sequence of results bernstein and vazirani in proc 25th annual acm symposium theory comput 1993 pp 11 20 siam j comput 26 1997 pp 1277 1339 simon in proc 35th annual ieee symposium foundations comput sci 1994 pp 116 123 siam j comput 26 1997 pp 1340 1349 shor in proc 35th annual ieee symposium foundations comput sci 1994 pp 124 134 suggesting that quantum computers are more powerful than classical probabilistic computers following shor s result that factoring and the extraction of discrete logarithms are both solvable in quantum polynomial time it is natural to ask whether all of np can be efficiently solved in quantum polynomial time in this paper we address this question by proving that relative to an oracle chosen uniformly at random with probability 1 the class np cannot be solved on a quantum turing machine qtm in time o 2 n 2 we also show that relative to a permutation oracle chosen uniformly at random with probability 1 the class np cap conp cannot be solved on a qtm in time o 2 n 3 the former bound is tight since recent work of grover in it proc 28 th annual acm symposium theory comput 1996 shows how to accept the class np relative to any oracle on a quantum computer in time o 2 n 2

counting by quantum eigenvalue estimation for every computation there corresponds the physical task of manipulating a starting state into an output state with a desired property as the classical theory of physics has been replaced by quantum physics it is interesting to consider the capabilities of a computer that can exploit the distinctive quantum features of nature the extra capabilities seem enormous for example with only an expected o square rootn evaluations of a function f 0 1 n 1 0 1 we can find a solution to f x 1 provided one exists another example is the ability to 1nd efficiently the order of an element g in a group by using a quantum computer to estimate a random eigenvalue of the unitary operator that multiplies by g in the group by using this eigenvalue estimation algorithm to estimate an eigenvalue of the unitary operator used in quantum searching we can approximately count the number of solutions to f x 1 this paper describes this eigenvector approach to quantum counting and related algorithms

quantum cryptographic algorithm for color images using quantum fourier transform and double random phase encoding abstract a novel encryption decryption method for color images is proposed in which quantum fourier transform qft and double random phase encoding drpe techniques have been used the encryption process can be realized by performing two secret random phase encoding operations respectively in the input and the qft planes because all quantum operations are invertible the decryption process is the inverse of the encryption process supported by detailed numerical simulation and theoretical analysis the method has clarified its robustness security and computational complexity over its classical counterpart and it opens the door for introducing color image encryption into quantum scenarios

cartoon computation quantum like computing without quantum mechanics we present a computational framework based on geometric structures no quantum mechanics is involved and yet the algorithms perform tasks analogous to quantum computation tensor products and entangled states are not needed they are replaced by sets of basic shapes to test the formalism we solve in geometric terms the deutsch jozsa problem historically the first example that demonstrated the potential power of quantum computation each step of the algorithm has a clear geometric interpretation and allows for a cartoon representation

characterizing classes of functions computable by quantum parallelism computation by quantum parallelism involves associating a quantum state v f to each function f z m z n v f is formed from superpositions of states labelled by the values of f the standard choice being an equally weighted superposition of all the values of f a joint property g f of the values f 0 f m 1 is called computable by quantum parallelism qpc if there is an observable g which will reveal the value g f with non zero probability when applied to v f and will never show a false value it is shown that the problem of deciding which g s are qpc can be formulated entirely in terms of the linear relations which exist among the v f s in the case of f z m z 2 g z 2 m z 2 we explicitly describe all properties which are qpc and show that this includes only m 2 m 2 of the 2 2 m such properties by using a suitable nonstandard definition for v f this number can be increased to 2 2 m 2 m 1 for m 1

matchgates and classical simulation of quantum circuits let g a b denote the two qubit gate that acts as the one qubit su 2 gates a and b in the even and odd parity subspaces respectively of two qubits using a clifford algebra formalism we show th

