Abstract: Certain algorithms for quantum computers are able to outperform their classical counterparts In 1994, Peter Shor came up with a quantum algorithm that calculates the prime factors of a large number vastly more efficiently than a classical computer For general scalability of such algorithms, hardware, quantum error correction, and the algorithmic realization itself need to be extensible Here we present the realization of a scalable Shor algorithm, as proposed by Kitaev We factor the number 15 by effectively employing and controlling seven qubits and four “cache qubits” and by implementing generalized arithmetic operations, known as modular multipliers This algorithm has been realized scalably within an ion-trap quantum computer and returns the correct factors with a confidence level exceeding 99%

Abstract: That superpositions of states can be useful for performing tasks in quantum systems has been known since the early days of quantum information, but only recently has a quantitative theory of quantum coherence been proposed. Here we apply that theory to an analysis of the Deutsch-Jozsa algorithm, which depends on quantum coherence for its operation. The Deutsch-Jozsa algorithm solves a decision problem, and we focus on a probabilistic version of that problem, comparing probability of being correct for both classical and quantum procedures. In addition, we study a related decision problem in which the quantum procedure has one-sided error while the classical procedure has two-sided error. The role of coherence on the quantum success probabilities in both of these problems is examined.

Abstract: The Quantum Approximate Optimization Algorithm (QAOA) is designed to run on a gate model quantum computer and has shallow depth. It takes as input a combinatorial optimization problem and outputs a string that satisfies a high fraction of the maximum number of clauses that can be satisfied. For certain problems the lowest depth version of the QAOA has provable performance guarantees although there exist classical algorithms that have better guarantees. Here we argue that beyond its possible computational value the QAOA can exhibit a form of Quantum Supremacy in that, based on reasonable complexity theoretic assumptions, the output distribution of even the lowest depth version cannot be efficiently simulated on any classical device. We contrast this with the case of sampling from the output of a quantum computer running the Quantum Adiabatic Algorithm (QADI) with the restriction that the Hamiltonian that governs the evolution is gapped and stoquastic. Here we show that there is an oracle that would allow sampling from the QADI but even with this oracle, if one could efficiently classically sample from the output of the QAOA, the Polynomial Hierarchy would collapse. This suggests that the QAOA is an excellent candidate to run on near term quantum computers not only because it may be of use for optimization but also because of its potential as a route to establishing quantum supremacy.

Abstract: In recent years, deep learning has had a profound impact on machine learning and artificial intelligence. At the same time, algorithms for quantum computers have been shown to efficiently solve some problems that are intractable on conventional, classical computers. We show that quantum computing not only reduces the time required to train a deep restricted Boltzmann machine, but also provides a richer and more comprehensive framework for deep learning than classical computing and leads to significant improvements in the optimization of the underlying objective function. Our quantum methods also permit efficient training of multilayer and fully connected models.

Abstract: The area of property testing tries to design algorithms that can efficiently handle very large amounts of data: given a large object that either has a certain property or is somehow "far" from having that property, a tester should efficiently distinguish between these two cases. In this survey we describe recent results obtained for quantum property testing. This area naturally falls into three parts. First, we may consider quantum testers for properties of classical objects. We survey the main examples known where quantum testers can be much (sometimes exponentially) more efficient than classical testers. Second, we may consider classical testers of quantum objects. This is the situation that arises for instance when one is trying to determine if quantum states or operations do what they are supposed to do, based only on classical input-output behavior. Finally, we may also consider quantum testers for properties of quantum objects, such as states or operations. We survey known bounds on testing various natural properties, such as whether two states are equal, whether a state is separable, whether two operations commute, etc. We also highlight connections to other areas of quantum information theory and mention a number of open questions.

Abstract: We propose a new application of quantum computing to the field of natural language processing. Ongoing work in this field attempts to incorporate grammatical structure into algorithms that compute meaning. In (Coecke, Sadrzadeh and Clark, 2010), the authors introduce such a model (the CSC model) based on tensor product composition. While this algorithm has many advantages, its implementation is hampered by the large classical computational resources that it requires. In this work we show how computational shortcomings of the CSC approach could be resolved using quantum computation (possibly in addition to existing techniques for dimension reduction). We address the value of quantum RAM (Giovannetti,2008) for this model and extend an algorithm from Wiebe, Braun and Lloyd (2012) into a quantum algorithm to categorize sentences in CSC. Our new algorithm demonstrates a quadratic speedup over classical methods under certain conditions.

