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Quantum Computers, one fully realized, can represent an exponential boost in computing power. However, the computational power of the current quantum computers, referred to as Noisy Internediate Scale Quantum, or NISQ, is severely limited because of environmental and intrinsic noise, as well as the very low connectivity between qubits compared to their total amount. We propose a virtual quantum processor that emulates a generic hybrid quantum machine which can serve as a logical version of quantum computing hardware. This hybrid classical quantum machine powers quantum-logical computations which are substitutable by future native quantum processors., IEEE peer reviewed, published September 2021

Quick Quantum Circuit Simulation (QQCS) is a software system for computing the result of a quantum circuit using a notation that derives directly from the circuit, expressed in a single input line. Quantum circuits begin with an initial quantum state of one or more qubits, which are the quantum analog to classical bits. The initial state is modified by a sequence of quantum gates, quantum machine language instructions, to get the final state. Measurements are made of the final state and displayed as a classical binary result. Measurements are postponed to the end of the circuit because a quantum state collapses when measured and produces probabilistic results, a consequence of quantum uncertainty. A circuit may be run many times on a quantum computer to refine the probabilistic result. Mathematically, quantum states are 2n -dimensional vectors over the complex number field, where n is the number of qubits. A gate is a 2n ×2n unitary matrix of complex values. Matrix multiplication models the application of a gate to a quantum state. QQCS is a mathematical rendering of each step of a quantum algorithm represented as a circuit, and as such, can present a trace of the quantum state of the circuit after each gate, compute gate equivalents for each circuit step, and perform measurements at any point in the circuit without state collapse. Output displays are in vector coefficients or Dirac bra-ket notation. It is an easy-to-use educational tool for students new to quantum computing.

Background COVID-19 is a novel virus that affects the upper respiratory tract, as well as the lungs. The scale of the global COVID-19 pandemic, its spreading rate, and deaths are increasing regularly. Computed tomography (CT) scans can be used carefully to detect and analyze COVID-19 cases. In CT images/scans, ground-glass opacity (GGO) is found in the early stages of infection. While in later stages, there is a superimposed pulmonary consolidation. Methods This research investigates the quantum machine learning (QML) and classical machine learning (CML) approaches for the analysis of COVID-19 images. The recent developments in quantum computing have led researchers to explore new ideas and approaches using QML. The proposed approach consists of two phases: in phase I, synthetic CT images are generated through the conditional adversarial network (CGAN) to increase the size of the dataset for accurate training and testing. In phase II, the classification of COVID-19/healthy images is performed, in which two models are proposed: CML and QML. Result The proposed model achieved 0.94 precision (Pn), 0.94 accuracy (Ac), 0.94 recall (Rl), and 0.94 F1-score (Fe) on POF Hospital dataset while 0.96 Pn, 0.96 Ac, 0.95 Rl, and 0.96 Fe on UCSD-AI4H dataset. Conclusion The proposed method achieved better results when compared to the latest published work in this domain.

This work presents the mapping of the traveling salesperson problem (TSP) based in pseudo-Boolean constraints to a graph of the D-Wave Systems Inc. We first formulate the problem as a set of constraints represented in propositional logic and then resort to the SATyrus approach to convert the set of constraints to an energy minimization problem. Next, we transform the formulation to a quadratic unconstrained binary optimization problem (QUBO) and solve the problem using different approaches: (a) classical QUBO using simulated annealing in a von Neumann machine, (b) QUBO in a simulated quantum environment, (c) QUBO using the D-Wave quantum machine. Moreover, we study the amount of time and execution time reduction we can achieve by exploring approximate solutions using the three approaches. Results show that for every graph size tested with the number of nodes less than or equal to 7, we can always obtain at least one optimal solution. In addition, the D-Wave machine can find optimal solutions more often than its classical counterpart for the same number of iterations and number of repetitions. Execution times, however, can be some orders of magnitude higher than the classical or simulated approaches for small graphs. For a higher number of nodes, the average execution time to find the first optimal solution in the quantum machine is 26% ( $$n = 6$$ ) and 47% ( $$n = 7$$ ) better than the classical.

