Quantum circuit compilation is an indispensable part of executing quantum circuits on quantum devices. It translates logical quantum circuits into physical quantum circuits that meet the device constraints. However, nonspecialist users require extensive expertise to effectively select and evaluate quantum circuit compilation processes. Therefore, this paper proposes a quantum circuit compilation option prediction method based on Deep Residual Attention Neural Network. The method aims to automate the selection of the best compilation scheme and enhance the efficiency and accuracy of quantum circuit compilation. Firstly, a quantum circuit feature extraction algorithm based on Time-Weighted Interaction Graph is proposed. This algorithm can effectively represent quantum circuits using fixed-length vectors, making the model input scalable. Secondly, for existing one-dimensional features, a quantum circuit compilation option prediction model based on Deep Residual Attention Neural Network is designed and trained. This model is capable of quickly and accurately predicting the optimal compilation option combination. Extensive experimental evaluations and comparisons are carried out on the MQT (Munich Quantum Toolkit) quantum circuit compilation dataset. These evaluations verify the effectiveness and advancement of the proposed method. Compared with the current state-of-the-art method (Random Forest), the proposed method improves the accuracy by 5.44%, the Top-3 accuracy by 2.6%, and the F1 by 2.05%.
Associated to every finite abelian group G, there is a generalization of qubit Clifford group associated to G. We demonstrate that every G-Clifford gate can be decomposed into some distinguished elementary types: Fourier transforms, quadratic phase gates, and automorphism gates. Combined with earlier results on classical simulation of normalizer circuits, this implies a generalized Gottesman-Knill-type result. We additionally provide circuits for a universal quantum computing scheme based on local two-qudit G-Clifford gates and magic states.
We contribute further to recent theoretical studies of entanglement dynamics in open quantum systems to include a continuous variable N-harmonic oscillator ring system bathed in Ornstein-Uhlenbeck noise. Despite the fact that harmonic oscillator systems are one of the most studied systems in physics, we believe that our work here is unique and sheds a new perspective in terms of a potential application. We present two sets of differential equations that govern the dynamics of N harmonic oscillators derived from first principles, one for a Markovian environment and the other for non-Markovian one. With these two sets, we are able to compare their entanglement dynamics between environments given an initial state of our oscillators. Across several system and environmental parameters, we show that the entanglement dynamics between oscillator pairs in a non-Markovian environment may be significantly enhanced in both magnitude and duration when compared to its Markovian approximation. We showcase this by numerically simulating a specific solution, i.e., we choose N = 4 oscillators, where two harmonic oscillators are initialized as a two-mode squeezed state while the remaining oscillators are vacuum states. By leveraging our N = 4 results, we consider a slightly larger number of oscillators, i.e., N = 6, and show how we can generate a hidden quantum network, in the absence of direct coupling, that may allow multiple parties to secretly and passively entangle oscillators in their possession. This is accomplished by exploiting the environmental memory effect and maintaining resonance with other oscillators or the central frequency in a shared non-Markovian bath, which may allow for autonomous entanglement distribution over a network of oscillators and aid in future quantum technologies.
In the Internet of Medical Things (IoMT), sensors automatically collect data and transmit it to hospital servers, where doctors provide professional medical advice. The emergence of IoMT has significantly reduced the burden on chronic-disease patients and improved their life security. However, the transmission of patients' medical data still faces serious confidentiality and integrity risks. This paper proposes a novel healthcare-system architecture that integrates a controlled-authentication semi-quantum key-negotiation (SQKN) protocol, leveraging the unconditional security of quantum cryptography to mitigate potential data attacks. The hospital server acts as a trusted controller that supervises every protocol run and authenticates all participants, which effectively thwarts man-in-the-middle and identity-spoofing attacks. The semi-quantum design further minimizes the quantum-device burden on patients' side. Experimental simulation under realistic noise (QBER approximate to 0.03 at 0.02/0.04 noise level, 3 000 shots) shows the protocol keeps the quantum-bit error rate below 3 %, while the overall key-generation efficiency reaches 92 %, demonstrating that the scheme resists known attacks and maintains high quantum efficiency for safeguarding IoMT data security.