Abstract: Because of inevitable coupling with the environment, nearly all practical quantum systems are open system, where the evolution is not necessarily unitary. In this paper, we propose a duality quantum algorithm for simulating Hamiltonian evolution of an open quantum system. In contrast to unitary evolution in a usual quantum computer, the evolution operator in a duality quantum computer is a linear combination of unitary operators. In this duality quantum algorithm, the time evolution of the open quantum system is realized by using Kraus operators which is naturally implemented in duality quantum computer. This duality quantum algorithm has two distinct advantages compared to existing quantum simulation algorithms with unitary evolution operations. Firstly, the query complexity of the algorithm is O(d3) in contrast to O(d4) in existing unitary simulation algorithm, where d is the dimension of the open quantum system. Secondly, By using a truncated Taylor series of the evolution operators, this duality quantum algorithm provides an exponential improvement in precision compared with previous unitary simulation algorithm.

Abstract: Quantum image processing (QIP) means the quantum-based methods to speed up image processing algorithms Many quantum image processing schemes claim that their efficiency is theoretically higher than their corresponding classical schemes However, most of them do not consider the problem of measurement As we all know, measurement will lead to collapse That is to say, executing the algorithm once, users can only measure the final state one time Therefore, if users want to regain the results (the processed images), they must execute the algorithms many times and then measure the final state many times to get all the pixels' values If the measurement process is taken into account, whether or not the algorithms are really efficient needs to be reconsidered In this paper, we try to solve the problem of measurement and give a quantum image matching algorithm Unlike most of the QIP algorithms, our scheme interests only one pixel (the target pixel) instead of the whole image It modifies the probability of pixels based on Grover's algorithm to make the target pixel to be measured with higher probability, and the measurement step is executed only once An example is given to explain the algorithm more vividly Complexity analysis indicates that the quantum scheme's complexity is $$O(2^{n})$$O(2n) in contradistinction to the classical scheme's complexity $$O(2^{2n+2m})$$O(22n+2m), where m and n are integers related to the size of images

Abstract: The question of whether a fully classical client can delegate a quantum computation to an untrusted quantum server while fully maintaining privacy (blindness) is one of the big open questions in quantum cryptography. Both yes and no answers have important practical and theoretical consequences, and the question seems genuinely hard. The state-of-the-art approaches to securely delegating quantum computation, without exception, rely on granting the client modest quantum powers, or on additional, non-communicating, quantum servers. In this work, we consider the single server setting, and push the boundaries of the minimal devices of the client, which still allow for blind quantum computation. Our approach is based on the observation that, in many blind quantum computing protocols, the "quantum" part of the protocol, from the clients perspective, boils down to the establishing classical-quantum correlations (independent from the computation) between the client and the server, following which the steering of the computation itself requires only classical communication. Here, we abstract this initial preparation phase, specifically for the Universal Blind Quantum Computation protocol of Broadbent, Fitzsimons and Kashefi. We identify sufficient criteria on the powers of the client, which still allow for secure blind quantum computation. We work in a universally composable framework, and provide a series of protocols, where each step reduces the number of differing states the client needs to be able to prepare. As the limit of such reductions, we show that the capacity to prepare just two pure states, which have an arbitrarily high overlap (thus are arbitrarily close to identical), suffices for efficient and secure blind quantum computation.

Abstract: The use of superposition of states in quantum computation, known as quantum parallelism, has significant advantage in terms of speed over the classical computation. It can be understood from the early invented quantum algorithms such as Deutsch's algorithm, Deutsch-Jozsa algorithm and its variation as Bernstein-Vazirani algorithm, Simon algorithm, Shor's algorithms etc. Quantum parallelism also significantly speeds up the database search algorithm, which is important in computer science because it comes as a subroutine in many important algorithms. Quantum database search of Grover achieves the task of finding the target element in an unsorted database in a time quadratically faster than the classical computer. We review the Grover quantum search algorithms for a singe and multiple target elements in a database. The partial search algorithm of Grover and Radhakrishnan and its optimization by Korepin, called GRK algorithm are also discussed.