As the popularity of quantum computing continues to grow, efficient quantum machine access over the cloud is critical to both academic and industry researchers across the globe. And as cloud quantum computing demands increase exponentially, the analysis of resource consumption and execution characteristics are key to efficient management of jobs and resources at both the vendor-end as well as the client-end. While the analysis and optimization of job / resource consumption and management are popular in the classical HPC domain, it is severely lacking for more nascent technology like quantum computing. This paper proposes optimized adaptive job scheduling to the quantum cloud taking note of primary characteristics such as queuing times and fidelity trends across machines, as well as other characteristics such as quality of service guarantees and machine calibration constraints. Key components of the proposal include a) a prediction model which predicts fidelity trends across machine based on compiled circuit features such as circuit depth and different forms of errors, as well as b) queuing time prediction for each machine based on execution time estimations. Overall, this proposal is evaluated on simulated IBM machines across a diverse set of quantum applications and system loading scenarios, and is able to reduce wait times by over 3x and improve fidelity by over 40\% on specific usecases, when compared to traditional job schedulers., Comment: Appeared at the 2021 IEEE International Conference on Quantum Computing and Engineering. arXiv admin note: text overlap with arXiv:2203.13121. substantial text overlap with arXiv:2203.13121

Quantum Secure Direct Communication (QSDC) is a distinctive protocol of quantum communication. It transmits confidential message straight through a quantum channel without the requirement of a secret key and ciphertext. It is also helpful in preventing eavesdropper during transmission. In this article, during the detailed study about QSDC, challenges faced while implementing the mitigation techniques w.r.t possible threats available in practical QSDC, have been studied and demonstrated. From the experiments and results it is observed that practical QSDC has inherent challenges. In actual quantum communication systems, flaws in measurement devices could give rise to disclosure of secret information to Eve without even being noticed. Measurement-device-independent QSDC protocol has been proposed using more than one swapping circuit as a mitigation technique. The efficacy of proposed protocol is verified using quantum simulator and quantum machine in the ideal scenario as well as possible threat scenarios. The results demonstrate its potential over other protocols of quantum communication and contribution towards enabling secure communication.

Quantum machine learning has seen considerable theoretical and practical developments in recent years and has become a promising area for finding real world applications of quantum computers. In pursuit of this goal, here we combine state-of-the-art algorithms and quantum hardware to provide an experimental demonstration of a quantum machine learning application with provable guarantees for its performance and efficiency. In particular, we design a quantum Nearest Centroid classifier, using techniques for efficiently loading classical data into quantum states and performing distance estimations, and experimentally demonstrate it on a 11-qubit trapped-ion quantum machine, matching the accuracy of classical nearest centroid classifiers for the MNIST handwritten digits dataset and achieving up to 100% accuracy for 8-dimensional synthetic data.

Thermal transport and quantum thermodynamics at the nanoscale is nowadays garnering an increasing attention, in particular in the context of quantum technologies. Experiments relevant for quantum technology are expected to be performed in the non-linear regime. In this work, we build on previous results derived in the linear response regime for the performance of an Aharonov-Bohm (AB) interferometer operated as heat engine. In the non-linear regime, we demonstrate the tunability, large efficiency and thermopower that this mesoscopic quantum machine can achieve, confirming the exciting perspectives that this AB ring offers for developing efficient thermal machines in the fully quantum regime., 6 pages, 5 figures, invited contribution to AVS Quantum Science, Special Topic Collection on Quantum Thermodynamics, published version. Featured paper by the Editor

Quantum machine learning [QML] is a new formulation on quantum hardware platform will try to achieve more enhanced data analysis and prediction which classical computer will not be able to generate. Classical computers are having computational limitations in terms of large volume data processing. Quantum machine are not to replace classical machines but quantum computers will solve operational difficulties of classical machines in terms of computational time. Quantum machine learning accelerates the supervised, unsupervised, and reinforcement learning methods. Classical ML methods such as SVM, PCA, Clustering, Neural networks are giving promising results but classical machines are inadequate to perform certain computations. Proposed Quantum machine learning would result in complex and weird patterns. Quantum support vector machine(QSVM) is a method used in supervised learning for classification and regression. QSVM uses high-dimensional feature space possibly on infinite dimension called as enhanced feature space for generating hyperplane. This hyperplane will classify non-linear and complex data on multiclass domain to achieve improved accuracy in less computational time. This paper investigates various strategies for quantum enhanced machine learning algorithm in supervised learning method.

