Quantum Information Processing最新文献

Quantum error-correcting codes have always been important technologies to ensure the reliability and security of quantum communication. In this paper, we construct some optimal quantum subsystem codes using generalized Reed–Solomon codes over finite fields with odd characteristics. These new construction methods enrich the construction ideas of quantum subsystem codes, and many optimal quantum subsystem codes can be derived.

We derive the Fock and position-space representations of squeezed vacuum states and their photon-added extensions associated with the para-Bose oscillator algebra of order (mathcal{P}=2lambda +1), which constitutes a parity deformation of the standard harmonic oscillator algebra recovered at (mathcal{P}=1). For orders greater than one, we establish the resolution of the identity for both squeezed vacuum states and arbitrary m-photon-added squeezed vacuum states over the unit disk by constructing appropriate positive-definite measures, which depend on (lambda ) and on the pair ((lambda ,m)), respectively. For odd values of the deformation order, we obtain the Wigner function of the squeezed vacuum states in phase space in the position representation and show that the emergence of negative regions, absent in the harmonic oscillator case, serves as a clear signature of nonclassicality for (mathcal{P}>1). We further analyze the individual roles of the parameters (lambda ) and m in enhancing or suppressing nonclassical features, including quadrature squeezing, sub-Poissonian photon statistics, photon antibunching, and entanglement in their corresponding quasi-Bell states. Optical tomograms of the m-photon–added squeezed vacuum states are constructed for even values of (lambda ) by solving a real eigenvalue equation for the annihilation operator. Finally, a schematic analysis is presented to elucidate how the parameters (lambda ) and m govern the structure of the resulting optical tomograms.

We investigate the process of quantum teleportation in an expanding universe modeled by Friedmann–Robertson–Walker spacetime, focusing on two cosmologically relevant scenarios: a power-law expansion and the de Sitter universe. Adopting a field-theoretical approach, we analyze the quantum correlations between two comoving observers who share an entangled mode of a scalar field. Using the Bogoliubov transformation, we compute the teleportation fidelity and examine its dependence on the expansion rate, initial entanglement, and the mode frequency. Our findings indicate that spacetime curvature and the underlying cosmological background significantly affect the efficiency of quantum teleportation, particularly through mode mixing and vacuum structure. We also compare our results with the flat Minkowski case to highlight the role of cosmic expansion in degrading or preserving quantum information.

This survey presents a comprehensive analysis of the quantum Fourier transform (QFT), a fundamental tool in quantum computing, in comparison to its classical counterpart, the fast Fourier transform (FFT). The study begins with an introduction to the classical Fourier transform, which is widely used in different disciplines such as signal and image processing. The article introduces the QFT as a quantum version of the Fourier transform, detailing how it leverages quantum parallelism and superposition to reduce the time complexity of the operation, and highlighting its crucial role in quantum algorithms like Shor’s algorithm for integer factorization. The analysis also addresses the mathematical foundations of the QFT, its implementation in quantum circuits, and the key advantages and challenges associated with its use, such as measurement precision and quantum decoherence. Finally, it concludes with an exploration of the current and potential applications of QFT in quantum computing.

The integration of symmetry into quantum models within geometric quantum machine learning has attracted increasing research attention. In this work, we introduce a symmetry-constrained quantum convolutional neural network framework tailored to few-shot learning in the noisy intermediate-scale quantum (NISQ) setting. By unifying equivariant data embeddings with symmetry-constrained quantum gate sets, our approach compresses the hypothesis space into group-invariant subspaces, enforcing geometric inductive biases that mitigate overfitting. Theoretically, we specialize existing generalization results for parameterized quantum circuits to our symmetry-constrained QCNN architecture and show that, under (T in mathcal {O}(log n)) and (M = textrm{poly}(n)), the resulting bounds exhibit polylogarithmic scaling in the system size. This perspective complements more fine-grained, architecture-specific error decompositions by providing an alternative view that highlights how symmetry and parameter sharing compress the QCNN hypothesis space and influence the scaling behavior of existing theoretical results. To address NISQ hardware constraints, we implement a brick-layer circuit architecture with frequency collision avoidance, ensuring nearest neighbor connectivity and practical feasibility. Numerical simulations on binary MNIST and Fashion-MNIST tasks with additive Gaussian input noise ((sigma = 0.2)) applied to the classical data and a noiseless statevector backend for all quantum models indicate that, for small-to-moderate training sets, the symmetric QCNN can reduce the generalization error by up to (64%) relative to a generic QCNN and by up to (74%) relative to a standard VQC under this input noise model. On the noisy MNIST task, the proposed framework attains up to (93.9%) test accuracy with a stabilized loss around 0.28 in our simulations, while maintaining competitive performance against classical baselines such as SVMs and random forests, suggesting that symmetry-driven dimensionality reduction can improve generalization and robustness to input perturbations in quantum learning. Overall, our work presents a QCNN framework that combines symmetry preservation, generalization analysis based on existing theory, and NISQ-compatible architectural design within a single coherent model, and illustrates how these ingredients can be jointly exploited in geometric quantum machine learning.

