Abstract: Shenvi, Kempe, and Whaley's quantum random-walk search (SKW) algorithm [Phys. Rev. A 67, 052307 (2003)] is known to require $O(\sqrt{N})$ number of oracle queries to find the marked element, where $N$ is the size of the search space. The overall time complexity of the SKW algorithm differs from the best achievable on a quantum computer only by a constant factor. We present improvements to the SKW algorithm which yield a significant increase in success probability, and an improvement on query complexity such that the theoretical limit of a search algorithm succeeding with probability close to one is reached. We point out which improvement can be applied if there is more than one marked element to find.

Abstract: Current proposals for special-purpose factorization hardware will become obsolete if large quantum computers are built: the number-field sieve scales much more poorly than Shor's quantum algorithm for factorization. Will all special-purpose cryptanalytic hardware become obsolete in a post-quantum world? A quantum algorithm by Brassard, HOyer, and Tapp has frequently been claimed to reduce the cost of b-bit hash collisions from 2^b/2 to 2^b/3. This paper analyzes the Brassard-HOyer-Tapp algorithm and shows that it has fundamentally worse price-performance ratio than the classical van Oorschot-Wiener hash-collision circuits, even under optimistic assumptions regarding the speed of quantum computers.

Abstract: Quantum walks, being the quantum analog of classical random walks, are expected to provide a fruitful source of quantum algorithms. A few such algorithms have already been developed, including the ``glued trees'' algorithm, which provides an exponential speedup over classical methods, relative to a particular quantum oracle. Here, we discuss the possibility of a quantum walk algorithm yielding such an exponential speedup over possible classical algorithms, without the use of an oracle. We provide examples of some highly symmetric graphs on which efficient quantum circuits implementing quantum walks can be constructed and discuss potential applications to quantum search for marked vertices along these graphs.

Abstract: Is there a general theorem that tells us when we can hope for exponential speedups from quantum algorithms, and when we cannot? In this paper, we make two advances toward such a theorem, in the black-box model where most quantum algorithms operate. First, we show that for any problem that is invariant under permuting inputs and outputs (like the collision or the element distinctness problems), the quantum query complexity is at least the 9 th root of the classical randomized query complexity. This resolves a conjecture of Watrous from 2002. Second, inspired by recent work of O’Donnell et al. and Dinur et al., we conjecture that every bounded low-degree polynomial has a “highly influential” variable. Assuming this conjecture, we show that every T-query quantum algorithm can be simulated on most inputs by a poly(T)query classical algorithm, and that one essentially cannot hope to prove P 6 BQP relative to a random oracle.

Abstract: Although quantum algorithms realizing an exponential time speed-up over the best known classical algorithms exist, no quantum algorithm is known performing computation using less space resources than classical algorithms. In this paper, we study, for the first time explicitly, space-bounded quantum algorithms for computational problems where the input is given not as a whole, but bit by bit. We show that there exist such problems that a quantum computer can solve using exponentially less work space than a classical computer. More precisely, we introduce a very natural and simple model of a space-bounded quantum online machine and prove an exponential separation of classical and quantum online space complexity, in the bounded-error setting and for a total language. The language we consider is inspired by a communication problem (the disjointness function) that Buhrman, Cleve and Wigderson used to show an almost quadratic separation of quantum and classical bounded-error communication complexity. We prove that, in the framework of online space complexity, the separation becomes exponential.

Abstract: There exist quantum algorithms that are more efficient than their classical counterparts; such algorithms were invented by Shor in 1994 and then Grover in 1996. A lack of invention since Grover's algorithm has been commonly attributed to the non-intuitive nature of quantum algorithms to the classically trained person. Thus, the idea of using computers to automatically generate quantum algorithms based on an evolutionary model emerged. A limitation of this approach is that quantum computers do not yet exist and quantum simulation on a classical machine has an exponential order overhead. Nevertheless, early research into evolving quantum algorithms has shown promise. This paper provides an introduction into quantum and evolutionary algorithms for the computer scientist not familiar with these fields. The exciting field of using evolutionary algorithms to evolve quantum algorithms is then reviewed.

Abstract: Quantum computers can outperform their classical counterparts at some tasks, but the full scope of their power is unclear. A new quantum algorithm hints at the possibility of far-reaching applications.