on the power of ambainis lower bounds the polynomial method and the ambainis lower bound or alb for short method are two main quantum lower bound techniques while recently ambainis showed that the polynomial method is not tight the present paper aims at studying the power and limitation of alb s we first use known alb s to derive n1 5 lower bounds for bipartiteness bipartiteness matching and graph matching in which the lower bound for bipartiteness improves the previous n one we then show that all the three known ambainis lower bounds have a limitation n min c0 f c1 f where c0 f and c1 f are the 0 and 1 certificate complexities respectively this implies that for many problems such as triangle k clique bipartiteness and bipartite graph matching which draw wide interest and whose quantum query complexities are still open the best known lower bounds cannot be further improved by using ambainis techniques another consequence is that all the ambainis lower bounds are not tight for total functions this upper bound for alb s can be further improved to min c0 f c1 f n ci f where ci f is the size of max intersection of a 0 and a 1 certificate set again this implies that alb s cannot improve the best known lower bound for some specific problems such as and or tree whose precise quantum query complexity is still open finally we generalize the three known alb s and give a new alb style lower bound method which may be easier to use for some problems

criterion for slocc equivalence of multipartite quantum states we study the stochastic local operation and classical communication slocc equivalence for arbitrary dimensional multipartite quantum states for multipartite pure states we present a necessary and sufficient criterion in terms of their coefficient matrices this condition can be used to classify some slocc equivalent quantum states with coefficient matrices having the same rank for multipartite mixed state we provide a necessary and sufficient condition by means of the realignment of matrix some detailed examples are given to identify the slocc equivalence of multipartite quantum states

determining acceptance possibility for a quantum computation is hard for the polynomial hierarchy abstract it is shown that determining whether a quantum computation has a non zero probability of accepting is at least as hard as the polynomial time hierarchy this hardness result also applies to determining in general whether a given quantum basis state appears with nonzero amplitude in a superposition or whether a given quantum bit has positive expectation value at the end of a quantum computation this result is achieved by showing that the complexity class nqp of adleman demarrais and huang a quantum analog of np is equal to the counting class co c equals p

unbounded violation of tripartite bell inequalities we prove that there are tripartite quantum states constructed from random unitaries that can lead to arbitrarily large violations of bell inequalities for dichotomic observables as a consequence these states can withstand an arbitrary amount of white noise before they admit a description within a local hidden variable model this is in sharp contrast with the bipartite case where all violations are bounded by grothendieck s constant we will discuss the possibility of determining the hilbert space dimension from the obtained violation and comment on implications for communication complexity theory moreover we show that the violation obtained from generalized greenberger horne zeilinger ghz states is always bounded so that in contrast to many other contexts ghz states do not lead to extremal quantum correlations in this case in order to derive all these physical consequences we will have to obtain new mathematical results in the theories of operator spaces and tensor norms in particular we will prove the existence of bounded but not completely bounded trilinear forms from commutative c algebras finally we will relate the existence of diagonal states leading to unbounded violations with a long standing open problem in the context of banach algebras

universality in quantum computation we show that in quantum computation almost every gate that operates on two or more bits is a universal gate we discuss various physical considerations bearing on the proper definition of universality for computational components such as logic gates

quantum algorithms for finding constant sized sub hypergraphs we develop a general framework to construct quantum algorithms that detect if a 3 uniform hypergraph given as input contains a sub hypergraph isomorphic to a prespecified constant sized hypergraph this framework is based on the concept of nested quantum walks recently proposed by jeffery kothari and magniez 2013 12 and extends the methodology designed by lee magniez and santha 2013 18 for similar problems over graphs as applications we obtain a quantum algorithm for finding a 4 clique in a 3 uniform hypergraph on n vertices with query complexity o n1 883 and a quantum algorithm for determining if a ternary operator over a set of size n is associative with query complexity o n2 113

exact quantum algorithm to distinguish boolean functions of different weights in this work we exploit the grover operator for the weight analysis of a boolean function specifically to solve the weight decision problem the weight w is the fraction of all possible inputs for which the output is 1 the goal of the weight decision problem is to find the exact weight w from the given two weights w1 and w2 satisfying a general weight condition as w1 w2 1 and 0 w 1 w 2 1 first we propose a limited weightdecision algorithm where the function has another constraint a weight is in w1 sin 2 k

