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Having access to a unique quantum circuit that one wants to protect against use by others is a very likely scenario in industrial computing. However, currently, users rely on classical computer security schemes, which have known shortcomings. In this paper, we introduce a novel protection scheme along with a survey of other known methods to protect quantum information. In particular, we review physically unclonable functions (PUFs), obfuscation, and introduce quantum logic locking (QLL). The latter technique provisions end users to protect their circuit from an adversary through the use of a secret key.

A common assumption in an open quantum system is that the noise induced by the environment, due to the interaction between a quantum system and its environment, is responsible for the disappearance of quantum properties. Interestingly, Barreiro et al. [Nature470 (2011) 486] show, experimentally, using an open-system quantum ion traps simulator, an environment state can be engineered and controlled to pump an arbitrary quantum system toward a maximally entangled state and thus can be considered a resource for quantum information processing. Here, we demonstrate this idea to pump an arbitrary maximally mixed state into Greenberger–Horne–Zeilinger (GHZ) state by simulating our quantum circuit using one of the IBM Q processors. Barreiro et al. [Nature470 (2011) 486] offer the circuits for the execution of the GHZ pumping. Nevertheless, those are collected gates that are suitable to the trapped-ions platform, so their circuits implementation on the IBM Q devices would result in large depth circuits and thus requires many gates. Consequently, we suggest a different circuit structure that follows a similar goal, but has been considered the features of the IBM Q platform. Moreover, we run the simulation of our circuit using the QASM simulator and free-web-based interface, IBM Quantum Experience, with and without error mitigation, to investigate the effect of the noise on the preparation of the initial mixed states of the qubits in addition to the population of the target state of the system. [ABSTRACT FROM AUTHOR]

We propose a method for efficient mixed polarity multiple controlled Toffoli (MPMCT) gate decomposition from the perspective of a cost metric related to Toffoli gates, namely Toffoli-depth. When using the technique presented in a previous study, there is a range in which Toffoli-depth (consequently T-depth) of the implemented circuit increases proportionally as the number of provided (clean) work qubits increases. In other words, using the previous technique may result in more inefficient MPMCT gates even though the number of helpful work qubits has increased. In this work, a technique is devised to provide sufficient help from clean work qubits at the central part of the implemented circuit as many as possible, thereby addressing the issues with the previous technique. Meanwhile, one of the representative algorithms that use MPMCT gates is Grover’s algorithm. We show the implementation results for MPMCT gates according to the number of work qubits, using Grover’s algorithm as an example. It is experimentally demonstrated that T-depth decreases much more quickly when using our method than the previous method. [ABSTRACT FROM AUTHOR]

With the advancement of technological footprints, high-end computation techniques, like quantum computation, have made significant progress in the design industry. Although quantum computation has proved itself as the next-generation computing paradigm, it is facing several design challenges, and one such design issue is in the form of the Nearest Neighbour (NN)t. This much-talked NN property demands the qubits in operating quantum gates to be adjacent, and a circuit should satisfy this NN property to be eligible for implementation. Considering the importance of NN enforcement in implementing circuits, we introduce a synthesis approach for the efficient transformation of reversible circuits to equivalent LNN representations. Our main focus in this work is to minimize the use of SWAP gates in designing NN-satisfied MCT-based reversible circuits. Towards transforming input circuits to LNN architecture, we have exploited a template matching scheme followed by two-qubit reordering policies, global and local, to improve the NN designs and reduce SWAP utilization. In finding the global solution, here we have used a dynamic programming algorithm where the initial order of qubit lines gets changed, while a heuristic-based SWAP placement function is used for finding a local qubit order sequence. The proposed synthesis workflow has been tested over an extensive set of benchmark functions, and comparison with the reported design approaches showed a substantial reduction in cost parameters. [ABSTRACT FROM AUTHOR]

Quantum Fisher information matrix (QFIM) is a fundamental quantity in quantum physics, which closely links to diverse fields such as quantum metrology, phase transitions, entanglement witness, and quantum speed limit. It is crucial in quantum parameter estimation, central to the ultimate Cramér-Rao bound. Recently, the evaluation of QFIM using quantum circuit algorithms has been proposed for systems with multiplicative parameters Hamiltonian. However, systems with generic Hamiltonians still lack these proposed schemes. This work introduces a quantum-circuit-based approach for evaluating QFIM with generic Hamiltonians. We present a time-dependent stochastic parameter-shift rule for the derivatives of evolved quantum states, whereby the QFIM can be obtained. The scheme can be executed in universal quantum computers under the family of parameterized gates. In magnetic field estimations, we demonstrate the consistency between the results obtained from the stochastic parameter-shift rule and the exact results, while the results obtained from a standard parameter-shift rule slightly deviate from the exact ones. Our work sheds new light on studying QFIM with generic Hamiltonians using quantum circuit algorithms. [ABSTRACT FROM AUTHOR]