Abstract: The inherent parallelism of quantum systems determined not only the investigation of innovative applications that can be developed using these high performance computing systems, but also of ways to improve the performances over the classical case. Exploiting this parallelism recently led to the emergence of innovative ideas in the field of computer graphics, sketching the development of quantum rendering and quantum computational geometry. Following these tracks, we propose a new quantum algorithm for the RANdom SAmple Consensus (RANSAC) voting scheme. In this paper we show that by exploiting the unique features of quantum computing, generating uniform superpositions of states in the problem space and applying quantum operators to all states simultaneously, the performance of our quantum algorithm is orders of magnitude faster than the classical variant.

Abstract: Coin flipping is a cryptographic primitive in which two spatially separated players, who do not trust each other, wish to establish a common random bit. If we limit ourselves to classical communication, this task requires either assumptions on the computational power of the players or it requires them to send messages to each other with sufficient simultaneity to force their complete independence. Without such assumptions, all classical protocols are so that one dishonest player has complete control over the outcome. If we use quantum communication, on the other hand, protocols have been introduced that limit the maximal bias that dishonest players can produce. However, those protocols would be very difficult to implement in practice because they are susceptible to realistic losses on the quantum channel between the players or in their quantum memory and measurement apparatus. In this paper, we introduce a quantum protocol and we prove that it is completely impervious to loss. The protocol is fair in the sense that either player has the same probability of success in cheating attempts at biasing the outcome of the coin flip. We also give explicit and optimal cheating strategies for both players.

Abstract: Most quantum algorithms that give an exponential speedup over classical algorithms exploit the Fourier transform in some way. In Shor's algorithm, sampling from the quantum Fourier spectrum is used to discover periodicity of the modular exponentiation function. In a generalization of this idea, quantum Fourier sampling can be used to discover hidden subgroup structures of some functions much more efficiently than it is possible classically. Another problem for which the Fourier transform has been recruited successfully on a quantum computer is the hidden shift problem. Quantum algorithms for hidden shift problems usually have a slightly different flavor from hidden subgroup algorithms, as they use the Fourier transform to perform a correlation with a given reference function, instead of sampling from the Fourier spectrum directly. In this paper we show that hidden shifts can be extracted efficiently from Boolean functions that are quadratic forms. We also show how to identify an unknown quadratic form on n variables using a linear number of queries, in contrast to the classical case were this takes ?(n 2) many queries to a black box. What is more, we show that our quantum algorithm is robust in the sense that it can also infer the shift if the function is close to a quadratic, where we consider a Boolean function to be close to a quadratic if it has a large Gowers U 3 norm.

Abstract: Conventional vector-based simulators for quantum computers are quite limited in the size of the quantum circuits they can handle, due to the worst-case exponential growth of even sparse representations of the full quantum state vector as a function of the number of quantum operations applied. However, this exponential-space requirement can be avoided by using general space-time tradeoffs long known to complexity theorists, which can be appropriately optimized for this particular problem in a way that also illustrates some interesting reformulations of quantum mechanics. In this paper, we describe the design and empirical space/time complexity measurements of a working software prototype of a quantum computer simulator that avoids excessive space requirements. Due to its space-efficiency, this design is well-suited to embedding in single-chip environments, permitting especially fast execution that avoids access latencies to main memory. We plan to prototype our design on a standard FPGA development board.

Abstract: In this paper, we build upon the model of two-party quantum computation introduced by Salvail et al. [SSS09] and show that in this model, only trivial correct two-party quantum protocols are weakly self-composable. We do so by defining a protocol \Pi, calling any non-trivial sub-protocol \pi N times and showing that there is a quantum honest-but-curious strategy that cannot be modeled by acting locally in every single copy of \pi. In order to achieve this, we assign a real value called "payoff" to any strategy for \Pi and show that that there is a gap between the highest payoff achievable by coherent and local strategies.

Abstract: Recently several quantum search algorithms based on quantum walks were proposed. Those algorithms differ from Grover's algorithm in many aspects. The goal is to find a marked vertex in a graph faster than classical algorithms. Since the implementation of those new algorithms in quantum computers or in other quantum devices is error-prone, it is important to analyze their robustness under decoherence. In this work we analyze the impact of decoherence on quantum search algorithms implemented on two-dimensional grids and on hypercubes.