Abstract: Processes such as quantum computation, or the evolution of quantum cellular automata are typically described by a unitary operation implemented by an external observer. In particular, an interaction is generally turned on for a precise amount of time, using a classical clock. A fully quantum mechanical description of such a device would include a quantum description of the clock whose state is generally disturbed because of the back-reaction on it. Such a description is needed if we wish to consider finite sized autonomous quantum machines requiring no external control. The extent of the back-reaction has implications on how small the device can be, on the length of time the device can run, and is required if we want to understand what a fully quantum mechanical treatment of an observer would look like. Here, we consider the implementation of a unitary by a finite sized device, and show that the back-reaction on it can be made exponentially small in the device's dimension with only a linear increase in energy. As a result, an autonomous quantum machine need only be of modest size. We are also able to solve a long-standing open problem by using a finite sized quantum clock to approximate the continuous evolution of an idealised clock. The result has implications on the equivalence of different paradigms of quantum thermodynamics, some which allow external control and some which only allow autonomous thermal machines.

Abstract: We propose a quantum machine learning algorithm for efficiently solving a class of problems encoded in quantum controlled unitary operations. The central physical mechanism of the protocol is the iteration of a quantum time-delayed equation that introduces feedback in the dynamics and eliminates the necessity of intermediate measurements. The performance of the quantum algorithm is analyzed by comparing the results obtained in numerical simulations with the outcome of classical machine learning methods for the same problem. The use of time-delayed equations enhances the toolbox of the field of quantum machine learning, which may enable unprecedented applications in quantum technologies.

Abstract: Quantum image processing has been a hot topic as a consequence of the development of quantum computation. Many quantum image processing algorithms have been proposed, whose efficiency are theoretically higher than their corresponding classical algorithms. However, most of the quantum schemes do not consider the problem of measurement. If users want to get the results, they must measure the final state many times to get all the pixels’ values. Moreover, executing the algorithm one time, users can only measure the final state one time. In order to measure it many times, users must execute the algorithms many times. If the measurement process is taken into account, whether or not the algorithms are really efficient needs to be reconsidered. In this paper, we try to solve the problem of measurement and give a quantum image location algorithm. This scheme modifies the probability of pixels to make the target pixel to be measured with higher probability. Furthermore, it only has linear complexity.

Abstract: Blind quantum computation protocols allow a user to delegate a computation to a remote quantum computer in such a way that the privacy of their computation is preserved, even from the device implementing the computation. To date, such protocols are only known for settings involving at least two quantum devices: either a user with some quantum capabilities and a remote quantum server or two or more entangled but noncommunicating servers. In this work, we take the first step towards the construction of a blind quantum computing protocol with a completely classical client and single quantum server. Specifically, we show how a classical client can exploit the ambiguity in the flow of information in measurement-based quantum computing to construct a protocol for hiding critical aspects of a computation delegated to a remote quantum computer. This ambiguity arises due to the fact that, for a fixed graph, there exist multiple choices of the input and output vertex sets that result in deterministic measurement patterns consistent with the same fixed total ordering of vertices. This allows a classical user, computing only measurement angles, to drive a measurement-based computation performed on a remote device while hiding critical aspects of the computation.

Abstract: Blind quantum computation (BQC) can allow a client with limited quantum power to delegate his quantum computation to a powerful server and still keep his own data private. In this paper, we present a multiple-server flexible BQC protocol, where a client who only needs the ability of accessing qua ntum channels can delegate the computational task to a number of servers. Especially, the client’s quantum computation also can be achieved even when one or more delegated quantum servers break down in networks. In other words, when connections to certain quantum servers are lost, clients can adjust flexibly and delegate their quantum computation to other servers. Obviously it is trivial that the computation will be unsuccessful if all servers are interrupted.

Abstract: The realization of reliable quantum channels, able to transfer a quantum state with high fidelity, is a fundamental step in the construction of scalable quantum devices. In this paper we describe a transmission scheme based on the genuinely quantum effect known as Bloch oscillations. The proposed protocol makes it possible to carry a quantum state over different distances with a minimal engineering of the transmission medium and can be implemented and verified on current quantum technology hardware.

Abstract: We present a new scheme for quantum homomorphic encryption which is compact and allows for efficient evaluation of arbitrary polynomial-sized quantum circuits. Building on the framework of Broadbent and Jeffery and recent results in the area of instantaneous non-local quantum computation, we show how to construct quantum gadgets that allow perfect correction of the errors which occur during the homomorphic evaluation of T gates on encrypted quantum data. Our scheme can be based on any classical (leveled) fully homomorphic encryption (FHE) scheme and requires no computational assumptions besides those already used by the classical scheme. The size of our quantum gadget depends on the space complexity of the classical decryption function -- which aligns well with the current efforts to minimize the complexity of the decryption function. Our scheme (or slight variants of it) offers a number of additional advantages such as ideal compactness, the ability to supply gadgets "on demand", circuit privacy for the evaluator against passive adversaries, and a three-round scheme for blind delegated quantum computation which puts only very limited demands on the quantum abilities of the client.

