Quantum Information Processing最新文献

If a local Hamiltonian eigenstate is mapped to another state by local operators commuting with the Hamiltonian terms, the latter is also an eigenstate. This basic observation implies a no-go result for both being a unique ground state and having a degeneracy protected against local perturbations.

We derive a generalization error bound for quantum neural networks (QNNs) using the framework of dynamical Lie algebras (DLAs). By constructing covering numbers from the DLA structure and applying Rademacher complexity theory, we show that the generalization error bound scales as ( mathcal {O}(sqrt{ dim ( mathfrak {g}) }) ), where ( mathfrak {g} ) denotes the associated Lie algebra. Additionally, we establish an upper bound on the number of trainable parameters required to ensure this generalization property. Numerical experiments using the transverse-field Ising model confirm the validity of our theoretical findings and illustrate the effect of boundary conditions and training strategies on generalization. Our results highlight the importance of algebraic structure in the design and analysis of QNNs.

We consider the problem of entanglement routing in heterogeneous quantum networks where each link and node may offer a different entanglement generation quality. We consider that each link offers a base rate and fidelity of entanglement generation. These base values can be altered by performing entanglement purification on each link. Furthermore, we consider that each repeater node offers a different probability of a successful entanglement swapping. With this setting, we design a reinforcement learning-based approach for flexible entanglement routing on future quantum networks. Specifically, we formulate the problem of entanglement routing in the Q-learning framework where the main objective of the agent is to deliver end-to-end entanglement while maximizing a user-specified objective function in the form of a weighted sum of achieve fidelity and rate. We demonstrate the efficacy and flexibility of developed framework by simulating random quantum networks where the random requests in fidelity maximizing, rate maximizing, or balanced mode are generated. We also numerically assess the effects of infrastructure developments and technology enhancements in future quantum networks.

Information transfer between different nodes, particularly parallel information transfer, is fundamental to the realization of quantum networks. In this paper, we propose a scheme for implementing quantum information parallel transfer that utilizes multimode cat state encoding within a cavity-magnon system. The quantum information parallel transfer module consists of four cavities, each containing a YIG sphere. Our findings indicate that by adjusting the coupling strength and detuning between the magnons and the cavities, the encoded information can be transferred from one pair of cavities to another with high fidelity. The model presented in this study has the potential to serve as a framework for the development of ring networks or one-dimensional cavity chain structures.

In this work, we investigate two measures of imaginarity: the maximum and minimum relative entropies of imaginarity, and provide their corresponding operational interpretations. For the maximum relative entropy of imaginarity, we demonstrate that it not only characterizes the maximum overlap between a given state and the maximally imaginary state through real operations, but also provides a lower bound for the efficiency of imaginarity distillation. For the minimum relative entropy of imaginarity, we show that it is related to the maximum probability of transformation between pure states using real operations, as well as the minimum time required for a unitary evolution to convert a given pure state into a real state. Furthermore, by introducing the concepts of smooth maximum and minimum relative entropies of imaginarity, as well as the one-shot imaginarity cost and one-shot distillable imaginarity, we establish that the smooth maximum relative entropy of imaginarity provides a lower bound for the one-shot imaginarity cost, while the smooth minimum relative entropy of imaginarity offers an upper bound for the one-shot distillable imaginarity. Finally, we prove that any nontrivial imaginarity measure is not additive under the tensor product of quantum states. Based on this, we prove that the regularized maximum and minimum relative entropies of imaginarity, as well as the regularized relative entropy of imaginarity are all equal to zero for any states, which highlights the distinction between the resource theory of imaginarity and those of entanglement and coherence.

Simon’s algorithm is a well-known quantum algorithm that can achieve exponential acceleration. This paper studies the applications of Simon’s algorithmin analyzing the security of Feistel variants, namely, several well-known cryptographic structures derived from the Feistel structure. Specifically, we study quantum related-key attacks on Feistel variants in the setting that adversaries can only control part of the key difference in quantum superposition. We delve into observing the quantum related-key attacks on the balanced Feistel structure given by Cid et al. and slightly improve the existing method to design periodic functions, ultimately providing a new approach to building periodic functions in single-key settings. Based on these results, we propose a general technique to construct quantum related-key distinguishers exploiting the quantum single-key distinguishers construction technique. As applications of our proposed technique, we demonstrate how to construct new polynomial-time quantum related-key chosen-plaintext distinguishers on several Feistel variants: Feistel-KF, SM4-like, MARS-like, and Type-1/2/3 generalized Feistel-KF structures.