Quantum Secure Direct Communication (QSDC) is a distinctive protocol of quantum communication. It communicates confidential message straight through a quantum channel without a requirement of secret key and cipher-text. It is not solely useful in preventing eavesdropping throughout transmission, but additionally removes the security flaw related with storing and managing the key. Therefore, this protocol of secure communication is different from its typical equivalents and other quantum protocols. In this article, we will bring out the facts that how QSDC is different and better than other protocols of Quantum Communication. The transient details of all the protocols of Quantum communication are studied rigorously and compared with QSDC to demonstrate how QSDC is capable of overcoming the loopholes/shortcomings of alternative protocols. In this paper, protocols of QSDC to mitigate the possible threats available in practical QSDC are discussed and one of the protocol Measurement Device Independent QSDC is demonstrated along with the efficacy of results verified using quantum simulator and quantum machine. The results demonstrate its potential over other protocols of quantum communication and contribution towards empowering secure communication. With the benefits of QSDC over other protocols, it helps as mitigating technique for the possible threats available in other protocols of Quantum communication.

The concept of sequential quantum machine (SQM) was firstly introduced by Gudder. Qiu further investigated some properties of SQMs and introduced the concept of quantum sequential machine (QSM) which was an equivalent version of SQM. A uninitialized sequential quantum machine (USQM) is a sequential quantum machine which has no initialized state. The main purpose of this paper is to investigate three coverings of products of USQMs: covering, probability covering and weak probability covering. More specifically, we firstly introduce the concepts of products of USQMs and study properties of these products. Secondly, we introduce the concept of covering of USQMs, and study covering properties of products of USQMs. Finally, we introduce the concepts of probability cove- ring and weak probability covering of USQMs, and study properties of these coverings of products.

An adiabatic quantum algorithm is essentially given by three elements: An initial Hamiltonian with known ground state, a problem Hamiltonian whose ground state corresponds to the solution of the given problem, and an evolution schedule such that the adiabatic condition is satisfied. A correct choice of these elements is crucial for an efficient adiabatic quantum computation. In this paper, we propose a hybrid quantum-classical algorithm that, by solving optimization problems with an adiabatic machine, determines a problem Hamiltonian assuming restrictions on the class of available problem Hamiltonians. The scheme is based on repeated calls to the quantum machine into a classical iterative structure. In particular, we suggest a technique to estimate the encoding of a given optimization problem into a problem Hamiltonian and we prove the convergence of the algorithm.

This work proposes a computational procedure that uses a quantum walk in a complete graph to train classical artificial neural networks. The idea is to apply the quantum walk to search the weight set values. However, it is necessary to simulate a quantum machine to execute the quantum walk. In this way, to minimize the computational cost, the methodology employed to train the neural network will adjust the synaptic weights of the output layer, not altering the weights of the hidden layer, inspired in the method of Extreme Learning Machine. The quantum walk algorithm as a search algorithm is quadratically faster than its classic analog. The quantum walk variance is $O(t)$ while the variance of its classic analog is $O(\sqrt{t})$, where $t$ is the time or iteration. In addition to computational gain, another advantage of the proposed procedure is to be possible to know \textit{a priori} the number of iterations required to obtain the solutions, unlike the classical training algorithms based on gradient descendent., Comment: 10 Pages, 4 Figures

We show that in a linear quantum machine, a driven quantum system that evolves while coupled with thermal reservoirs, entanglement between the reservoir modes is unavoidably generated. This phenomenon, which occurs at sufficiently low temperatures and is at the heart of the third law of thermodynamics, is a consequence of a simple process: the transformation of the energy of the driving field into pairs of excitations in the reservoirs. For a driving with frequency $\omega_{d}$ we show entanglement exists between environmental modes whose frequencies satisfy the condition $\omega_{i} + \omega_{j}= \omega_{d}$. We show that this entanglement can persist for temperatures that can be significantly higher than the lowest achievable ones with sideband resolved cooling methods., Comment: Added references