Abstract: The outcomes of quantum mechanical experiments are inherently random. It is therefore necessary to develop stringent methods for quantifying the degree of statistical uncertainty about the results of quantum experiments. For the particularly relevant task of quantum state estimation, it has been shown that a significant reduction in uncertainty can be achieved by taking the positivity of quantum states into account. However -- the large number of partial results and heuristics notwithstanding -- no efficient general algorithm is known that produces an optimal uncertainty region from experimental data and the prior constraint of positivity. Here, we make this problem precise and show that the general case is NP-hard. Our result leaves room for the existence of efficient approximate solutions, and therefore does not yet imply that the practical task of quantum uncertainty quantification is intractable. However, it does show that there exists a non-trivial trade-off between optimality and computational efficiency for error regions. We prove two versions of the result: One for frequentist and one for Bayesian statistics.

Abstract: We prove a general relation between adaptive and non-adaptive strategies in the quantum setting, i.e., between strategies where the adversary can or cannot adaptively base its action on some auxiliary quantum side information. Our relation holds in a very general setting, and is applicable as long as we can control the bit-size of the side information, or, more generally, its "information content". Since adaptivity is notoriously difficult to handle in the analysis of quantum cryptographic protocols, this gives us a very powerful tool: as long as we have enough control over the side information, it is sufficient to restrict ourselves to non-adaptive attacks. We demonstrate the usefulness of this methodology with two examples. The first is a quantum bit commitment scheme based on 1-bit cut-and-choose. Since bit commitment implies oblivious transfer in the quantum setting, and oblivious transfer is universal for two-party computation, this implies the universality of 1-bit cut-and-choose, and thus solves the main open problem ofi¾?[9]. The second example is a quantum bit commitment scheme proposed in 1993 by Brassard et al. It was originally suggested as an unconditionally secure scheme, back when this was thought to be possible. We partly restore the scheme by proving it secure in a variant of the bounded quantum storage model. In both examples, the fact that the adversary holds quantum side information obstructs a direct analysis of the scheme, and we circumvent it by analyzing a non-adaptive version, which can be done by means of known techniques, and applying our main result.

Abstract: Hyperentangled states, entangled states with more than one degree of freedom, are considered as promising resource in quantum computation. Here we present a hyperparallel quantum algorithm for matrix multiplication with time complexity O(N2), which is better than the best known classical algorithm. In our scheme, an N dimensional vector is mapped to the state of a single source, which is separated to N paths. With the assistance of hyperentangled states, the inner product of two vectors can be calculated with a time complexity independent of dimension N. Our algorithm shows that hyperparallel quantum computation may provide a useful tool in quantum machine learning and “big data” analysis.

Abstract: Quantum mechanics dramatically differs from classical physics. An interesting consequence of this fact is that quantum resources offer an advantage over classical resources in many information-theoretic tasks. In quantum information, the goal of which is to understand information processing from a quantum perspective, it is thus natural to focus on tasks where quantum resources provide an advantage over classical ones, and to overlook tasks where quantum mechanics provides no advantage. But are the latter tasks really useless from a more general perspective? In this review we focus on a simple information-theoretic game called ‘guess your neighbour’s input’, for which classical and quantum players perform equally well. Interestingly, this seemingly innocuous game turns out to be useful in various contexts. From a fundamental point of view, the game provides a sharp separation between quantum mechanics and other more general physical theories, hence bringing a deeper understanding of the foundations of quantum mechanics. The game also finds unexpected applications in quantum foundations and quantum information theory, related to Gleason’s theorem, and to bound entanglement and unextendible product bases.

Abstract: Quantum computing field is evolving rapidly these days. The difference between this new field and the classical field is the extension of the main domain from just using two bits (0, 1) to a complete space which is the result of the superposition of the same mentioned bits. By applying the superposition property in the quantum algorithms, this ensures that the system is more secured than the classical one and gives the quantum algorithms the advantage of breaking the classical ones. Databases, like any other system, require security due to the fact that it contains massive amounts of information that needs to be accessed only by the right user. The following survey will take a more in depth look into quantum databases.