Problem Statement Accurate estimation of extreme financial risks, such as Conditional Value-at-Risk (CVaR) at high confidence levels (alpha >= 0.95), poses significant computational challenges for classical Monte Carlo methods, which require O(1/& varepsilon;(2)) samples and struggle to scale under rare-event scenarios. Methodology To address this, we propose a hybrid variational quantum-spintronic framework integrating Variational Quantum State Preparation (VQA), a threshold comparator oracle, and Maximum-Likelihood Amplitude Estimation (MLAE) to enable quantum-accelerated CVaR estimation suitable for NISQ devices. Results Using only 6 qubits and K = 6 amplification levels, our approach achieves CVaR<^>(0.95)=0.281 +/- 0.012 (error < 1.1% compared to classical benchmarks), with tail probability p=0.0478 +/- 0.0009 and state fidelity 0.967 on the ibm_brisbane backend. MLAE reduces circuit depth by 3.3 & times; relative to canonical QAE, and a conceptual spintronic implementation achieves similar to 2.0 fJ/gate, corresponding to an 80% energy reduction versus CMOS. Contributions This work introduces the first NISQ-compatible, energy-efficient quantum-spintronic pipeline for regulatory-compliant financial risk analytics, providing a quadratic sampling speedup, accurate tail-risk estimation, and a pathway toward sustainable quantum finance.
We present a literature survey of the mathematical aspects of optimization and optimal synthesis of quantum circuits. The optimization techniques we consider perform the synthesis of quantum circuit by minimizing a given cost function. A total of 179 papers were filtered by inclusion/exclusion criteria and reviewed according to representation models adopted, the techniques used or developed, the kind of benchmarks adopted and the comparison against competitors performed. The survey shows that a very diverse literature has been accumulating in the recent years and although it resists a common formalization, some trends can be individuated. In particular, there is a lack of shared benchmarks with some exceptions. Moreover, many approaches change the representation of the problem to a formulation other than the simple sequence of gates. Final conclusions are drawn and possible lines of future research are suggested.
Characterizing complex Hadamard matrices (CHMs) of order six is an open problem in both algebra and quantum information theory. Analyzing the eigenvalues of CHMs provides a novel approach to this problem. We construct a class of two-parameter CHMs of order six with two sorts of eigenvalues. All matrices in this class are H2-reducible, and the Di & tcedil;& abreve; matrix, Haagerup matrices and Hermitian matrices are both included. This class turns out to be complex equivalent to the class of all CHMs in the dephased form whose eigenvalues are of the form 6\sqrt 6 , - 6\sqrt 6 , lambda 1, lambda 1, lambda 2, lambda 2 with lambda j of modulus 6\sqrt 6 excluding Tao matrix S6(0)S_6<^>{(0)}. We further show that some CHMs including all Hermitian CHMs in the former class have Schmidt rank at most three up to complex equivalence, and they are actually controlled unitary gates implementable in experiments. Our result demonstrates the feasibility of using eigenvalues for characterizing order-six CHMs and their application in quantum circuits.
The swift expansion of Internet of Things (IoT) applications in telemedicine, defense communication, and copyright protection has heightened the necessity for scalable, lightweight, and quantum-resistant multimedia security frameworks. AES and DES are two examples of old symmetric algorithms that are hard to use and have security holes when it comes to sharing keys. Quantum adversaries can still assault classical public-key techniques. This paper presents QRAND-AVS, a hybrid video steganography framework that combines quantum randomness, lightweight cryptography, and adaptive intelligence. The Koblitz method makes plain text messages readable, while Elliptic Curve Cryptography (ECC) makes them unreadable. To make sure that the private keys are truly random, a Quantum Random Number Generator (QRNG) is used. The ciphertext is encoded into DNA nucleotides and adaptively embedded into key video frames selected via histogram-variance analysis. Strong transform-domain embedding is possible with a two-level Discrete Wavelet Transform (DWT) and Singular Value Decomposition (SVD). An AI-based optimizer changes the rules for DNA, the strength of the embedding, and the levels of quantization in real time to find the right balance between payload and invisibility. When tested on a number of benchmark videos, the proposed method had a PSNR that was up to 2.4 dB higher and an embedding capacity that was 40% higher than the LSB and baseline SVD methods. It also cut down on encryption overhead by 35%. Security analysis shows that the system is safe from brute-force, replay, and steganalysis attacks as long as the PSNR/SSIM limits are followed. The results show that QRAND-AVS is a smart, light, and quantum-safe way to protect multimedia that works well in IoT and post-quantum communication settings.