Abstract: The oracle chooses a function out of a known set of functions and gives to the player a black box that, given an argument, evaluates the function. The player should find out a certain character of the function (e.g. its period) through function evaluation. This is the typical problem addressed by the quantum algorithms. In former theoretical work, we showed that a quantum algorithm requires the number of function evaluations of a classical algorithm that knows in advance 50% of the information that specifies the solution of the problem. This requires representing physically, besides the solution algorithm, the possible choices of the oracle.

Abstract: Solving a problem requires a problem solving step (deriving, from the formulation of the problem, the solution algorithm) and a computation step (running the algorithm). The latter step is generally oblivious of the former. We unify the two steps into a single physical interaction: a many body interaction in an idealized classical framework, a measurement interaction in the quantum framework. The many body interaction is a useful conceptual reference. The coordinates of the moving parts of a perfect machine are submitted to a relation representing problem-solution interdependence. Moving an “input” part nondeterministically produces a solution through a many body interaction. The kinematics and the statistics of this problem solving mechanism apply to quantum computation—once the physical representation is extended to the oracle that produces the problem. Configuration space is replaced by phase space. The relation between the coordinates of the machine parts now applies to a set of variables representing the populations of the qubits of a quantum register during reduction. The many body interaction is replaced by the measurement interaction, which changes the population variables from the values before to the values after measurement (and the forward evolution into the backward evolution, the same unitary transformation but ending with the state after measurement). Quantum computation is reduction on the solution of the problem under the problem-solution interdependence relation. The speed up is explained by a simple consideration of time-symmetry, it is the gain of information about the solution due to backdating, to before running the algorithm, a time-symmetric part of the reduction on the solution. This advanced cognition of the solution reduces the solution space to be explored by the algorithm. The quantum algorithm takes the time taken by a classical algorithm that knows in advance 50% of the information acquired by reading the solution (i.e. by measuring the content of the computer register at the end of the quantum algorithm). From another standpoint, the notion that a computation process is condensed into a single physical interaction explains the fact that we perceive many things at the same time in the introspective “present” (the instant of the interaction in the classical case, the time interval spanned by backdated reduction in the quantum case).

Abstract: Quantum computing is an extremely promising research combining theoretical and experimental quantum physics, mathematics, quantum information theory and computer science. Classical simulation of quantum computations will cover part of the gap between the theoretical mathematical formulation of quantum mechanics and the realization of quantum computers. One of the most important problems in "quantum computer science" is the development of new symbolic languages for quantum computing and the adaptation of existing symbolic languages for classical computing to quantum algorithms. The present paper is devoted to the adaptation of the Mathematica symbolic language to known quantum algorithms and corresponding simulation on the classical computer. Concretely we shall represent in the Mathematica symbolic language Simon's algorithm, the Deutsch-Josza algorithm, Grover's algorithm, Shor's algorithm and quantum error-correcting codes. We shall see that the same framework can be used for all these algorithms. This framework will contain the characteristic property of the symbolic language representation of quantum computing and it will be a straightforward matter to include this framework in future algorithms.

Abstract: We show how to use a programming language for formally describing and reasoning about errors in quantum computation. The formalisation is based on the concept of performing the correct operation with probability at least p, and the erroneous one with probability at most 1 − p. We apply the concept to two examples: Bell’s inequalities and the Deutsch–Jozsa quantum algorithm. The former is a fundamental thought experiment aimed at showing that Quantum Mechanics is not “local and realist”, and it is used in quantum cryptography protocols. We study it assuming faulty measurements, and we derive hardware reliability conditions that must be satisfied in order for the experiment to support its conclusions. The latter is a quantum algorithm for efficiently solving a classification problem for Boolean functions. The algorithm solves the problem with no error, but when we introduce faulty operations it becomes a two-sided error algorithm. Reasoning is accomplished via standard programming laws and quantum laws.