Abstract: : The unique principles of quantum mechanics may one day enable computers to perform operations that would be impossible on a classical computer. Although no one knows whether it will be possible to build a large-scale, functional, and stable quantum computer, researchers can study quantum-mechanical systems and develop algorithms and circuits by simulating quantum systems in software. Performance and memory bottlenecks prevent most current quantum computer simulators from being able to simulate quantum systems that are large enough to be useful. In this thesis, we develop a matrix-free sequential quantum computer simulator to vastly improve both time and memory performance of sequential code on a single processor. Next, we distribute the matrix-free algorithm over multiple parallel processors using the Message Passing Interface in order to simulate quantum systems that are too large to reside wholly within the memory of a single processor. Finally, we simulate various quantum circuits using the Hamming high-performance computing cluster in order to conduct algorithmic analysis.

Abstract: The decoy-state high-dimensional quantum key distribution provides a practical secure way to share more private information with high photon-information efficiency. In this paper, based on detector-decoy method, we propose a detector-decoy high-dimensional quantum key distribution protocol. Employing threshold detectors and a variable attenuator, we can estimate single-photon fraction of postselected events and Eves Holevo information under the Gaussian collective attack with much simpler operations in practical implementation. By numerical evaluation, we show that without varying source intensity and optimizing decoy-state intensity, our protocol could perform much better than one-decoy-state protocol and as well as the two-decoy-state protocol. Specially, when the detector efficiency is lower, the advantage of the detector-decoy method becomes more prominent.

Abstract: Dealing with errors in a quantum computer typically requires complex programming and many additional quantum bits. A technique for controlling errors has been proposed that alleviates both of these problems.

Abstract: We study a quantum algorithm that consists of a simple quantum Markov process, and we analyze its behavior on restricted versions of Quantum 2-SAT. We prove that the algorithm solves this decision problem with high probability for n qubits, L clauses, and promise gap c in time O(n^2 L^2 c^{-2}). If the Hamiltonian is additionally polynomially gapped, our algorithm efficiently produces a state that has high overlap with the satisfying subspace. The Markov process we study is a quantum analogue of Schoning's probabilistic algorithm for k-SAT.

Abstract: The rapid progress seen in the development of quantum coherent devices for information processing has motivated serious consideration of quantum computer architecture and organization. One topic which remains open for investigation and optimization relates to the design of the classical-quantum interface, where control operations on individual qubits are applied according to higher-level algorithms; accommodating competing demands on performance and scalability remains a major outstanding challenge. In this work we present a resource-efficient, scalable framework for the implementation of embedded physical-layer classical controllers for quantum information systems. Design drivers and key functionalities are introduced, leading to the selection of Walsh functions as an effective functional basis for both programming and controller hardware implementation. This approach leverages the simplicity of real-time Walsh-function generation in classical digital hardware, and the fact that a wide variety of physical-layer controls such as dynamic error suppression are known to fall within the Walsh family. We experimentally implement a real-time FPGA-based Walsh controller producing Walsh timing signals and Walsh-synthesized analog waveforms appropriate for critical tasks in error-resistant quantum control and noise characterization. These demonstrations represent the first step towards a unified framework for the realization of physical-layer controls compatible with large-scale quantum information processing.

Abstract: In supervised learning, an inductive learning algorithm extracts general rules from observed training instances, then the rules are applied to test instances. We show that this splitting of training and application arises naturally, in the classical setting, from a simple independence requirement with a physical interpretation of being non-signalling. Thus, two seemingly different definitions of inductive learning happen to coincide. This follows from very specific properties of classical information, which break down in the quantum setup. We prove a quantum de Finetti theorem for quantum channels, which shows that in the quantum case, the equivalence holds in the asymptotic setting (for large number of test instances). This reveals a natural analogy between classical learning protocols and their quantum counterparts, thus allowing to naturally enquire about standard elements in computational learning theory, such as structural risk minimization, model and sample complexity.

Abstract: In the one-way quantum computation (1WQC) model, computations are done by correlated sequences of entanglement, measurement and local corrections commands. As scalable and reliable quantum computers have not been implemented yet, the only widely available tools for designing and testing quantum algorithms are quantum computation simulators. However, simulating quantum computations on a standard classical computer in most cases requires very large memory and time. Recently, an array-based simulator, called one-way quantum computation simulator (OWQS) has been proposed to directly simulate the 1WQC model. OWQS outperforms the previously proposed quantum computation simulators to simulate the 1WQC model. In this paper, OWQS is modified in a way that it utilizes the graph-based representation of system states using algebraic decision diagram (ADD) in order to benefit from the similarities in the quantum states of 1WQC. This simulator is called graph-based OWQS, GOWQS. Experimental results validate the considerable improvement of the proposed simulator as compared to OWQS.