de quantisation of the quantum fourier transform the quantum fourier transform qft plays an important role in many known quantum algorithms such as shor s algorithm for prime factorisation in this paper we show that the qft algorithm can on a restricted set of input states be de quantised into a classical algorithm which is both more efficient and simpler than the quantum algorithm by working directly with the algorithm instead of the circuit we develop a simple classical version of the quantum basis state algorithm we formulate conditions for a separable state to remain separable after the qft is performed and use these conditions to extend the de quantised algorithm to work on all such states without loss of efficiency our technique highlights the linearity of quantum mechanics as the fundamental feature accounting for the difference between quantum and de quantised algorithms and that it is this linearity which makes the qft such a useful tool in quantum computation

quantum communication and complexity in the setting of communication complexity two distributed parties want to compute a function depending on both their inputs using as little communication as possible the required communication can sometimes be significantly lowered if we allow the parties the use of quantum communication we survey the main results of the young area of quantum communication complexity its relation to teleportation and dense coding the main examples of fast quantum communication protocols lower bounds and some applications

multi image encryption by circular random grids visual secret sharing vss can encode a secret image into several share images where the original secret can be reconstructed and recognized by sight by stacking all share images there are two categories of vss schemes visual cryptography vc and random grids rg vc has three main drawbacks the large size the need for the codebook to be redesigned for specific applications and the ability to encode only one secret image at a time rg removes the first two drawbacks this paper proposes a novel rg based vss scheme that encodes multiple secret images at a time the scheme encrypts multiple secret images into two circular cipher grids and decrypts the images by stacking two circular cipher grids to obtain the first secret and gradually rotating one circular cipher grid at a fixed degree based on the quantity of the secret images encrypted to disclose other secrets compared with conventional vc based vss the proposed scheme has no pixel expansion a higher capacity for secret sharing and no need for a complex vc codebook to be redesigned theoretical analysis of visual quality and security is demonstrated

separations in query complexity based on pointer functions in 1986 saks and wigderson conjectured that the largest separation between deterministic and zero error randomized query complexity for a total boolean function is given by the function f on n 2k bits defined by a complete binary tree of nand gates of depth k which achieves r0 f o d f 0 7537 we show that this is false by giving an example of a total boolean function f on n bits whose deterministic query complexity is n while its zero error randomized query complexity is o n we further show that the quantum query complexity of the same function is o n1 4 giving the first example of a total function with a super quadratic gap between its quantum and deterministic query complexities we also construct a total boolean function g on n variables that has zero error randomized query complexity n log n and bounded error randomized query complexity r g o n this is the first super linear separation between these two complexity measures the exact quantum query complexity of the same function is qe g o n these functions show that the relations d f o r1 f 2 and r0 f o r f 2 are optimal up to polylogarithmic factors further variations of these functions give additional separations between other query complexity measures a cubic separation between q and r0 a 3 2 power separation between qe and r and a 4th power separation between approximate degree and bounded error randomized query complexity all of these examples are variants of a function recently introduced by goos pitassi and watson which they used to separate the unambiguous 1 certificate complexity from deterministic query complexity and to resolve the famous clique versus independent set problem in communication complexity

image encryption to protect image contents most existing encryption algorithms are designed to transform an original image into a texture like or noise like image which is however an obvious visual sign indicating the presence of an encrypted image and thus results in a significantly large number of attacks to address this problem this paper proposes a new image encryption concept to transform an original image into a visually meaningful encrypted one as an example of the implementation of this concept we introduce an image encryption system simulation results and security analysis demonstrate excellent encryption performance of the proposed concept and system

quantification of entanglement by means of convergent iterations the relative entropy of entanglement of a given bipartite quantum state is calculated by means of a convergent iterative algorithm when this state turns out to be nonseparable the algorithm also provides the corresponding optimal entanglement witness measurement

