Basis States Research Articles

Multiparty quantum key agreement based on GHZ states

This paper introduces the design process of a multiparty quantum key agreement protocol based on the Greenberger-Horne-Zeilinger state in detail. Building on the traditional circle-type quantum key agreement protocol, we introduce a star structure, which significantly improves the speed and efficiency of key agreement. To facilitate the reader’s understanding, we provide an example of a four participants quantum key agreement protocol. In the process of quantum state transmission, we perform operations using the Pauli matrix and the Hadamard matrix to ensure that the quantum state remains in one of the four basis states. This significantly enhances the security of the protocol. After rigorous security analysis, we find that the protocol can effectively resist intercept-resend attack, entangle-measure attack, collective attack, and dishonest participant attack. Under a collective attack, if the first particle is subjected to bit-flipping noise, then p<0.2430 only guarantees r>0.20.2$\\end{document}]]> when a=1. Additionally, we conduct a fairness analysis and evaluate the practical performance of the proposed protocol. In an ideal depolarization noise-free environment, the protocol can achieve a positive key rate only when the global detection efficiency exceeds 0.9636. Finally, we conduct a comprehensive comparative analysis of the protocols. The results show that our proposed protocol is superior to other existing schemes in terms of efficiency and running time.

On the dynamics of single-vertex states in quantum-reduced loop gravity

Abstract In this article we examine a Hamiltonian constraint operator governing the dynamics of simple quantum states, whose graph consists of a single six-valent vertex, in quantum-reduced loop gravity. To this end, we first derive the action of the Hamiltonian constraint on generic basis states in the Hilbert space of quantum-reduced loop gravity. Specializing to the example of the single-vertex states, we find that the Euclidean part of the Hamiltonian bears a close formal similarity to the Hamiltonian constraint of Bianchi I models in loop quantum cosmology. Extending the formal analogy to the Lorentzian part of the Hamiltonian suggests a possible modified definition of the Hamiltonian constraint for loop quantum cosmology, in which the Lorentzian part, corresponding to the scalar curvature of the spatial surfaces, is not assumed to be identically vanishing, and is represented by a non-trivial operator in the quantum theory.

Real-Time Operator Evolution in Two and Three Dimensions via Sparse Pauli Dynamics

We study real-time operator evolution using sparse Pauli dynamics, a recently developed method for simulating expectation values of quantum circuits. On the examples of energy and charge diffusion in one-dimensional (1D) spin chains and sudden quench dynamics in the 2D transverse-field Ising model, it is shown that this approach can compete with state-of-the-art tensor network methods. We further demonstrate the flexibility of the approach by studying quench dynamics in the 3D transverse-field Ising model that is highly challenging for tensor network methods. For the simulation of expectation value dynamics starting in a computational basis state, we introduce an extension of sparse Pauli dynamics that truncates the growing sum of Pauli operators by discarding terms with a large number of X and Y matrices. This is validated by our 2D and 3D simulations. Finally, we argue that sparse Pauli dynamics is not only capable of converging challenging observables to high accuracy, but can also serve as a reliable approximate approach even when given only limited computational resources. Published by the American Physical Society 2025

Odd-order quantum noise-like stream cipher scheme based on joint index modulation constellation shaping.