The emergence of quantum computers threatens current cryptographic systems, and NIST is preparing for the post-quantum era through the post-quantum cryptography (PQC) contest. CRYSTALS-Kyber is a lattice-based cipher suite that is used as a PQC standard. Lattice-based cryptography is considered quantum-safe for quantum computing because a quantum algorithm that can more efficiently solve the lattice problem of lattice-based cryptography compared to a classic algorithm has not been reported as yet. In this paper, we present quantum circuits tailored to NTT and inverse NTT, employed for optimized polynomial multiplication within CRYSTALS-Kyber. The proposed quantum circuits operate at Z 3329 [ X ] /( X 256 +1), which are the parameters of CRYSTALS-Kyber. We provide an in-depth description of the NTT/InvNTT quantum circuit's operation and subsequently assess and analyze the quantum resources necessary for these functions. The NTT/InvNTT quantum circuits comprise four unique sub-functions, with the InvNTT additionally incorporating Barrett reduction. To the best of our knowledge, this represents the inaugural implementation of the CRYSTALS-Kyber NTT/InvNTT quantum circuits. We anticipate that our findings will aid in analyzing the security strengths of quantum computers for lattice-based cryptography. [ABSTRACT FROM AUTHOR]

In recent years, there has been a growing interest in the potential of quantum computing for enhancing the security and efficiency of blockchain technology. While quantum blockchain protocols offer improved security over their classical counterparts, implementing such protocols on present-day quantum computers poses difficulties due to the limited number of qubits and quantum gates and the significant effects of noise. In this paper, we propose a set of improvements for implementing a quantum blockchain protocol based on hypergraphs that aim to reduce the required resources and operations and increase noise tolerance. Specifically, we focus on enhancing the state-of-the-art quantum circuits that underpin the quantum blockchain by optimizing the so-called T-count and T-depth, which represent the number of quantum gates and the circuit depth, respectively. Our proposed implementations also leverage proven error detection and correction codes to improve noise tolerance. To evaluate the effectiveness of our proposed improvements, we tested them on real quantum devices. Our results demonstrate a significant reduction in the T-count and T-depth. Overall, our proposed improvements provide a promising direction for the practical implementation of quantum blockchain protocols on current quantum computers and lay a foundation for further research in this area. [ABSTRACT FROM AUTHOR]

This work researches the implementation of the AES family with Pauli-X gates, CNOT gates and Toffoli gates as the underlying quantum logic gate set. First, the properties of quantum circuits are investigated, as well as the influence of Pauli-X gates, CNOT gates and Toffoli gates on the performance of the circuits constructed with those gates. Based on these properties and the observations on the hardware circuits built by Boyar et al. and Zou et al., it is possible to construct quantum circuits for AES's Substitution-box (S-box) and its inverse (S-box - 1 ) by rearranging the classical implementation to three parts. Since the second part is treated as a 4-bit S-box in this paper and can be dealt with by existing tools, a heuristic is proposed to search optimized quantum circuits for the first and the third parts. In addition, considering the number of parallelly executed S-boxes, the trade-offs between the qubit consumption and T · M values for the round function and key schedule of AES are studied. As a result, quantum circuits of AES-128, AES-192 and AES-256 can be constructed with 269, 333 and 397 qubits, respectively. If more qubits are allowed, quantum circuits that outperform state-of-the-art schemes in the metric of T · M value for the AES family can be reported, and it needs only 474, 538 and 602 qubits for AES-128, AES-192 and AES-256, respectively. [ABSTRACT FROM AUTHOR]

Reversible logic is used increasingly to design digital circuits with lower power consumption. The parity preserving (PP) property contributes to detect permanent and transient faults in reversible circuits by comparing the input and output parity. Multiplication is also considered one of the primary operations in both digital and analog circuits due to its wide applications in digital signal processing and computer arithmetic operations. Accordingly, Vedic mathematics, as a set of techniques sutras, has become popular and is extensively used to solve mathematical problems more efficiently and faster. This work proposes three PP reversible blocks, N1, N2, and N3, which are used to develop a novel effective 2‐bit PP reversible Vedic multiplier and 4‐bit ripples carry adders (RCAs). Moreover, 2‐bit Vedic multiplier and RCA are used to develop the 4‐bit PP reversible Vedic multiplier. The proposed designs outperform the most relevant state‐of‐the‐art structures in terms of garbage output (GO), constant input (CI), gate count (GC), and quantum cost (QC). Average savings of 22.37%, 35.44%, 35.44%, and 34.76%, and 17.76%, 26.60%, 24.52%, and 27.27% respectively, are observed for two‐bit and four‐bit PP reversible Vedic multipliers in terms of QC, GO, CI and GC as compared to previous works. [ABSTRACT FROM AUTHOR]

The max independent set problem is a well-known NP problem and has applications in many scenarios. Traditional exact algorithms need exponential time complexity to solve the max independent set problem. In order to solve the max independent set problem more efficiently, proposes a quantum circuit solution based on the quantum approximate optimization algorithm. In this scheme, derives the Hamiltonian expression of the max independent set problem from the mathematical model of the max independent set, designes the quantum circuit based on the quantum approximation optimization algorithm. Using the COBYLA classical optimization algorithm to optimize the parameters in the parameter quantum gate, and using the quantum development framework Qiskit provided by IBM to conduct simulation experiments. Simulation results show that the solution of the max independent set problem can be obtained in polynomial time with high probability using the quantum approximate optimization algorithm, achieving an exponential speedup. Quantum approximate optimization algorithm is feasible and effective for solving the max independent set problem. [ABSTRACT FROM AUTHOR]