The substitution box (S-box) is often used as the only nonlinear component in symmetric-key ciphers, leading to a significant impact on the implementation performance of ciphers in both classical and quantum application scenarios by S-box circuits. Taking the Pauli-X gate, the CNOT gate, and the Toffoli gate (i.e., the NCT gate set) as the underlying logic gates, this work investigates the quantum circuit implementation of S-boxes based on the SAT solver. Firstly, we propose encoding methods of the logic gates and the NCT-based circuit, based on which we construct STP models for implementing S-boxes. By applying the proposed models to the S-boxes of several well-known cryptographic algorithms, we construct optimal implementations with different criteria for the 4-bit S-boxes and provide the implementation bounds of different criteria for the 5-bit S-boxes. Since S-boxes in the same affine equivalence class share most of the important properties, we then build STP models to further investigate optimizing S-box circuits based on affine equivalence. According to the applications, for almost all the tested 4-bit S-boxes, there always exists an equivalent S-box that can be implemented with half the number of logic gates. Besides, we encode some important cryptographic properties and construct STP models to design S-boxes with given criteria configurations on implementation and properties. As an application, we find an S-box with the same cryptographic properties as the S-box of KECCAK that can be implemented with only 5 NCT gates, even though the application of our models indicates that implementing the KECCAK S-box requires more than 9 NCT gates. Notably, the inputs of the proposed models are tweakable, which makes the models possess some functions not currently available in the public tools for constructing optimized NCT-based circuits for S-boxes.

The sum of quantum computing errors is the key element both for the estimation and control of errors in quantum computing and for its statistical study. In this article, we analyze the sum of two independent quantum computing errors in an (n-)qubit and obtain a formula for the fidelity of the sum of these errors. We prove this result for isotropic quantum computing errors and conjecture that it also holds true for general quantum computing errors.

The Quadratic Assignment Problem (QAP) is an NP-hard fundamental combinatorial optimization problem introduced by Koopmans and Beckmann in 1957. The problem is to assign n facilities to n different locations with the goal of minimizing the cost of the total distances between facilities weighted by the corresponding flows. We initiate the study of using Rydberg arrays to find optimal solutions to the QAP and provide a complementing circuit theory to facilitate an easy representation of other hard problems. We provide an algorithm for finding valid and optimal solutions to the QAP using Rydberg arrays.

In this paper, we use generalized Reed–Solomon (GRS) codes as block codes to construct classical convolutional codes and classical convolutional GRS codes with arbitrary memory and flexible degrees are derived. Particularly, for unit-memory and double-memory, some of the convolutional GRS codes are exactly convolutional maximum-distance-separable (MDS) codes. From the resulting convolutional GRS codes, under Euclidean and Hermitian inner products, quantum convolutional codes are obtained, respectively. A connection between quantum convolutional codes and GRS codes is also established.

The variational quantum eigensolver (VQE) is a key algorithm for near-term quantum computers, yet its performance is often limited by the classical optimization of circuit parameters. We propose using the velocity Verlet algorithm, inspired by classical molecular dynamics, to address this challenge. By introducing an inertial “velocity” term, our method efficiently explores complex energy landscapes. We compare its performance against standard optimizers on H₂ and LiH molecules. For H₂, our method achieves chemical accuracy with fewer quantum circuit evaluations than L-BFGS-B. For LiH, it attains the lowest final energy, demonstrating its potential for high-accuracy VQE simulations.