Based on the Pekar-type variational approach, we systematically investigate the dynamical evolution of electron quantum states under strong electron-LO-phonon coupling in an asymmetric Gaussian potential quantum well (QW) subject to an applied electric field. The eigenenergies and wave functions of the ground and first excited states are accurately determined, confirming that this Gaussian potential QW system can serve as a stable two-level qubit. We focus on the spatiotemporal evolution of the electron in a superposition state, revealing that the electron probability density exhibits periodic oscillations within the quantum well. Notably, due to the asymmetric Gaussian potential along the growth direction, the electron probability density displays a distinct double-peak structure, in sharp contrast to the single-peak distribution observed in conventional two-dimensional symmetric potential wells. The oscillation period shows significant parameter dependence: it increases monotonically with the applied electric field strength but decreases with both the potential well height and the polaron radius. Particularly noteworthy is the non-monotonic dependence of the oscillation period on the confinement potential range-the period decreases as the range increases below a critical value, increases above it, and reaches a minimum at the critical point. The above research results can provide important theoretical support for the regulation of the photoelectric properties of low-dimensional materials and the development of their applications.
We propose an algorithm to create an arbitrary n-qubit pure quantum superposition state with precision of m-decimals (binary representation) for each probability amplitude. The algorithm uses one-qubit rotations, Hadamard transformations and, C-NOT operations with multi-qubit controls. The depth of the circuit is O(2(n)n), its space is O(n). We emphasize that the parameters of the utilized unitary transformations are predicted in advance by the required precision and therefore there is no classical calculation supplementing this quantum algorithm. Finalizing the state-creation we perform the measurement of the ancilla state with a certain desired output with the purpose of removing all the garbage from the created superposition state. If n and m are independent and n >> m, the probability of access to the desired ancilla-state (success probability) is similar to 2(-n), which requires O(2(n)) runs of the algorithm and leads to the overall depth O(4(n)n). However, the situation can be significantly improved by replacing the usual measurement with the controlled measurement of the ancilla state that, first of all, removes the garbage part of the superposition state and, second (and most important), allows to avoid both the problem of small success probability to the desired ancilla state and multiple runs of the algorithm. As a consequence, the depth of the algorithm is O(2(n)n) in this case. If m serves to provide the required fidelity of state approximation, then the above parameters increase. This algorithm can be a subroutine generating the required input state in various algorithms, in particular, in matrix-manipulation algorithms developed earlier.
Imaginary-time evolution plays an important role in algorithms for computing ground-state and thermal equilibrium properties of quantum systems, but can be challenging to simulate on classical computers. Many quantum algorithms for imaginary-time evolution have resource requirements that are prohibitive for current quantum devices and face performance issues due to noise. Here, we propose a new algorithm for computing imaginary-time evolved expectation values on quantum computers, inspired by probabilistic error cancellation, an error-mitigation technique. Our algorithm works by decomposing a Trotterization of imaginary-time evolution into a probabilistic linear combination of operations, each of which is then implemented on a quantum computer. The measurement data is then classically post-processed to obtain the expectation value of the imaginary-time evolved state. Our algorithm requires no ancillary qubits and can be made noise-resilient without additional error mitigation. It is well-suited for estimating thermal expectation values by making use of the notion of a thermal pure quantum state. We demonstrate our algorithm by performing numerical simulations of thermal pure quantum state preparation for the 1D Heisenberg Hamiltonian on 8 qubits, and by using an IBM quantum computer to estimate the energy of the same Hamiltonian on 2 qubits. We observe promising results compared to the exact values, illustrating the potential of our algorithm for probing the physics of quantum many-body systems on current hardware.