Having access to a unique quantum circuit that one wants to protect against use by others is a very likely scenario in industrial computing. However, currently, users rely on classical computer security schemes, which have known shortcomings. In this paper, we introduce a novel protection scheme along with a survey of other known methods to protect quantum information. In particular, we review physically unclonable functions (PUFs), obfuscation, and introduce quantum logic locking (QLL). The latter technique provisions end users to protect their circuit from an adversary through the use of a secret key. [ABSTRACT FROM AUTHOR]

This paper presents an innovative way of quantum circuit optimization; we propose an automated superconducting circuit calibration using deep reinforcement learning (ASCC-DRL). A simplified model of a transmon qubit coupled to a cavity resonator is used to demonstrate a quantum circuit. We analyzed the circuit through its equivalent two-mode lumped-element representation of the distributed circuit and derived the equivalent Hamiltonian translation of the circuit with the non-linearity of the Josephson Junctions. We adopted the parametrized qubit junctions and used the component physical value to tune the circuits to maximize the fidelity of the desired entangle state and the resulting quantum circuit state. However, quantum systems are susceptible to environmental parasitics and noise; therefore, a reliable optimization technique is essential to maintain high fidelity across the system. For optimization, we integrate deep reinforcement learning using deep deterministic policy gradient techniques as our mechanism for our AI module to optimize the fidelity of the superconducting quantum circuit. We demonstrate the feasibility of this approach by training the agent in three distinct environments to achieve the highest possible best rewards. We achieved an average fidelity (best rewards) of 0.92, which is 94% of the statically tuned circuit.

The creation of quantum circuit architecture based on the quantum perceptron algorithm to classify marketing bank data is proposed in this work. A quantum circuit is a quantum gate made up of two quantum gates. Quantum bits are used in this study's computation. The primary proposed learning method was not ideal, which is the context of this study. The percentage of qubits measurement value is still 90.7 percent. It is essential to raise the value of the qubit rate. Using the IBM Quantum Experience quantum computer, researchers measured, trained, and tested the quantum circuit architecture. Bank marketing data from the UCI Machine Learning Repository was used. A quantum circuit architecture model results from this research the quantum circuit measurement results.

Current quantum computers have a limited number of resources and are heavily affected by internal and external noise. Therefore, small, noise-tolerant circuits are of great interest. With regard to circuit size, it is especially important to reduce the number of required qubits. Concerning to fault-tolerance, circuits entirely built with Clifford+T gates allow the use of error correction codes. However, the T-gate has an excessive cost, so circuits with a high number of T-gates should be avoided. This work focuses on optimising in such terms an operation that is widely used in larger circuits and algorithms: the calculation of the absolute-value of two's complement encoded integers. The proposed circuit halves the number of required T gates with respect to the best circuit currently available in the literature. Moreover, our circuit requires at least 2 qubits less than the other circuits for such an operation. [ABSTRACT FROM AUTHOR]

The electronic computer possesses powerful computing capabilities, but it is still limited by Moore's law. Quantum computers are thus found capable of not only overcoming the constraints of Moore's law but also taking advantage of the quantum effect to increase their arithmetic power for many problems. The minimum vertex cover problem is a classical NP-complete problem, and its traditional algorithms usually require exponential computational complexity. Herein, two algorithms are proposed to solve the minimum vertex cover problem. The first algorithm achieves its classical solution, while the second algorithm is based on the Grover search algorithm to obtain the solution to the quantum computing algorithm of the problem and verify its feasibility via quantum circuit experiments. Comparing the two algorithms, it can be concluded that the quantum algorithm can improve the operational speed of the minimum vertex cover problem by order of magnitude of the square root. [ABSTRACT FROM AUTHOR]

One of the most famous algorithms in quantum computations is the Grover search algorithm. Under certain assumptions, this algorithm provides quantum speedup for the search problem. We always assume that we can build it efficiently, but assume for a moment that you are limited in the gates you are allowed to use for the implementation of the Grover diffusion operator. For example, if you need to use at most two-channel gates, what would be the complexity of the decomposition circuit for the diffusion operator itself? Here, we show that it is sufficient to use just only the Z-base operators (such Z 2 n and controlled CZ) and Hadamard operators, but also we show that in this case, the number of used gates can grow exponentially. At least, the number of the multi-controlled Z gates needed to build diffusion operator decomposition circuit only of the following gates: Z, controlled Z, multi-controlled Z gates, or is summed into 2 n - 1 for the n-dimensional phase shift and cannot be decreased if we will not allow other gates. [ABSTRACT FROM AUTHOR]