quantum weakly nondeterministic communication complexity in this paper we study a weak version of quantum nondeterministic communication complexity in which a classical proof has to be checked with probability one by a quantum protocol we prove that in the framework of communication complexity even this weak version of quantum nondeterminism is strictly stronger than classical nondeterminism more precisely we show a separation for a total function of quantum weakly nondeterministic and classical nondeterministic communication complexity this separation is quadratic and shows that classical proofs can be checked more efficiently by quantum protocols than by classical ones

quantum algorithms and the fourier transform the quantum algorithms of deutsch simon and shor are described in a way which highlights their dependence on the fourier transform the general construction of the fourier transform on an abelian group is outlined and this provides a unified way of understanding the efficacy of the algorithms finally we describe an efficient quantum factoring algorithm based on a general formalism of kitaev and contrast its structure to the ingredients of shor9 algorithm

computing algebraic formulas using a constant number of registers it is shown that over an arbitrary ring the functions computed by polynomial size algebraic formulas are also computed by polynomial length algebraic straight line programs that use only three registers this was previously known for boolean formulas d a barrington j comput system sci 38 1989 pp 150 164 which are equivalent to algebraic formulas over the ring gf 2 for formulas over arbitrary rings the result is an improvement over previous methods that require the number of registers to be logarithmic in the size of the formulas in order to obtain polynomial length straight line programs moreover the straight line programs that arise in these constructions have the property that they consist of statements whose actions on the registers are linear and bijective a consequence of this is that the problem of determining the iterated product of n3 times 3 matrices is complete under p projections for algebraic nc 1 also when the ring is gf 2 the programs that arise in the c

quantum associative memory abstract this paper combines quantum computation with classical neural network theory to produce a quantum computational learning algorithm quantum computation qc uses microscopic quantum level effects to perform computational tasks and has produced results that in some cases are exponentially faster than their classical counterparts the unique characteristics of quantum theory may also be used to create a quantum associative memory quam with a capacity exponential in the number of neurons this paper combines two quantum computational algorithms to produce such a quantum associative memory the result is an exponential increase in the capacity of the memory when compared to traditional associative memories such as the hopfield network the paper covers necessary high level quantum mechanical and quantum computational ideas and introduces a quam theoretical analysis proves the utility of the memory and it is noted that a small version should be physically realizable in the near future

comparison of unitary transforms we analyse the problem of comparing unitary transformations the task is to decide with minimal resources and maximal reliability whether two given unitary transformations are identical or different it is possible to make such comparisons without obtaining any information about the individual transformations different comparison strategies are presented and compared with respect to their efficiency with an interferometric setup it is possible to compare two unitary transforms using only one test particle another strategy makes use of a two particle singlet state this strategy is more efficient than using a non entangled two particle test state thus demonstrating the benefit of entanglement generalizations to higher dimensional transforms and to more than two transformations are made

quantum entanglement and communication complexity we consider a variation of the communication complexity scenario where the parties are supplied with an extra resource particles in an entangled quantum state we note that quantum nonlocality can be naturally expressed in the language of communication complexity these are communication complexity problems where the output is embodied in the correlations between the outputs of the individual parties without entanglement the parties must communicate to produce the required correlations whereas with entanglement no communication is necessary to produce the correlations in this sense nonlocality proofs can also be viewed as communication complexity problems where the presence of quantum entanglement reduces the amount of necessary communication we show how to transform examples of nonlocality into more traditional communication complexity problems where the output is explicitly determined by each individual party the resulting problems require communication with or without entanglement but the required communication is less when entanglement is available all these results are a noteworthy contrast to the well known fact that entanglement cannot be used to actually simulate or compress classical communication between remote parties

geometric transformations of multidimensional color images based on nass we present quantum algorithms to realize geometric transformations two point swappings symmetric flips local flips orthogonal rotations and translations based on an n qubit normal arbitrary superposition state nass these transformations are implemented using quantum circuits consisting of basic quantum gates which are constructed with polynomial numbers of single qubit and two qubit gates complexity analysis shows that the global operators symmetric flips local flips orthogonal rotations can be implemented with o n gates the proposed geometric transformations are used to facilitate applications of quantum images with low complexity