Quantum computing represents a significant advancement in computational capabilities. Of particular concern is its impact on asymmetric cryptography through, notably, Shor's algorithm and the more recently developed Regev's algorithm for factoring composite numbers. We present our implementation of the latter. Our analysis encompasses both quantum simulation results and classical component examples, with particular emphasis on comparative cases between Regev's and Shor's algorithms. Our experimental results reveal that Regev's algorithm indeed outperforms Shor's algorithm for certain composite numbers in practice. However, we observed significant performance variations across different input values. Despite Regev's algorithm's theoretical asymptotic efficiency advantage, our implementation exhibited execution times longer than Shor's algorithm for small integer factorization in both quantum and classical components. These findings offer insights into the practical challenges and performance characteristics of implementing Regev's algorithm in realistic quantum computing scenarios.
Complex Hadamard matrices (CHMs) are intimately related to the number of distinct matrix elements. We investigate CHMs containing exactly three distinct elements, which is also the least number of distinct elements. In this paper, we show that such CHMs can only be complex equivalent to two kinds of matrices, one is H2-reducible and the other is the Tao matrix. Using our result one can further narrow the range of MUB trio (a set of four MUBs in & Copf;6 consists of an MUB trio and the identity) since we find that neither of the two CHMs belong to any MUB trio. Our results may lead to the more complete classification of 6 & times; 6 CHMs whose elements in the first row are all 1.
Solving large-scale linear systems is an integral part of many scientific disciplines. Classical linear solvers have a polynomial time complexity and it seems impossible to further improve their performance. This fact has directed scientific research to the study of corresponding quantum algorithms, which promise even exponential acceleration compared to existing methods. In this paper, we present and analyze some of the most important related results. In particular, we present the HHL and WZP algorithms based on the eigen-decomposition of a matrix, the row and column iteration methods, as well as two hybrid algorithms that require the cooperation of a classical and a quantum computer, namely an algorithm that uses random walks and the VQLS algorithm. The latter is also examined from an experimental standpoint using the Qiskit open-source framework and a suitable quantum circuit is proposed which can enhance its performance.
In classical logic design, there are machine learning methods based on converting a set of input-output traces to non-deterministic automata that are then converted to deterministic automata and synthesized using logic gates. This approach has not yet been extended to quantum automata. In this paper, we present a method to convert a set of input-output traces to a non-deterministic automaton, which is then converted to an incompletely specified multi-output Boolean function. The existing logic synthesis approaches for designing quantum circuits are insufficient to handle incompletely specified functions. So, we present a novel algorithm to synthesize logic functions with don't cares using permutative quantum gates. The original MMD (D.M.Miller, D. Maslov, and G.W.Dueck) algorithm minimizes only completely specified reversible functions using cascades of reversible gates. In this paper, this algorithm is modified to allow for the inclusion of don't cares within the given function's truth table (reversible or irreversible). The distinguishing property of our presented algorithm QAS, is that it does not add any ancilla qubits if it is not necessary. This algorithm solves the problem of synthesizing deterministic and non-deterministic quantum state machines, both completely specified and incompletely specified.