In recent years, the quantum implementation of symmetric ciphers has received much attention. In this paper, we investigate the construction of quantum circuits based on different gate sets for the SM4 block cipher, which is the national standard of commercial cryptography of China and is standardized in ISO/IEC. First, we construct reversible circuits using Pauli-X gates, CNOT gates and Toffoli gates (i.e., the NCT gate set) for the SM4 S-box, based on which we design two circuits for the SM4 S-box with Clifford+T gates by applying the quantum And gate and existing decomposition scheme of the Toffoli gate, respectively. In addition, we propose a new in-place 1 implementation for the linear transformation in the SM4 round function. Finally, taking the qubit consumption and the T · M value (the product of qubit consumption and nonlinear gate depth of a quantum circuit) as metrics, we investigate the application of various circuits we designed to the construction of quantum circuits for SM4. The results show that we can always construct a subroutine/stand-alone circuit based on the NCT gate set, or based on Clifford+T gates for SM4 with fewer qubits or lower T · M value than existing state-of-the-art implementations. [ABSTRACT FROM AUTHOR]

Reversible quantum circuits are constructed using different types and numbers of quantum gates. Optimizing the number of gates to be used while creating quantum circuits reduces the cost and complexity. It is important to know the number of inputs, outputs, and gates for obtaining and optimizing state tables in reversible quantum circuits. In addition, these parameters are also used to detect faults that may occur in quantum circuits. There is a lack of determination of the input, output, and gate numbers for quantum circuits in the literature. In addition, a limited number of standard quantum circuits are used to test the applications made in the literature. It has been determined that there are very few datasets that can be used in this context. Elimination of these deficiencies in the literature constitutes the aim of our study, and the proposed method constitutes the originality of our study. In this study, the number of gates and inputs were determined by using Yolo (You Only Look Once) based methods. A large dataset consisting of CNOT, Feynman, and Toffoli gates was created using the "MATLAB" and "RCViewer+" programs. In this study, a total of 5000 quantum circuits with 1-8 gate numbers and 3-7 input numbers were created. Gates and inputs are labeled on the obtained datasets. YoloV4, YoloV7, and YoloV7x methods were applied to the tagged datasets with a training and testing ratio of 80:20. 87.1%, 89.7% and 89.3% mAP were calculated for the YoloV4, YoloV7 and YoloV7x methods, respectively. The proposed method was run for 2800 iterations and the best result was obtained with the YoloV7 algorithm. [ABSTRACT FROM AUTHOR]

Problem instances of a size suitable for practical applications are not likely to be addressed during the noisy intermediate‐scale quantum (NISQ) period with (almost) pure quantum algorithms. Hybrid classical‐quantum algorithms have potential, however, to achieve good performance on much larger problem instances. One such hybrid algorithm on a problem of substantial importance: vehicle routing for supply chain logistics with multiple trucks and complex demand structure is investigated. Reinforcement learning with neural networks with embedded quantum circuits is used. In such neural networks, projecting high‐dimensional feature vectors down to smaller vectors is necessary to accommodate restrictions on the number of qubits of NISQ hardware. However, a multi‐head attention mechanism is used where, even in classical machine learning, such projections are natural and desirable. Data from the truck routing logistics of a company in the automotive sector is considered, and the methodology is applied by decomposing into small teams of trucks and results are found comparable to human truck assignment. [ABSTRACT FROM AUTHOR]

We propose a novel and hybrid quantum-classical algorithm that requires only O (log HW) qubits and reduces the multi-qubit gate costs required to represent an image of dimension (H × W) . In this algorithm, no qubit is needed to store the color information of the image. We represent the location information of an image with a superposition of mutually orthogonal vectors of an arbitrary basis and store the pixel information in the phases of the corresponding basis vectors without any extra qubit cost. We further present a classical algorithm to encode the phases and show that the inclusion of the classical algorithm significantly reduces the number of multi-qubit quantum gates required for image representation. Finally, we implement our algorithm on the classical simulator provided by IBM quantum as a proof of concept. [ABSTRACT FROM AUTHOR]

Crosstalk is the primary source of noise in quantum computing equipment. The parallel execution of multiple instructions in quantum computation causes crosstalk, which causes coupling between signal lines and mutual inductance and capacitance between signal lines, destroying the quantum state and causing the program to fail to execute correctly. Overcoming crosstalk is a critical prerequisite for quantum error correction and large-scale fault-tolerant quantum computing. This paper provides an approach for suppressing crosstalk in quantum computers based on multiple instruction exchange rules and duration. Firstly, for the majority of the quantum gates that can be executed on quantum computing devices, a multiple instruction exchange rule is proposed. The multiple instruction exchange rule reorders quantum gates in quantum circuits and separates double quantum gates with high crosstalk on quantum circuits. Then, time stakes are inserted based on the duration of different quantum gates, and quantum gates with high crosstalk are carefully separated in the process of quantum circuit execution by quantum computing equipment to reduce the influence of crosstalk on circuit fidelity. Several benchmark experiments verify the proposed method's effectiveness. In comparison to previous techniques, the proposed method improves fidelity by 15.97% on average. [ABSTRACT FROM AUTHOR]