analogies and differences between quantum and stochastic automata abstract we analyze some features of the behaviour of quantum automata providing analogies and differences with the corresponding stochastic models in particular we prove there is a quantum automaton where the change of state depends on unitary transformations defined by matrices with nonnull amplitudes that accepts a non regular language with cut point zero and inverse error polynomially bounded stochastic automata with matrices having nonnull elements and with polynomial bounds on the inverse error recognize only regular languages the class of stochastic languages contains the class of quantum languages quantum languages are empty or contain an infinite number of words the class of quantum languages is not closed under complementation

hitting sets for roabp and sum of set multilinear circuits we give an n o log n time n is the input size blackbox polynomial identity testing algorithm for unknown order read once oblivious arithmetic branching programs roabps the best time complexity known for blackbox polynomial identity testing pit for this class was n o log 2 n due to forbes saptharishi and shpilka proceedings of the 2014 acm symposium on theory of computing 2014 pp 867 875 moreover their result holds only when the individual degree is small while we do not need any such assumption with this we match the time complexity for the unknown order roabp with the known order roabp due to forbes and shpilka proceedings of the 2013 ieee 54th annual symposium on foundations of computer science 2013 pp 243 252 and also with the depth 3 set multilinear circuits due to agrawal saha and saxena proceedings of the 2013 acm symposium on theory of computing 2013 pp 321 330 our proof is simpler and involves a new technique called basis isolation the depth 3

a universal two bit gate for quantum computation we prove the existence of a class of two input two output gates any one of which is universal for quantum computation this is done by explicitly constructing the three bit gate introduced by deutsch proc r soc lond a 425 73 1989 as a network consisting of replicas of a single two bit gate

rapid solution of problems by quantum computation a class of problems is described which can be solved more efficiently by quantum computation than by any classical or stochastic method the quantum computation solves the problem with certainty in exponentially less time than any classical deterministic computation

quantum walks for the determination of commutativity of finite dimensional algebras abstract quantum walks provide a framework for the construction of quantum algorithms based on this approach we consider different walks for testing the commutativity of a finite dimensional algebra in particular we consider szegedy s and santos quantum walks constructed from complete and torus graphs results of numerical experiments are presented showing that for some choices of the quantum walks we can obtain better detections probabilities than with previous quantum algorithms addressing this problem that were based on grover s quantum search additionally we introduce a general notion of quantum detection system that encompasses all the methods considered in this work among others and develop the concept of quantum hitting time for this kind of systems as an extension of szegedy s seminal ideas

scheme for cloning an unknown single qutrit state with assistance abstract we propose a scheme for cloning an unknown single qutrit state with assistance the scheme includes a qutrit state teleportation at the cloner s site during this process different states i e the maximally entangled or non maximally entangled two qutrit states as quantum channel are taken into account after the teleportation to help the cloner alice to reestablish the unknown state the state preparer victor should perform a single qutrit measurement and tell her the outcome in this scheme the success probability of cloning the original state is determined by the used quantum channel

family of bell like inequalities as device independent witnesses for entanglement depth we present a simple family of bell inequalities applicable to a scenario involving arbitrarily many parties each of which performs two binary outcome measurements we show that these inequalities are members of the complete set of full correlation bell inequalities discovered by werner wolf ifmmode dot z else z fi ukowski brukner for scenarios involving a small number of parties we further verify that these inequalities are facet defining for the convex set of bell local correlations moreover we show that the amount of quantum violation of these inequalities naturally manifests the extent to which the underlying system is genuinely many body entangled in other words our bell inequalities when supplemented with the appropriate quantum bounds naturally serve as device independent witnesses for entanglement depth allowing one to certify genuine k partite entanglement in an arbitrary n ensuremath ge k partite scenario without relying on any assumption about the measurements being performed or the dimension of the underlying physical system a brief comparison is made between our witnesses and those based on some other bell inequalities as well as quantum fisher information a family of witnesses for genuine k partite nonlocality applicable to an arbitrary n ensuremath ge k partite scenario based on our bell inequalities is also presented