In recent years, quantum computing has gradually extended its influence beyond the realm of physics research into the fields of electrical engineering and computer science. Most researchers and programmers remain more familiar with traditional algorithmic techniques based on conventional computer architectures. To address this gap, this study proposes a quantum algorithmic circuit design framework with Grover's search speedup technique and provides theoretical proofs for some design techniques, aiming to facilitate knowledge transfer and ease the learning curve for designers entering the field of quantum algorithm development. Since combinatorial optimization problems in graph theory serve as the foundation for many practical applications, this study adopts the well-known Connected Dominating Set (CDS) problem as a design example to illustrate the practical applicability of the proposed quantum algorithmic design framework and presents a quantum circuit as a potential solution for addressing realworld challenges in network optimization and related applications. In addition, the circuit proposed in this paper can serve as a quantum oracle to identify connected dominating sets (CDSs) of a graph. When the oracle is applied to a superposition of vertex subsets, Grover's search algorithm achieves a quadratic speedup. We designed a method for adjusting the initial amplitudes so that the search can be biased toward smaller CDSs, which maximizes the probability of finding the minimum CDS.
Quantum information and quantum computing are based on the concept and manipulation of qubits. In this pedagogical Tutorial-written with the aim of assisting self-motivated undergraduate mathematics, physics, and engineering students-transformation of these qubits, especially the Hadamard transformation (H) and the phase shifter transformation (Phi), is illustrated. Two-qubit gates and their application in production of entangled states, along with quantum algorithms (including Deutsch-Jozsa algorithm), are included as well. With 2025 being declared as the International Year of Quantum Science and Technology (IYQ) by the United Nations General Assembly (UNGA), under the leadership of United Nations Educational, Scientific and Cultural Organization (UNESCO), the timeliness and relevance of this Tutorial, in order to nudge the budding researchers in the "quantum" direction, cannot be emphasized enough.
Quantum algorithms of matrix operations are of great significance in many fields in science and technology. In this paper, by leveraging multi-qubit Toffoli gates and basic single-qubit operations, the quantum algorithms of matrix operations of row addition, row swapping, trace calculation and transpose are obtained. In particular, the complexities of these quantum algorithms are presented, too.
Quantum computing has attracted increased attention in recent years owing to substantial advancements in quantum algorithms and system architecture. Quantum algorithms are implemented using quantum circuits. These circuits include an intrinsic reversibility and often have a substantial Boolean component that requires synthesis. A crucial characteristic of reversible circuits is the preservation of parity. Parity-preserving logic is a category that maintains the parity of both inputs and outputs, facilitating the detection of permanent and transient errors. Multiplier circuits are essential components in digital computing systems, playing a crucial role in the development of various hardware, including arithmetic circuits. This paper first introduces a novel block based on a transformationbased synthesis technique from the elementary quantum gates. Then it proposes a distinctive 2x2 parity-preserving reversible quantum Vedic multiplier based on the recommended block and prior gates. In addition, further designs of Vedic multipliers are provided, encompassing 4-bit, 8-bit, and 16-bit configurations. We illustrate that our design brings superior outcomes regarding quantum cost (QC), constant inputs (CI) count, CNOT-V/V+ count, garbage outputs (GO) count, and gate count (GC) in comparison to earlier designs. This study achieves an average decrease of 23.09%, 37.51%, 37.51%, 54.89%, and 19.38% in QC, CI, GO, GC, and CNOT-V/V+ count, respectively. Furthermore, all suggested circuits undergo appraisal and validation within the IBM quantum laboratory.
The combination of quantum algorithms is one promising approach to attacking symmetric cryptography. In this paper, we study in detail the Grover-meets-Simon and Alg-PolyQ2 algorithms under deferred measurement, which combine the ideas of Grover's and Simon's algorithms and are applicable to attacking the FX construction. By converting intermediate measurements into unitary operations deferred to the end of the quantum circuit, both quantum algorithms involve a quantum rank-solving problem. To address it, we first provide a formal analysis of the generalized quantum Gauss-Jordan elimination and characterize the resulting quantum state after the corresponding unitary operations, which serves as a subroutine in these two algorithms. Subsequently, we derive the tight bounds of the attack success probability of these two algorithms based on the initial amplitude, offering a novel perspective that confirms their effectiveness. Furthermore, our research perspective provides an idea for analyzing the attack success probability for some quantum algorithms integrating Grover's algorithm without considering quantum input length, and contributes to a deeper understanding of these attacks' underlying mechanisms under the deferred measurement principle.