We demonstrate the existence of universal features in the finite-time thermodynamics of quantum machines by considering a many-body quantum Otto cycle in which the working medium is driven across quantum critical points during the unitary strokes. Specifically, we consider a quantum engine powered by dissipative energizing and relaxing baths. We show that under very generic conditions, the output work is governed by the Kibble-Zurek mechanism, i.e., it exhibits a universal power-law scaling with the driving speed through the critical points. We also optimize the finite-time thermodynamics as a function of the driving speed. The maximum power and the corresponding efficiency take a universal form, and are reached for an optimal speed that is governed by the critical exponents. We exemplify our results by considering a transverse-field Ising spin chain as the working medium. For this model, we also show how the efficiency and power vary as the engine becomes critical., Comment: 11 pages, 7 figures

Quantum annealing provides a method to solve combinatorial optimization problems in complex energy landscapes by exploiting thermal fluctuations that exist in a physical system. This work introduces the mapping of a graph coloring problem based on pseudo-Boolean constraints to a working graph of the D-Wave Systems Inc. We start from the problem formulated as a set of constraints represented in propositional logic. We use the SATyrus approach to transform this set of constraints to an energy minimization problem. We convert the formulation to a quadratic unconstrained binary optimization problem (QUBO), applying polynomial reduction when needed, and solve the problem using different approaches: (a) classical QUBO using simulated annealing in a von Neumann machine; (b) QUBO in a simulated quantum environment; (c) actual quantum 1, QUBO using the D-Wave quantum machine and reducing polynomial degree using a D-Wave library; and (d) actual quantum 2, QUBO using the D-Wave quantum machine and reducing polynomial degree using our own implementation. We study how the implementations using these approaches vary in terms of the impact on the number of solutions found (a) when varying the penalties associated with the constraints and (b) when varying the annealing approach, simulated (SA) versus quantum (QA). Results show that both SA and QA produce good heuristics for this specific problem, although we found more solutions through the QA approach.

Effective quantum computation relies upon making good use of the exponential information capacity of a quantum machine. A large barrier to designing quantum algorithms for execution on real quantum machines is that, in general, it is intractably difficult to construct an arbitrary quantum state to high precision. Many quantum algorithms rely instead upon initializing the machine in a simple state, and evolving the state through an efficient (i.e. at most polynomial-depth) quantum algorithm. In this work, we show that there exist families of quantum states that can be prepared to high precision with circuits of linear size and depth. We focus on real-valued, smooth, differentiable functions with bounded derivatives on a domain of interest, exemplified by commonly used probability distributions. We further develop an algorithm that requires only linear classical computation time to generate accurate linear- depth circuits to prepare these states, and apply this to well-known and heavily-utilized functions including Gaussian and lognormal distributions. Our procedure rests upon the quantum state representation tool known as the matrix product state (MPS). By efficiently and scalably encoding an explicit amplitude function into an MPS, a high fidelity, linear-depth circuit can directly be generated. These results enable the execution of many quantum algorithms that, aside from initialization, are otherwise depth-efficient.

We leverage the idea of a statistical ensemble to improve the quality of quantum annealing based binary compressive sensing. Since executing quantum machine instructions on a quantum annealer can result in an excited state, rather than the ground state of the given Hamiltonian, we use different penalty parameters to generate multiple distinct quadratic unconstrained binary optimization (QUBO) functions whose ground state(s) represent a potential solution of the original problem. We then employ the attained samples from minimizing all corresponding (different) QUBOs to estimate the solution of the problem of binary compressive sensing. Our experiments, on a D-Wave 2000Q quantum processor, demonstrated that the proposed ensemble scheme is notably less sensitive to the calibration of the penalty parameter that controls the trade-off between the feasibility and sparsity of recoveries.