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Random numbers are of vital importance in fields such as cyptography and scientific simulations. However, it is well known how difficult it is for classical computers to generate random numbers. This is not the case for quantum computers, which are able to genuinely generate random numbers thanks to the property of superposition and their counter-intuitive concept of measurement. However, despite the simplicity of designing a circuit that generates a random number between 0 and 2 N − 1 (being N the number of available qubits), designing a quantum circuit to generate a number within a specific interval is far from trivial. This paper proposes a customizable circuit design to generate random numbers. The circuit is non- hardware dependent, it allows fault-tolerance, and it can be used by current quantum devices. Therefore, it is a valuable tool for all those quantum applications and algorithms that need to work with random numbers. Moreover, a comparator circuit has also been designed as part of this work. This comparator is the best currently available in the literature in terms of qubits, T-count, and T-depth. It is therefore a useful tool for any other circuit or algorithm where this operation is needed. [ABSTRACT FROM AUTHOR]

Universal quantum gates lie at the heart of designing quantum computer. Here two compact quantum circuits for implementing post‐selected controlled‐phase‐flip (CPF) gate and Toffoli gate with linear optics are constructed assisted by one and two single photons, respectively. The current existing maximum success probability of 1/4 for linear optical CPF gate is achieved by resorting to an ancillary single photon rather than an entangled photon pair or two single photons. Remarkably, the presented Toffoli gate is accomplished with current maximum success probability of 1/30 and unity fidelity in principle, without using additional entangled photon pairs and the standard decomposition‐based approach. Linear optical implementations of the presented two universal gates are feasible and economical under current technology, and provide a potential application in large‐scale optical quantum computing. [ABSTRACT FROM AUTHOR]

Sentiment classification is a valuable application of natural language processing that has seen wide usage in optimizing business processes. This paper explores a novel implementation of sentiment analysis using the Variational Quantum Algorithms (VQA) framework. As ansatz choice determines model performance in VQA, this paper proposes an alternative ansatz for the sentiment classification task in quantum representation. Specifically, it builds upon previous work in quantum sentiment classification by proposing an alternative ansatz to the Instantaneous Quantum Polytime ansatz, entitled Simple Sentiment Analysis (SimpleSA) ansatz. A key feature of the SimpleSA ansatz is the decision to neglect noun parameterization. The proposed SimpleSA has less complexity than the other ansätze in terms of the number of parameters and the number of gates. Moreover, experimental results show that the SimpleSA ansatz with H-CNOT-Rz-H compound block construction outperforms the Instantaneous Quantum Polytime (IQP) ansatz at 85.00% accuracy. Furthermore, SimpleSA optimization converges 20.89% faster than Instantaneous Quantum Polytime (IQP) for the Simultaneous Perturbation Stochastic Approximation (SPSA) method with 130 iterations. The proposed work is useful for applications of quantum computers for sentiment analyses and classifications.

Quantum machine learning (QML) has received increasing attention due to its potential to outperform classical machine learning methods in problems, such as classification and identification tasks. A subclass of QML methods is quantum generative adversarial networks (QGANs), which have been studied as a quantum counterpart of classical GANs widely used in image manipulation and generation tasks. The existing work on QGANs is still limited to small-scale proof-of-concept examples based on images with significant downscaling. Here, we integrate classical and quantum techniques to propose a new hybrid quantum–classical GAN framework. We demonstrate its superior learning capabilities over existing quantum techniques by generating $28 \times 28$ pixels grayscale images without dimensionality reduction or classical pre/postprocessing on multiple classes of the standard Modified National Institute of Standards and Technology (MNIST) and Fashion MNIST datasets, which achieves comparable results to classical frameworks with three orders of magnitude less trainable generator parameters. To gain further insight into the working of our hybrid approach, we systematically explore the impact of its parameter space by varying the number of qubits, the size of image patches, the number of layers in the generator, the shape of the patches, and the choice of prior distribution. Our results show that increasing the quantum generator size generally improves the learning capability of the network. The developed framework provides a foundation for future design of QGANs with optimal parameter set tailored for complex image generation tasks.

Variational quantum algorithms, which utilize parameterized quantum circuits (PQCs), are promising tools to achieve quantum advantage for optimization problems on near-term quantum devices. Their PQCs have been conventionally constructed from parameterized rotational angles of single-qubit gates around a predetermined set of axes and two-qubit entangling gates, such as cnot gates. We propose a method to construct a PQC by continuous parameterization of both the angles and the axes of its single-qubit rotation gates. The method is based on the observation that when rotational angles are fixed, optimal axes of rotations can be computed by solving a system of linear equations whose coefficients can be determined from the PQC with small computational overhead. The method can be further simplified to select axes freely from continuous parameters with rotational angles fixed to $\pi$. We show the simplified free-axis selection method has better expressibility against other structural optimization methods when measured with Kullback–Leibler divergence. We also demonstrate PQCs with free-axis selection are more effective to search the ground states of Hamiltonians for condensed matter physics, quantum chemistry, and combinatorial optimization. Because free-axis selection allows designing PQCs without specifying their single-qubit rotational axes, it may significantly improve the handiness of PQCs.