This paper proposes an odd-order quantum noise-like stream cipher scheme based on joint index modulation (JIM) constellation shaping. By utilizing subcarrier index modulation and dual-mode index techniques, additional information is transmitted through the combination distribution of silent subcarrier positions and constellation modes associated with subcarriers. An odd-order 9QAM signal is constructed, and by optimizing the index rule, constellation shaping is achieved while transmitting more information, increasing the distribution of constellation points within the signal. A 4D hyper-chaotic system is employed to implement multi-dimensional disturbances, including bitwise XOR of the original signal, subcarriers, symbols, and elevate the constellation order. Furthermore, the scheme performs upsampling on the chaotic system's initial values and actively introduces noise bits, which are appended to the initial signal as a basis state to enable key-accompanying transmission. Ultimately, the constellation-shaped 9QAM signal is escalated to a 576QAM signal with constellation shaping features. Experimental results demonstrate the successful transmission of a 2.94 Gb/s quantum noise stream signal over a 25 km single-mode fiber intensity modulation direct detection (IMDD) system. The experimental results show that the proposed JIM-576QAM1 signal provides a 0.7 dB gain at Forward error correction (FEC) = 3.8 × 10-3 compared to random distribution of the two constellation modes. The proposed scheme maintains a bit error rate (BER) of 0 for key transmission, and abruptly increases to 0.5 in the event of misalignment, indicating a high sensitivity and accuracy of the system with respect to the key. At varying received optical power, the number of masked signal power remain consistent at 20480, and the detection failure probability stays around 1, demonstrating the stability and security of the proposed quantum noise stream encryption scheme. With a key space as large as 10149, the scheme can effectively counter brute-force attacks from unauthorized receivers. The proposed scheme exhibits high reliability and security, making it a promising candidate for future optical access applications.

The structure and symmetry of modular state space for complex quantum systems.

Understanding the state space structure of complex quantum systems can help to effectively characterize the system properties and explore underlying mechanisms. The structure of the state space could be quite complicated for quantum many-body systems, and the systematic decomposition of the state space is normally involved. Recently, a modular tensor diagram approach was proposed to reorganize the state space hierarchically based on a modular basis. Here, we review the construction of spin eigenfunctions for multiple exciton systems and further develop modular tensor diagrams to exemplify the hierarchical symmetry of the state space. The newly constructed spin eigenfunctions for quadruple excitons, along with the results for triple excitons, are used to demonstrate the effective decomposition of the state space into hierarchical tensorial structures. A universal recursive relation is derived to determine the coefficients of spin eigenfunctions exhibiting transformation symmetry between different classes of elementary modules for an arbitrary number of exciton units. Interestingly, different coupling schemes mapped to quantum many-body interactions lead to different spin adapted basis states, which may correspond to different realistic systems upon the breakdown of spin degeneracy. This work highlights the hierarchical symmetry of the tensorial structure of quantum many-body systems, which may facilitate a better understanding of the structure property relationship toward the object-oriented materials design.

The variation after projection shell model

In this paper, we review a recently developed approximated shell model method called as the variation after projection shell model (VAPSM). Some novel features in the VAPSM are presented. First of all, the VAPSM wave function can be considerably simplified by adopting just one projected basis state rather than previously adopting all [Formula: see text] angular-momentum projected basis states for each selected reference state. This is crucial in application of the VAPSM to the study of high-spin states. Second, the wave functions of the yrast and nonyrast states can be optimized simultaneously based on the Hylleraas–Undheim–MacDonald (HUM) theorem, which is famous in the field of quantum chemistry. Finally, the wave functions with different spins generated from the same reference state can be varied simultaneously. This makes it very convenient to study the rotational bands in deformed nuclei. In this sense, the VAPSM is also a microscopic collective model, but based on the shell model foundation.

Quantumlike Product States Constructed from Classical Networks.

Can complex classical systems be designed to exhibit superpositions of tensor products of basis states, thereby mimicking quantum states? We exhibit a one-to-one map between the product basis of quantum states comprising an arbitrary number of qubits and the eigenstates of a construction comprising classical oscillator networks. Specifically, we prove the existence of this map based on Cartesian products of graphs, where the graphs depict the layout of oscillator networks. We show how quantumlike gates can act on the classical networks to allow quantumlike operations in the state space.