The machine learning model can infer desired information on processing data sets without being explicitly programmed. It needs refined data to train the perfect model, hence preprocessing is mandatory. The principal component analysis is desired classical existing methods for preprocessing and it requires polynomial time. Now, the research field of computer science is getting influenced by existence of quantum computations, as it supports exponential operations to be performed in parallel over single step of execution. An intrinsic realization of quantum machine provides simultaneous access to either classical or quantum memory. The objective of paper is to understand the importance of data preprocessing and to suggest quantum based solution that takes the advantage of quantum parallelism and thus can obtain computational speedups. So, we contribute to the emergence of quantum computations, processing aspects using quantum accessible memory models and then classical equivalent quantum principal component analysis algorithm. At last we conclude with the mathematical justification over complexity analysis, computational speedups, and prove that quantum algorithms are efficient along with the suggestions of further directions.

Hybrid quantum-classical algorithms such as the Quantum Approximate Optimization Algorithm (QAOA) are considered as one of the most encouraging approaches for taking advantage of near-term quantum computers in practical applications. Such algorithms are usually implemented in a variational form, combining a classical optimization method with a quantum machine to find good solutions to an optimization problem. The solution quality of QAOA depends to a high degree on the parameters chosen by the classical optimizer at each iteration. However, the solution landscape of those parameters is highly multi-dimensional and contains many low-quality local optima. In this study we apply a Cross-Entropy method to shape this landscape, which allows the classical optimizer to find better parameter more easily and hence results in an improved performance. We empirically demonstrate that this approach can reach a significant better solution quality for the Knapsack Problem.

In the last decades, we have witnessed the rapid growth of Quantum Computing. In the current Noisy Intermediate-Scale Quantum (NISQ) era, the capability of a quantum machine is limited by the decoherence time, gate fidelity and the number of Qubits. Current quantum computing applications are far from the real “quantum supremacy” due to the fragile physical Qubits, which can only be entangled for a few microseconds. Recent works use quantum optimal control to reduce the latency of quantum circuits, thereby effectively increasing quantum volume. However, the key challenge of this technique is the large overhead due to long compilation time. In this paper, we propose AccQOC, a comprehensive static/dynamic hybrid workflow to transform gate groups (equivalent to matrices) to pulses using QOC (Quantum Optimal Control) with a reasonable compilation time budget. AccQOC is composed of static pre-compilation and accelerated dynamic compilation. After the quantum program is mapped to the quantum circuit with our heuristic mapping algorithm considering crosstalk, we leverage static pre-compilation to generate pulses for the frequently used groups to eliminate the dynamic compilation time for them. The pulse is generated using QOC with binary search to determine the latency. For a new program, we use the same policy to generate groups, thus avoid incurring overhead for the “covered” groups. The dynamic compilation deals with “un-covered” groups with accelerated pulse generation. The key insight is that the pulse of a group can be generated faster based on the generated pulse of a similar group. We propose to reduce the compilation time by generating an ordered sequence of groups in which the sum of similarity among consecutive groups in the sequence is minimized. We can find the sequence by constructing a similarity graph – a complete graph in which each vertex is a gate group and the weight of an edge is the similarity between the two groups it connects, then construct a Minimum Spanning Tree (MST) for SG. With the methodology of AccQOC, we reached a balanced point of compilation time and overall latency. The results show that accelerated compilation based on MST achieves $9.88\times$ compilation speedup compared to the standard compilation of each group while maintaining an average $2.43\times$ latency reduction compared with gate-based compilation.

Developing quantum machines which can outperform their classical counterparts, thereby achieving quantum supremacy or quantum advantage, is a major aim of the current research on quantum thermodynamics and quantum technologies. Here we show that a fast-modulated cyclic quantum heat machine operating in the non-Markovian regime can lead to significant heat-current and power boosts induced by the anti-Zeno effect. Such boosts signify a quantum advantage over almost all heat-machines proposed thus far that operate in the conventional Markovian regime, where the quantumness of the system-bath interaction plays no role. The present effect owes its origin to the time-energy uncertainty relation in quantum mechanics, which may result in enhanced system-bath energy exchange for modulation periods shorter than the bath correlation-time., Comment: 16 pages, 10 figures

We study a model of an isothermal steady-state work-to-work converter, where a single quantum two-level system (TLS) driven by time-dependent periodic external fields acts as the working medium and is permanently put in contact with a thermal reservoir at fixed temperature $T$. By combining short-iterative Lanczos (SIL) method and analytic approaches, we study the converter performance in the linear response regime and in a wide range of driving frequencies, from weak to strong dissipation. We show that for our ideal quantum machine several parameter ranges exist where a violation of thermodynamics uncertainty relations (TUR) occurs. We find the violation to depend on the driving frequency and on the dissipation strength, and we trace it back to the degree of coherence of the quantum converter. We eventually discuss the influence of other possible sources of violation, such as non-Markovian effects during the converter dynamics.