Works on quantum computing and cryptanalysis have increased significantly in the past few years. Various constructions of quantum arithmetic circuits as one of the primary elements in the field have also been proposed. However, there have only been a few studies on finite field inversion despite its essential use in realizing quantum algorithms, such as in Shor’s algorithm for Elliptic Curve Discrete Logarithm Problem (ECDLP). In this study, we propose to reduce the depth of the existing quantum Fermat’s Little Theorem (FLT)-based inversion circuit for the binary finite field. In particular, we propose to follow a complete waterfall approach to translate the Itoh-Tsujii’s variant of FLT to the corresponding quantum circuit and remove the inverse squaring operations employed in the previous work by Banegas et al., lowering the number of CNOT gates (i.e., CNOT count) as well as slightly reducing the $T$ depth, which contributes to a reduced overall depth and gate count. Furthermore, we concretely verify our method and compare it with the previous work in Qiskit, a quantum computer simulation environment, by constructing both our method and the previous work from scratch and performing the resource analysis. Additionally, we propose employing the relative-phase Toffoli gate by Gidney as opposed to the standard Toffoli implementation, which yields a significantly lower $T$ depth while further reducing the overall depth. Our approach can serve as an alternative for a time-efficient implementation.

The negative effects caused by geometric distortion can be removed to the maximum extent possible through appropriate geometric transformations, allowing us to focus on the image content itself in subsequent processing and recognition. Therefore, geometric transformations are often used as a pre-processing step for other image processing applications. In this paper, quantum algorithms are designed to implement geometric transformations, including two-point swapping, circular translation, flipping transformations and right-angle rotation, across a quantum image representation QIRHSI (Quantum Image Representation based on HSI color space) which is built on HSI (Hue-Saturation-Intensity) color space. The above geometric transformations are realized by quantum circuits composed of elementary quantum gates. By analyzing the complexity of the fundamental quantum gates needed for the above geometric transformations, it is found that the global transformations (circular translation, flip transformation and right-angle rotation) are lower than the local transformation (two-point swapping). The proposed geometric transforms are used to facilitate the applications of quantum images with low complexity and high efficiency.

Quantum computing is a rapidly growing area that solves certain problems with exponential speed up. Quantum software is more error-prone than conventional software due to the principle of quantum mechanics and the cryogenic environment of a quantum computer. Cyclomatic complexity play a significant role in the generation of test cases. In this paper, we will introduce the Cyclomatic complexity concept to represent the logical complexity of a quantum program. Cyclomatic complexity represents the number of independent paths and paths generated due to the superposition of each control qubit. Furthermore, coverage criteria based on structural testing have been proposed for testing a quantum program. [ABSTRACT FROM AUTHOR]

In the development of quantum image steganography, the visual effect of the image has always been the focus of scholars’ research. Based on the classical Gray code algorithm and the least significant bit (LSB) algorithm, a novel quantum image steganography algorithm is proposed in this paper. Firstly, the Arnold scrambling method is used to scramble the information image. In the meantime, the scrambled information image is expanded to the same size as the carrier image by using the quantum expansion method. Secondly, the double-layer Gray code rule is applied to the carrier pixels. This operation can reduce the change rate of LSB of carrier pixels. At the same time, the key image used in the extracting phase is generated. The key image improves the security of the algorithm. The classical Gray code algorithm needs to change 50% bits of the LSB of the carrier pixels when embedding. The proposed algorithm in this paper only needs to change 25% bits of the LSB of the carrier pixels when embedding. The PSNR value of the algorithm proposed in this paper can be around 54dB in the visual effect experiment, which is around 3dB higher than that of the classical Gray code algorithm. The robustness experiment is also better compared with other algorithms. [ABSTRACT FROM AUTHOR]

Grover algorithm is a quantum search algorithm that can find the target state efficiently. However, with the increase of the amount of searching data, Grover􀆳s quantum circuit is faced with the complex gate decomposition problem. In today􀆳s NISQ era, resources are very limited, so circuit depth is an important metric. This paper introduces a two-stage quantum search algorithm based on divideand-conquer, which can run quickly in parallel on a quantum computer. A circuit optimization method is proposed to reduce the number of iterations by using block-level oracle circuit. Combining this method with divide-and-conquer idea, it is defined as 2P-Grover algorithm. The simulation experiment was carried out on the quantum computing framework Cirq. The experimental results show that, compared with Grover algorithm, the 2P-Grover algorithm can reduce the circuit depth by at least 1.2 times and maintain a high probability of search success. [ABSTRACT FROM AUTHOR]

A quantum implementation of image registration is proposed based on a quantum version of Powell's conjugate direction method in this study. Quantum Powell's method can find the minimum parameters of similarity measurement between the quantum fixed and moving images in the solution space when the quantum moving image performs geometric transformation. By combining quantum computing units and basic quantum gates, a series of quantum circuits are designed to implement the quantum image registration method which contains quantum image similarity measure, quantum one-dimensional search algorithm, quantum updating search direction array and quantum termination condition of Powell's iteration. To improve the search efficiency of the algorithm, a quantum version of golden section search method is proposed. The simulation experiments verify the validity of quantum Powell's image registration method. [ABSTRACT FROM AUTHOR]