compression unimpaired batch image encryption combining vector quantization and index compression as the network bandwidth has grown rapidly it has become common to share a large number of still images via the internet by means of batch transmission unfortunately most existing methods encrypt only a single image so there is room for improvement in our ability to send batches of images at one time a complete reconstruction of the methods is sometimes necessary especially when considering performance criteria this paper presents a novel batch image encryption algorithm that combines vector quantization vq and additional index compression process to benefit from their computational efficiency and low transmission bandwidth without affecting the original compression rate the experimental results show the performance of this new scheme in terms of compression rate and computational cost

revisiting deutsch jozsa algorithm abstract the deutsch jozsa algorithm is essentially faster than any possible deterministic classical algorithm for solving a promise problem that is in fact a symmetric partial boolean function named as the deutsch jozsa problem the deutsch jozsa problem can be equivalently described as a partial function d j n 0 0 1 n 0 1 defined as d j n 0 x 1 for x n 2 d j n 0 x 0 for x 0 n and it is undefined for the remaining cases where n is even and x is the hamming weight of x the deutsch jozsa algorithm needs only one query to compute d j n 0 but the classical deterministic algorithm requires n 2 1 queries to compute it in the worse case we present all symmetric partial boolean functions with degree 1 and 2 we prove the exact quantum query complexity of all symmetric partial boolean functions with degree 1 and 2 we prove deutsch jozsa algorithm can compute any symmetric partial boolean function f with exact quantum 1 query complexity

classical quantum and nonsignalling resources in bipartite games we study bipartite games that arise in the context of nonlocality with the help of graph theory our main results are alternate proofs that deciding whether a no communication classical winning strategy exists for certain games called forbidden edge and covering games is np complete while the problem of deciding if these games admit a nonsignalling winning strategy is in p we discuss relations between quantum winning strategies and orthogonality graphs we also show that every pseudotelepathy game yields both a proof of the bell kochen specker theorem and an instance of a two prover interactive proof system that is classically sound but that becomes unsound when provers use shared entanglement

geometric aspects of iterated matrix multiplication abstract this paper studies geometric properties of the iterated matrix multiplication polynomial and the hypersurface that it defines we focus on geometric aspects that may be relevant for complexity theory such as the symmetry group of the polynomial the dual variety and the jacobian loci of the hypersurface that are computed with the aid of representation theory of quivers

quantum theory the church turing principle and the universal quantum computer it is argued that underlying the church turing hypothesis there is an implicit physical assertion here this assertion is presented explicitly as a physical principle every finitely realizable physical system can be perfectly simulated by a universal model computing machine operating by finite means classical physics and the universal turing machine because the former is continuous and the latter discrete do not obey the principle at least in the strong form above a class of model computing machines that is the quantum generalization of the class of turing machines is described and it is shown that quantum theory and the universal quantum computer are compatible with the principle computing machines resembling the universal quantum computer could in principle be built and would have many remarkable properties not reproducible by any turing machine these do not include the computation of non recursive functions but they do include quantum parallelism a method by which certain probabilistic tasks can be performed faster by a universal quantum computer than by any classical restriction of it the intuitive explanation of these properties places an intolerable strain on all interpretations of quantum theory other than everett s some of the numerous connections between the quantum theory of computation and the rest of physics are explored quantum complexity theory allows a physically more reasonable definition of the complexity or knowledge in a physical system than does classical complexity theory

fast fourier transform using matrix decomposition to reduce both the multiplicative complexity and total number of operations this paper introduces a modeling scheme of the fast fourier transform fft to decompose the discrete fourier transform dft matrix recursively into a set of sparse matrices integrating three orthogonal transforms the hadamard modified haar and hybrid transforms the proposed scheme is able to obtain different fft representations with less computation operations than state of the arts to investigate the applications of the proposed fft scheme a multi stage image encryption algorithm is also introduced experimental results and security analysis are provided to show its encryption performance