Abstract: We study a new realizable architecture for a universal quantum computer based on dierent optimized compo-nents and computational models. Simulation demonstrates it has a higher computing eciency compared withothers. Error correction, fault tolerance and robustness are also discussed for this architecture.Keywords: quantum computer, quantum computation, architecture, error correcting, robustness, realizable 1. INTRODUCTION Quantum computation is an interdisciplinary “eld of science and technology, combining and drawing on thedisciplines of physics, mathematics, computer science, and engineering. Indeed, scientists predict that withinthe next 30 to 50 years there will be applicable quantum computers. The architecture of a quantum computeris therefore worthy of study. Today, most of the physically implemented quantum devices can deal with onlyspeci“c problems or algorithms. People have been trying to build a universal quantum computer, which wouldbe able to solve all kinds of problems using a single architecture.In recent years, quantum algorithms, quantum computational models and physical quantum computers havebeen studied. The results of these studies provide us the necessary theoretical and experimental basis to designthe next generationŽ scalable universal quantum computer with new features such as fault tolerance, higheciency, and high-“delity teleportation, etc. These features also help us implement the quantum operatingsystem and their processing systems, and execute the quantum programming languages (QPLs).There are several necessary criteria in the design of an architecture for a realizable quantum computer. The“rst is the universality, which means all the programs for any quantum algorithm or bounded-size input datacan be solved on a universal quantum computer without revising its architecture. Second, it should be partiallyimmune to decoherence. Decoherence will cause information to be lost and corrupt the computation. An idealarchitecture should be considered to suppress the decoherence. Third, the architecture should be easy to programand control. The programming languages can help people search for new algorithms and discover new aspectsof computer science. For quantum computing, a good architecture is helpful for people to read, write, andmaintain programs easily, and execute them eciently. Fourth, the architecture should include an essential errorcorrection and a fault-tolerance mechanism. Compared with a classical computer, the most signi“cant dierencefor a quantum computer is its poor precision, both in information preservation and transformation operation.The quantum error correction codes (QECCs) and fault-tolerance mechanics can improve the precision. Last,the architecture should be easily simulated. We see a lot of improvement in the experimental implementationof quantum computers, however no evidence has been seen on todays quantum computing devices to processmore than 15 qubits simultaneously. Therefore, it is more feasible to simulate a quantum computer on a classicalcomputer.In this paper we propose a novel architecture for a realizable quantum computer, mainly focusing on itsproperties in the decoherence suppression, error correction and scalability. The computing eciency is alsodiscussed.

Abstract: Quantum algorithms require less operations than classical algorithms. The exact reason of this has not been pinpointed until now. Our explanation is that quantum algorithms know in advance 50% of the solution of the problem they will find in the future. In fact they can be represented as the sum of all the possible histories of a respective “advanced information classical algorithm”. This algorithm, given the advanced information (50% of the bits encoding the problem solution), performs the operations (oracle’s queries) still required to identify the solution. Each history corresponds to a possible way of getting the advanced information and a possible result of computing the missing information. This explanation of the quantum speed up has an immediate practical consequence: the speed up comes from comparing two classical algorithms, with and without advanced information, with no physics involved. This simplification could open the way to a systematic exploration of the possibilities of speed up.

Abstract: The control of quantum phenomena is a topic that has carried out many challenging problems. Among others, the Hamiltonian identification, i.e, the inverse problem associated with the unknown features of a quantum system is still an open issue. In this work, we present an algorithm that enables to design a set of selective laser fields that can be used, in a second stage, to identify unknown parameters of quantum systems.

Abstract: Quantum algorithms can be analyzed in a query model to compute Boolean functions. Function input is provided in a black box, and the aim is to compute the function value using as few queries to the black box as possible. A repetition code is an error detection scheme that repeats each bit of the original message r times. After a message with redundant bits is transmitted via a communication channel, it must be verified. If the received message consists of r-size blocks of equal bits, the conclusion is that there were no errors. The verification procedure can be interpreted as an application of a query algorithm, where input is a message to be checked. Classically, for N-bit message, values of all N variables must be queried. We demonstrate an exact quantum algorithm that uses only N/2 queries.

Abstract: This paper proves that, if quantum communication and computation are available and the number of parties is given, the leader election problem can exactly (i.e., without error in bounded time) be solved with at most the same complexity up to a constant factor as that of computing certain symmetric functions on an anonymous network of any unknown topology. Together with a novel quantum algorithm that computes a certain symmetric function, this characterization yields a quantum leader election algorithm that is more efficient than existing algorithms.

Abstract: Quantum communication allows for deep space communication and secure transmission of information. The perfomance and security of such protocols is based on the non-orthogonality of the used states, which is a key feature of quantum mechanics. The task of a quantum receiver is to discriminate between different states in a given alphabet with minimum error. This gives rise to the necessity of having receivers with a minimum amount of discrimination errors approaching the limits imposed by quantum mechanics [1,2]. Conventional detection schemes fail to fulfill this task, which makes the study of quantum receivers an important field in the realm of quantum communication.