Coherence plays a key role in quantum information, which is why it has been considered as a potential resource for quantum machines, with the aim of surpassing classical ones [1, 2, 3, 4, 5, 6]. In Refs. [5, 6], the quantum coherence in the working substance is injected by the drive while in Ref. [1] it comes from the bath which is non-thermal. However there has been no experimental implementation of such a quantum machine using a single qubit as working substance so far.

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 which we call the "Quasi-Ideal clock", 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 and or energy. 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.

An aggregate signature turns multi-message multi-authentication into multi-message single-authentication, reducing the required storage space, transmission cost, and number of verification calculations, and is suitable for fast message authentication in the big data era, particularly in wireless sensor networks and secure email systems. Many aggregate signature schemes have been proposed, including lattice-based ones, which have good resistance to quantum machine attacks. However, the existing lattice-based aggregate signature schemes, which either have strict requirements on the signing order or encounter security risks, are not suitable for the unordered polymerization environment. In this paper, we accordingly propose a lattice-based unordered aggregate signature scheme. The proposed scheme makes use of the intersection method and solves the unordered aggregate problem of lattice signatures with different public keys. Therefore, it avoids both the signing order limitation and the risk of single signature forgery. Furthermore, the scheme follows the improved security model; hence, it is robust against collusion attacks. In addition, the scheme's security depends on the small integer solution problem, which enables the scheme to resist quantum algorithm attacks.

Oblivious transfer (OT) is the most fundamental process in cryptosystems and serves as the basic building block for implementing protocols, such as the secure multi-party computation and the fair electronic contract. However, since most implementations of the Internet of Things are time-sensitive, existing works that are based on traditional public cryptosystems are not efficient or secure under quantum machine attacks. In this paper, we argued that the fastest known 1-out-of-n oblivious transfer ( ${\mathrm {OT}}_{n}^{1}$ ) protocol, which was proposed by Chou, cannot achieve semantic security and is time-consuming due to exponent arithmetic of large parameters. Utilizing NTRUEncrypt and OT extension, we devised a one-round post-quantum secure ${\mathrm {OT}}_{n}^{1}$ protocol that is also proved to be active and adaptively secure under the universal composability framework. Compared with Chou’s protocol, the computational overheads of our scheme are approximately 6 and 1.7 times smaller on the sender and receiver sides, in line with the standard security level.

Quantum bit commitment (QBC) is a quantum version of the classical bit commitment security primitive. As other quantum security primitives and protocols, QBC improves on cheating detection over its classical counterpart. The implementation of the QBC protocol below relies on the use of common quantum gates: the Hadamard gate used for orthonormal bases and the CNOT gate used to swap qubits. The protocol was run and tested on IBM quantum experience (IBM QX). IBM QX offers two different quantum environments: as a simulator and as a real quantum machine. In our implementation, honest and dishonest participants were considered. Results of both the simulation and the quantum execution were compared against the theoretical expectations. The IBM QX simulator gives results that match the theoretical model. The IBM QX real computer deviates from the expected behavior by a measurable amount. Using the standard deviation and the Hamming distance, the conclusion is that the quantum computer is usable as the difference to the simulator is within an acceptable margin of error. The QBC protocol of choice is fully secure against cheating by Bob. The only way Alice can cheat is using multi-dimensional entanglement. The cost for Alice to cheat is exponential in the number of qubits used, namely $$ O(2^{6n + 3k + 1} ) $$.