resolving the forecasting problems of overshoot and volatility clustering using anfis coupling nonlinear heteroscedasticity with quantum tuning in this paper an approach to resolving two crucial problems of the overshoot and volatility clustering effects in time series forecast has been proposed in time series prediction big residuals round the turning point region of a data sequence due to the overshoot phenomenon volatility clustering effect suggests a time series with successive disturbances being serially dependent both effects degrade the efficiency and effectiveness of time series prediction and give rise to large residual errors to overcome the overshoot and volatility clustering problems an adaptive neuro fuzzy inference system anfis coupling a nonlinear generalized autoregressive conditional heteroscedasticity ngarch which is adapted by quantum minimization qm is introduced to resolve the drawbacks of the predicted outputs with big residuals around the inflection points of a data sequence and time varying conditional variance in residual errors besides the trial of two distinct quantum amplitude amplification qaa techniques called by qm is also considered to show their different computational complexity two experiments on the financial time series were taken and a performance evaluation was made between the proposed one and several well known alternative methods results show that our proposed method gains the best predictive accuracy to outperform the others goodness of fit of the proposed method was tested successfully by ljung box q test it followed that the proposed method in fact can reduce large residual errors significantly in time series forecast because the overshoot and volatility clustering effects are simultaneously regulated to the trivial levels

bounds on the power of proofs and advice in general physical theories quantum theory presents us with the tools for computational and communication advantages over classical theory one approach to uncovering the source of these advantages is to determine how computation and communication power vary as quantum theory is replaced by other operationally defined theories from a broad framework of such theories such investigations may reveal some of the key physical features required for powerful computation and communication in this paper we investigate how simple physical principles bound the power of two different computational paradigms which combine computation and communication in a non trivial fashion computation with advice and interactive proof systems we show that the existence of non trivial dynamics in a theory implies a bound on the power of computation with advice moreover we provide an explicit example of a theory with no non trivial dynamics in which the power of computation with advice is unbounded finally we show that the power of simple interactive proof systems in theories where local measurements suffice for tomography is non trivially bounded this result provides a proof that formula see text is contained in formula see text which does not make use of any uniquely quantum structure such as the fact that observables correspond to self adjoint operators and thus may be of independent interest

the continuous variable deutsch jozsa algorithm using realistic quantum systems this paper is a study of the continuous variable deutsch jozsa algorithm first we review an existing version of the algorithm for qunat states pati and braunstein 2002 arxiv 0207108v1 and then we present a realistic version of the deutsch jozsa algorithm for continuous variables which can be implemented in a physical quantum system given the appropriate oracle under these conditions we have a probabilistic algorithm for deciding the function with a very high success rate with a single call to the oracle finally we look at the effects of errors in both of these continuous variable algorithms and how they affect the chances of success we find that the algorithm is generally robust for errors in initialization and the oracle but less so for errors in the measurement apparatus and the fourier transform this article is part of a special issue of journal of physics a mathematical and theoretical devoted to coherent states mathematical and physical aspects

average case quantum query complexity we compare classical and quantum query complexities of total boolean functions it is known that for worst case complexity the gap between quantum and classical can be at most polynomial we show that for average case complexity under the uniform distribution quantum algorithms can be exponentially faster than classical algorithms under non uniform distributions the gap can even be super exponential we also prove some general bounds for average case complexity and show that the average case quantum complexity of majority under the uniform distribution is nearly quadratically better than the classical complexity a preliminary version of this paper appeared in the proceedings of the 17th annual symposium on theoretical aspects of computer science stacs 2000 lecture notes in computer science vol 1770 berlin springer

generalized probabilistic scale space for image restoration a novel generalized sampling based probabilistic scale space theory is proposed for image restoration we explore extending the definition of scale space to better account for both noise and observation models which is important for producing accurately restored images a new class of scale space realizations based on sampling and probability theory is introduced to realize this extended definition in the context of image restoration experimental results using 2 d images show that generalized sampling based probabilistic scale space theory can be used to produce more accurate restored images when compared with state of the art scale space formulations particularly under situations characterized by low signal to noise ratios and image degradation