Abstract: In former work, we showed that a quantum algorithm requires the number of operations (oracle's queries) of a classical algorithm that knows in advance 50% of the information that specifies the solution of the problem. We gave a preliminary theoretical justification of this "50% rule" and checked that the rule holds for a variety of quantum algorithms. Now, we make explicit the information about the solution available to the algorithm throughout the computation. The final projection on the solution becomes acquisition of the knowledge of the solution on the part of the algorithm. Backdating to before running the algorithm a time-symmetric part of this projection, feeds back to the input of the computation 50% of the information acquired by reading the solution.

Abstract: Coin flipping is a cryptographic primitive in which two spatially separated players, who in principle do not trust each other, wish to agree on a random bit Classical and quantum coin flipping protocols have been studied extensively for more than twenty‐five years However, until recently, quantum coin flipping protocols were designed without taking into consideration the losses of quantum information that would be unavoidable in any realistic implementation We introduced in 2008 a novel protocol and proved its security even when losses are taken into account: no cheating player could obtain a desired outcome with a probability greater than (6+2)/8≈93% Here, we refine our earlier protocol by making it fair in the sense that the optimal cheating strategies allow either player to bias the outcome by the same amount Specifically, either player can cheat to obtain a desired outcome with probability exactly 90%, but no more An implementation is underway

Abstract: We observe an enormous increase in the computational power of digital computers. This was due to the revolution in manufacturing processes and controlling semiconductor structures on submicron scale, ultimately leading to the control of individual atoms. Eventually, the classical electric circuits encountered the barrier of quantum mechanics and its effects. However, the laws of quantum mechanics can be also used to produce computational devices that lead to extraordinary speed increases over classical computers. Thus quantum computing becomes a very promising and attractive research area. The Computer Aided Design for Quantum circuits becomes an essential ingredient for such emerging research which may lead to these powerful computers to be realized—an era of Quantum computing. This thesis presents an integrated theoretical study of software algorithms to design circuits of quantum oracles as well as methods for designing quantum oracles for Grover algorithm to solve combinatorial problems. An implementation of quantum algorithm involves the initialization of the input state and its manipulation with quantum gates followed by the measurements. In Grover algorithm the problem to be solved is specified by a permutative logic oracle – the fundamental problem is then how to build this oracle from quantum logic circuits and how to optimize these circuits. These problems are NP-hard and require search algorithms. In future, the search will be also done in quantum and this thesis leads to quantum algorithms to design quantum circuits more efficiently.

Abstract: We investigate the generalisation of quantum search of unstructured and totally orderedsets to search of partially ordered sets (posets) Two models for poset search are consid-ered In both models, we show that quantum algorithms can achieve at most a quadraticimprovement in query complexity over classical algorithms, up to logarithmic factors; wealso give quantum algorithms that almost achieve this optimal reduction in complexityIn one model, we give an improved quantum algorithm for searching forest-like posets;in the other, we give an optimal O(√m)-query quantum algorithm for searching posetsderived from m×m arrays sorted by rows and columns This leads to a quantum algo-rithm that finds the intersection of two sorted lists of n integers in O(√n) time, whichis optimal

Abstract: This paper presents an effective test pattern generation approach for FPGA circuits by applying quantum computing algorithms. A prototypical new algorithm named QFPGA is developed utilizing the properties of quantum theory, such as quantum superposition and quantum parallelism. The effectiveness of this technique in terms of result quality, CPU requirements, fault detection and number of iterations is experimentally compared with some of the existing classical approaches, like exhaustive search, simulated annealing and genetic algorithms. The algorithm developed is so efficient that it requires only √N (N is the total number of vectors) iterations to find the desired test vector, whereas in classical computing it takes N/2 iterations. Simulation results on various benchmark circuits are also covered in this paper. The extendability of the new approach enables users to easily find the test vector from FPGA circuits and can be adapted for testing FPGA chips.

Abstract: In order to solve the ordered quantum database search problem, a quantum binary searching algorithm was proposed which can be used to implement the whole searching process in four steps. Considering the characteristic of quantum parallelism, this paper further improves the searching process, which can be realized in only two steps, and presents the circuit implementation. In this scheme, the number of the quantum logic gates doesn’t increase. Moreover, the losing-solution issue in the quantum binary searching algorithm can be efficiently prevented.