Quantum secret sharing (QSS) harnesses quantum entanglement to securely distribute information among multiple parties, overcoming the vulnerabilities of classical secret sharing schemes, which rely on computational complexity and are susceptible to quantum computing threats. Existing multi-party QSS protocols often exhibit declining efficiency as the number of participants N increases, limiting the scalability. This paper proposes two efficient and verifiable QSS protocols based on a seven-qubit entangled (SQE) state. The first protocol can be extended to multi-party sharing, achieving a sharing efficiency of (3/(2N+2))—a significant improvement over prior schemes. By retaining three particles and distributing the remaining four particles to participants in groups, the protocol enables the reconstruction of three classical secret bits per SQE state, resulting in a particle utilization rate of 75%. Security is ensured through random number generation, local unitary operations, and decoy state technology, which effectively defends against external eavesdropping and internal cheating. Scalable to ((N ge 3)) participants, this protocol reduces the secure multi-party quantum communication cost. The second protocol introduces the random dynamic distribution of particle pairs in three-party secret sharing. Compared to the first protocol, this approach simplifies the verification lists. Moreover, the use of random dynamic particle pair distribution enhances the security of the second protocol.

In this paper, we consider a special class of ((bar{lambda },theta ,ell ))-monomial codes over finite fields, where we describe the Galois duals of one-generator ((bar{lambda },theta ,ell ))-monomial codes generated by a generator of the form ((g(x), g(x)f_1(x), ldots , g(x)f_{ell -1}(x))). We give necessary and sufficient conditions to obtain the Galois self-orthogonality and Galois LCD properties. Furthermore, we construct certain maximum-distance-separable quantum error-correcting codes (MDS QECCs) using the CSS construction from Euclidean and Hermitian self-orthogonal codes. Similarly, we utilize LCD codes to construct certain maximum-distance-separable entanglement-assisted quantum error-correcting codes (MDS EAQECCs).

Quantum robotic systems hold promise for applications in molecular manipulation and high-precision sensing, but their operation is highly vulnerable to environmental noise. This work introduces a large deviation principle (LDP)-based control framework for mitigating stochastic perturbations in coupled master–slave quantum robots. The system Hamiltonian, expressed in terms of position and momentum operators, incorporates control terms alongside Gaussian and Poisson noise, capturing both gradual fluctuations and sudden jumps. By computing the large deviation rate function, we quantify the probability of rare noise-induced deviations and derive an optimal control strategy that minimizes such events in key observables. Simulations across distinct dynamical regimes demonstrate that the controlled trajectories remain close to the desired wave function, with deviations consistent with the theoretical bounds. These results validate the robustness and generality of the approach, providing a practical framework for stabilizing quantum robotic systems in noisy environments with potential applications in precision sensing, molecular chemistry, and quantum computing.

As one of the fundamental quantum circuits widely used today, the quantum modular exponentiation circuit has been applied in various quantum algorithms, including Shor’s algorithm. However, due to the limitations of quantum computers in the noisy intermediate-scale quantum (NISQ) era, excessive circuit depth and high quantum cost can lead to significant noise accumulation, thereby increasing the likelihood of computational errors. Consequently, reducing both circuit depth and quantum cost is essential. To address these issues, this work proposes two modular exponentiation circuits based on the V gate, with further improvements introduced through the use of zero resets. Comparative analysis shows that both proposed circuits achieve reductions in circuit depth and quantum cost within their respective domains, while preserving general applicability. Furthermore, by relaxing the constraint of circuit reversibility, the improved designs achieve an additional two to three fold reduction in circuit depth and quantum cost. Finally, the correctness of the proposed circuits was verified through experimental implementation using the Qiskit package in Python.