The essence of temporal universe creation is that any analytical solution has to comply with the boundary condition of our universe; dimensionality and causality constraints. The essence of this book is to show that everything has a price within our temporal (t > 0) universe; energy and time. In mathematics, every postulation needs proof; there exists a solution before searching for the solution. Yet science does not have seem to have a criterion as mathematics does; to prove first that a postulated science exists within our temporal universe. Without such a criterion, fictitious science emerges, as already have been happening in every day’s event. In this book, the author has shown there exists a criterion for a postulated science whether or not it is existed within our universe. The author started this book from Einstein’s relativity to the creation of our temporal universe. He has shown that every subspace within our universe is created by energy and time, in which subspace and time are coexisted. The important aspect is that every science has to satisfy the boundary condition of our universe; causality and dimensionality. Following up with temporal universe, the author has shown a profound relationship with the second law of thermodynamics. He examines the relationship between entropy with science as well as communication with quantum limited subspace throughout the book. The author discusses the paradox of Schrodinger’s Cat (which has been debated by Einstein, Bohr, Schrodinger and many others since 1935) that triggered his discovering that Schrodinger’s quantum mechanics is a timeless machine, in which he has disproved the fundamental principle of superposition within our universe. Since quantum mechanics is a virtual mathematics, he has shown that a temporal quantum machine can, in principle, be built on the top of a temporal platform. This book is intended for cosmologists, particle physicists, astrophysicists, quantum physicists, computer scientists, engineers, professors and students as a reference and research-oriented book.

A quantum annealer solves optimization problems by exploiting quantum effects. Problems are represented as Hamiltonian functions that define an energy landscape. The quantum-annealing hardware relaxes to a solution corresponding to the ground state of the energy landscape. Expressing arbitrary programming problems in terms of real-valued Hamiltonian-function coefficients is unintuitive and challenging. This paper addresses the difficulty of programming quantum annealers by presenting a compilation framework that compiles a subset of C code to a quantum machine instruction (QMI) to be executed on a quantum annealer. Our work is based on a modular software stack that facilitates programming D-Wave quantum annealers by successively lowering code from C to Verilog to a symbolic “quantum macro assembly language” and finally to a device-specific Hamiltonian function. We demonstrate the capabilities of our software stack on a set of problems written in C and executed on a D-Wave 2000Q quantum annealer.

Hybrid quantum-classical algorithms such as the quantum approximate optimization algorithm (QAOA) are considered one of the most promising approaches for leveraging near-term quantum computers for practical applications. Such algorithms are often implemented in a variational form, combining classical optimization methods with a quantum machine to find parameters that maximize performance. The quality of the QAOA solution depends heavily on quality of the parameters produced by the classical optimizer. Moreover, the presence of multiple local optima makes it difficult for the classical optimizer to identify high-quality parameters. In this paper we study the use of a multistart optimization approach within QAOA to improve the performance of quantum machines on important graph clustering problems. We also demonstrate that reusing the optimal parameters from similar problems can improve the performance of classical optimization methods, expanding on similar results for MAXCUT.

Quantum algorithms of factoring problem have been paid more and more attention since Shor’s algorithm was proposed. Combining the current quantum computer hardware level and integer factorization quantum algorithms, this paper proposes a “classical + quantum” hybrid solution. This scheme first adopts classical methods and corresponding rules in the preprocessing step to simplify the nonlinear equations, which is used to reduce the number of qubits needed for the cost Hamiltonian. Then the variational quantum algorithm is used to find the approximate ground state of the cost Hamiltonian, which encodes the solution of the nonlinear equations. The program was verified on the IBM QX4 quantum machine, and the results showed that this hybrid solution can effectively reduce the quantum resources required to solve the nonlinear equations.

We present a quantumly-enhanced protocol to achieve unconditionally secure delegated classical computation where the client and the server have both their classical and quantum computing capacity limited. We prove the same task cannot be achieved using only classical protocols. This extends the recent work of Anders and Browne on the computational power of correlations to a security setting. Concretely, we present how a client with access to a non-universal classical gate such as a parity gate could achieve unconditionally secure delegated universal classical computation by exploiting minimal quantum gadgets. In particular, unlike the universal blind quantum computing protocols, the restriction of the task to classical computing removes the need for a full universal quantum machine on the side of the server and makes these new protocols readily implementable with the currently available quantum technology in the lab.