The maximum cut problem is a typical problem in the quantum approximate optimization algorithm (QAOA), and Ansatz circuit is an important part of the algorithm. In order to reduce the construction cost of various graph structures in Q AOA and improve its stability, this paper analyzed the optimizability of the circuit, combined the point edge storage characteristics of Dijkstra algorithm, proposed a Dijkstra-like optimization algorithm for the circuit, and applied it to the QAOA maximum cut problem. The paper used the Qiskit quantum framework to simulate the correctness of the optimization algorithm and used the real environment of IBM Quantum Composer to perform comparative experiments to verify the stability of the optimization. After comparing with the initial algorithm, the proposed algorithm reduced the CNOT gate by about 40% and significantly improves its stability. The results show that the Dijkstra-like optimization algorithm can optimize the QAOA maximum cut problem of multiple graph structures. [ABSTRACT FROM AUTHOR]

The unraveling of open quantum system dynamics in terms of stochastic quantum trajectories offers a picture of open system dynamics that consistently considers memory effects stemming from the finite correlation time of environment fluctuations. These fluctuations significantly influence the coherence and energy transport properties of excitonic systems. When their correlation time is comparable to the timescale of the Hamiltonian evolution, it leads to the departure of open system dynamics from the Markovian limit. In this work, we leverage the unraveling of exciton dynamics through stochastic Hamiltonian propagators to design quantum circuits that simulate exciton transport, capturing finite memory effects. In addition to enabling the synthesis of parametrizable quantum circuits, stochastic unitary propagators provide a transparent framework for investigating non-Markovian effects on exciton transport. Our analysis reveals a nuanced relationship between environment correlation time and transport efficiency, identifying a regime of ‘memory-assisted’ quantum transport where time-correlated fluctuations allow the system to reach higher efficiency. However, this property is not universal and can only be realized in conjunction with specific features of the system Hamiltonian.

Positioning of colloidal quantum dots (QDs) by nanoholes is applicable to fabricating quantum devices such as quantum circuits. A silica coating technique that facilitates the positioning manages the effective size of QDs while preserving the quantum state inside. In the reverse micelle method, which is commonly used for the silica coating, optical properties deteriorate due to the exposure of QD surface to moisture within the reverse micelle. We studied a thin silica coating on the surface of PbS QDs by pyrolyzing tetraethyl orthosilicate in an organic solvent before forming a thick silica shell by the reverse micelle method. As a result, highly luminous silica-coated PbS QDs with a diameter of about 110 nm were realized. [ABSTRACT FROM AUTHOR]

Optimizing the quantum circuit for implementing Advanced Encryption Standard (AES) is crucial for estimating the necessary resources in attacking AES by the Grover algorithm. Previous studies have reduced the number of qubits required for the quantum circuits of AES-128/-192/-256 from 984/1112/1336 to 270/334/398, which is close to the optimal value of 256/320/384. It becomes a challenging task to further optimize them. AimTaking aim at this task, we find a method for how the quantum circuit of AES S-box can be designed with the help of the automation tool LIGHTER-R. Particularly, the multiplicative inversion in F28, which is the main part of the S-box, is converted into the multiplicative inversion (and multiplication) in F24, then the latter can be implemented by LIGHTER-R because its search space is small enough. By this method, we construct the quantum circuits of S-box for mapping |a⟩|0⟩ to |a⟩|S(a)⟩ and |a⟩|b⟩ to |a⟩|b ⊕ S(a)⟩ with 20 qubits instead of 22 in the previous studies. In addition, we introduce new techniques to reduce the number of qubits required by the S-box circuit for mapping |a⟩ to |S(a)⟩ from 22 in the previous studies to 16. Accordingly, we synthesize the quantum circuits of AES-128/-192/-256 with 264/328/392 qubits, which implies a new record.

The classical neural network has provided remarkable results to diagnose neurological disorders against neuroimaging data. However, in terms of efficient and accurate classification, some standpoints need to be improved by utilizing high-speed computing tools. By integrating quantum computing phenomena with deep neural network approaches, this study proposes an AlexNet–quantum transfer learning method to diagnose neurodegenerative diseases using magnetic resonance imaging (MRI) dataset. The hybrid model is constructed by extracting an informative feature vector from high-dimensional data using a classical pre-trained AlexNet model and further feeding this network to a quantum variational circuit (QVC). Quantum circuit leverages quantum computing phenomena, quantum bits, and different quantum gates such as Hadamard and CNOT gate for transformation. The classical pre-trained model extracts the 4096 features from the MRI dataset by using AlexNet architecture and gives this vector as input to the quantum circuit. QVC generates a 4-dimensional vector and to transform this vector into a 2-dimensional vector, a fully connected layer is connected at the end to perform the binary classification task for a brain disorder. Furthermore, the classical–quantum model employs the quantum depth of six layers on pennyLane quantum simulators, presenting the classification accuracy of 97% for Parkinson's disease (PD) and 96% for Alzheimer's disease (AD) for 25 epochs. Besides this, pre-trained classical neural models are implemented for the classification of disorder and then, we compare the performance of the classical transfer learning model and hybrid classical–quantum transfer learning model. This comparison shows that the AlexNet–quantum learning model achieves beneficial results for classifying PD and AD. So, this work leverages the high-speed computational power using deep network learning and quantum circuit learning to offer insight into the practical application of quantum computers that speed up the performance of the model on real-world data in the healthcare domain. [ABSTRACT FROM AUTHOR]

Josephson junctions (JJs) with Josephson energy E J ≲ 1 K are widely employed as non-linear elements in superconducting circuits for quantum computing operating at milli-Kelvin temperatures. In the qubits with small charging energy E C ( E J / E C ≫ 1 ), such as the transmon, the incoherent phase slips (IPS) might become the dominant source of dissipation with decreasing E J . In this work, a systematic study of the IPS in low- E J JJs at milli-Kelvin temperatures is reported. Strong suppression of the critical (switching) current and a very rapid growth of the zero-bias resistance due to the IPS are observed with decreasing E J below 1 K. With further improvement of coherence of superconducting qubits, the observed IPS-induced dissipation might limit the performance of qubits based on low- E J junctions. These results point the way to future improvements of such qubits. [ABSTRACT FROM AUTHOR]

In this paper, we mainly discuss the quantum reversible circuits of multiplication over GF (2 8) , which has many applications in modern cryptography. The quantum circuits of multiplication over GF (2 8) implemented by using the existing methods need at least 64 Toffoli gates without auxiliary qubits. However, Toffoli gates need a lot of quantum resources in physical implementation. Therefore, we try to construct the quantum circuits with as few Toffoli gates as possible. We first convert multiplication over GF (2 8) into multiplication over composite field GF ((2 4) 2) , and then realize the quantum circuits of multiplication over GF (2 4) by means of product matrix and converting the multiplication into composite field GF ((2 2) 2) , respectively. In addition, we also discuss the case where the initial output qubits of the product are not | 0 ⟩ s, and give the quantum circuit of multiplication over GF (2 4) in this case according to the principle of minimizing the number of Toffoli gates. Finally, according to the calculation formula of multiplication over composite field GF ((2 4) 2) and the isomorphic mappings between GF (2 8) and GF ((2 4) 2) , the quantum circuits of multiplication over GF (2 8) are realized. These quantum circuits without auxiliary qubits only needs 42 Toffoli gates, which are 22 less than the quantum circuits realized by the existing methods. Specifically, we give the specific quantum circuits with irreducible polynomials f (x) = x 8 + x 4 + x 3 + x + 1 and f (x) = x 8 + x 4 + x 3 + x 2 + 1 , respectively. [ABSTRACT FROM AUTHOR]

Grover algorithm is a quantum search algorithm that can find the target state efficiently. However, with the increase in the amount of searching data, the circuit of Grover algorithm is faced with complex gate decomposition problem. In today's NISQ era, resources are very limited, so the depth of circuit is an important metric. This paper introduces a two-stage quantum search algorithm based on divide-and-conquer, which can run quickly in parallel on a quantum computer. A circuit optimization method is proposed to reduce the number of iterations by using block-level oracle circuit. Combining this method with divide-and-conquer idea, it is defined as the 2P-Grover algorithm. The simulation experiment was carried out on the quantum computing framework Cirq and compared with Grover algorithm. The experimental results show that the 2P-Grover algorithm can reduce the depth of circuit by at least 1.2 times and maintain a high probability of search success. [ABSTRACT FROM AUTHOR]

The algorithms that best demonstrate the potential of quantum computing are Shor's algorithm and Grover's algorithm. To this day, new evidence continues to emerge in the form of algorithms or ingenious applications that increase the field of application of this type of computing. However, given the limited number of qubits in current quantum computers, and also the noise problems they currently suffer from, implementing optimized circuits that allow us to take full advantage of the available resources, as well as detecting and correcting the errors caused by this noise, is a priority. In this work we present several leading zero detector circuits for quantum computers and simulators, optimized in terms of noise tolerance and number of qubits. These circuits are a fundamental part in major circuits that perform operations as important and basic in computation as addition and division. [ABSTRACT FROM AUTHOR]

Although the number of qubits in noisy intermediate scale quantum (NISQ) devices has been increased, they still face various physical restrictions, including nearest neighbor (NN) interaction and gate error. The NN interaction and the gate error affect the quantum circuit execution success rate. Since each gate of the CNOT circuit is composed of two qubits, its mapping and optimization are affected by these two constraints. In this paper, we present a physical constraint-aware CNOT quantum circuit synthesis and optimization approach. It consists of two components: the physical constraint-aware CNOT circuit synthesis and the matrix transformation-based optimization approach. The physical constraint-aware CNOT circuit synthesis uses a weighted Steiner tree to account for CNOT gate errors between adjacent qubits of the NISQ device. The matrix transformation-based optimization approach is to synthesize the transposed matrix, the flip matrix, and its transposed matrix according to the characteristics of the Boolean Matrix. The experimental results support the effectiveness of our strategy in enhancing circuit fidelity. Compared with existing methods, our solution can increase the success rate by 382.86% and reduce the number of gates by 58.3% on average. [ABSTRACT FROM AUTHOR]