Within the last several years quantum machine learning (QML) has begun to mature; however, many open questions remain. Rather than review open questions, in this perspective piece I will discuss my view about how we should approach problems in QML. In particular I will list a series of questions that I think we should ask ourselves when developing quantum algorithms for machine learning. These questions focus on what the definition of quantum ML is, what is the proper quantum analogue of QML algorithms is, how one should compare QML to traditional ML and what fundamental limitations emerge when trying to build QML protocols. As an illustration of this process I also provide information theoretic arguments that show that amplitude encoding can require exponentially more queries to a quantum model to determine membership of a vector in a concept class than classical bit-encodings would require; however, if the correct analogue is chosen then both the quantum and classical complexities become polynomially equivalent. This example underscores the importance of asking ourselves the right questions when developing and benchmarking QML algorithms.

We consider the problem of correctly classifying a given quantum two-level system (qubit) which is known to be in one of two equally probable quantum states. We assume that this task should be performed by a quantum machine which does not have at its disposal a complete classical description of the two template states, but can only have partial prior information about their level of purity and mutual overlap. Moreover, similarly to the classical supervised learning paradigm, we assume that the machine can be trained by $n$ qubits prepared in the first template state and by $n$ more qubits prepared in the second template state. In this situation we are interested in the optimal process which correctly classifies the input qubit with the largest probability allowed by quantum mechanics. The problem is studied in its full generality for a number of different prior information scenarios and for an arbitrary size $n$ of the training data. Finite size corrections around the asymptotic limit $n\rightarrow \infty$ are also derived. When the states are assumed to be pure, with known overlap, the problem is also solved in the case of d-level systems., 15 pages without appendix (total 19), 5 figures, typos corrected, added plots, new results on the d-level system case, new noise simulations with QISKit Aer

Machine learning algorithms often take inspiration from established results and knowledge from statistical physics. A prototypical example is the Boltzmann machine algorithm for supervised learning, which utilizes knowledge of classical thermal partition functions and the Boltzmann distribution. Recently, a quantum version of the Boltzmann machine was introduced by Amin, et. al., however, non-commutativity of quantum operators renders the training process by minimizing a cost function inefficient. Recent advances in the study of non-equilibrium quantum integrable systems, which never thermalize, have lead to the exploration of a wider class of statistical ensembles. These systems may be described by the so-called generalized Gibbs ensemble (GGE), which incorporates a number of "effective temperatures". We propose that these GGE's can be successfully applied as the basis of a Boltzmann-machine-like learning algorithm, which operates by learning the optimal values of effective temperatures. We show that the GGE algorithm is an optimal quantum Boltzmann machine: it is the only quantum machine that circumvents the quantum training-process problem. We apply a simplified version of the GGE algorithm, where quantum effects are suppressed, to the classification of handwritten digits in the MNIST database. While lower error rates can be found with other state-of-the-art algorithms, we find that our algorithm reaches relatively low error rates while learning a much smaller number of parameters than would be needed in a traditional Boltzmann machine, thereby reducing computational cost., Version published in J. Stat. Mech. Improved discussion, references added. 16 pages

Continuous-time stochastic processes pervade everyday experience, and the simulation of models of these processes is of great utility. Classical models of systems operating in continuous-time must typically track an unbounded amount of information about past behaviour, even for relatively simple models, enforcing limits on precision due to the finite memory of the machine. However, quantum machines can require less information about the past than even their optimal classical counterparts to simulate the future of discrete-time processes, and we demonstrate that this advantage extends to the continuous-time regime. Moreover, we show that this reduction in the memory requirement can be unboundedly large, allowing for arbitrary precision even with a finite quantum memory. We provide a systematic method for finding superior quantum constructions, and a protocol for analogue simulation of continuous-time renewal processes with a quantum machine., Comment: 13 pages, 8 figures, title changed from original version

Classical engines turn thermal resources into work, which is maximized for reversible operations. The quantum realm has expanded the range of useful operations beyond energy conversion, and incoherent resources beyond thermal reservoirs. This is the case of entanglement generation in a driven-dissipative protocol, which we hereby analyze as a continuous quantum machine. We show that for such machines the more irreversible the process the larger the concurrence. Maximal concurrence and entropy production are reached for the hot reservoir being at negative effective temperature, beating the limits set by classic thermal operations on an equivalent system., Comment: 4 figures, 10 pages