Codebase release 1.0 for DanceQ

The complexity of quantum many-body problems scales exponentially with the size of the system, rendering any finite-size scaling analysis a formidable challenge. This is particularly true for methods based on the full representation of the wave function, where one simply accepts the enormous Hilbert space dimensions and performs linear algebra operations, e.g., for finding the ground state of the Hamiltonian. If the system satisfies an underlying symmetry where an operator with a degenerate spectrum commutes with the Hamiltonian, it can be block-diagonalized, thus reducing the complexity at the expense of additional bookkeeping. At the most basic level required for Krylov space techniques (like the Lanczos algorithm), it is necessary to implement a matrix-vector product of a block of the Hamiltonian with arbitrary block-wavefunctions, potentially without holding the Hamiltonian block in memory. An efficient implementation of this operation requires the calculation of the position of an arbitrary basis vector in the canonical ordering of the basis of the block. We present here an elegant and powerful, multi-dimensional approach to this problem for the U(1)U(1) symmetry appearing in problems with particle number conservation. Our divide-and-conquer algorithm uses multiple subsystems and hence generalizes previous approaches to make them scalable. In addition to the theoretical presentation of our algorithm, we provide DanceQ, a flexible and modern – header only – C++20 implementation to manipulate, enumerate, and map to its index any basis state in a given particle number sector as open source software under https://DanceQ.gitlab.io/danceq.

DanceQ: High-performance library for number conserving bases

The complexity of quantum many-body problems scales exponentially with the size of the system, rendering any finite-size scaling analysis a formidable challenge. This is particularly true for methods based on the full representation of the wave function, where one simply accepts the enormous Hilbert space dimensions and performs linear algebra operations, e.g., for finding the ground state of the Hamiltonian. If the system satisfies an underlying symmetry where an operator with a degenerate spectrum commutes with the Hamiltonian, it can be block-diagonalized, thus reducing the complexity at the expense of additional bookkeeping. At the most basic level required for Krylov space techniques (like the Lanczos algorithm), it is necessary to implement a matrix-vector product of a block of the Hamiltonian with arbitrary block-wavefunctions, potentially without holding the Hamiltonian block in memory. An efficient implementation of this operation requires the calculation of the position of an arbitrary basis vector in the canonical ordering of the basis of the block. We present here an elegant and powerful, multi-dimensional approach to this problem for the U(1)U(1) symmetry appearing in problems with particle number conservation. Our divide-and-conquer algorithm uses multiple subsystems and hence generalizes previous approaches to make them scalable. In addition to the theoretical presentation of our algorithm, we provide DanceQ, a flexible and modern – header only – C++20 implementation to manipulate, enumerate, and map to its index any basis state in a given particle number sector as open source software under https://DanceQ.gitlab.io/danceq.

Entangling Schrödinger’s cat states by bridging discrete- and continuous-variable encoding

In quantum information processing, two primary research directions have emerged: one based on discrete variables (DV) and the other on the structure of quantum states in a continuous-variable (CV) space. Integrating these two approaches could unlock new potentials, overcoming their respective limitations. Here, we show that such a DV–CV hybrid approach, applied to superconducting Kerr parametric oscillators (KPOs), enables us to entangle a pair of Schrödinger’s cat states by two methods. The first involves the entanglement-preserving conversion between Bell states in the Fock-state basis (DV encoding) and those in the cat-state basis (CV encoding). The second method implements a iSWAP gate between two cat states following the procedure for Fock-state encoding. This simple and fast gate operation completes a universal quantum gate set in a KPO system. Our work offers powerful applications of DV–CV hybridization and marks a first step toward developing a multi-qubit platform based on planar KPO systems.

Quantum and Classical Dynamics with Random Permutation Circuits

Understanding thermalization in quantum many-body systems is among the most enduring problems in modern physics. A particularly interesting question concerns the role played by quantum mechanics in this process, i.e., whether thermalization in quantum many-body systems is fundamentally different from that in classical many-body systems and, if so, which of its features are genuinely quantum. Here, we study this question in minimally structured many-body systems that are only constrained to have local interactions, i.e., local random circuits. In particular, we introduce random permutation circuits (RPCs), which are circuits comprising gates that locally permute basis states, as a counterpart to random unitary circuits (RUCs), a standard toy model for generic quantum dynamics. RPCs represent a model for generic microscopic classical reversible dynamics but, interestingly, can be interpreted both as classical or as quantum dynamics. We show that, upon averaging over all circuit realizations, RPCs permit the analytical computation of several key quantities such as out-of-time-order correlators (OTOCs) and entanglement entropies. In the classical setting, we obtain similar exact results relating (quantum) purity to (classical) growth of mutual information and (quantum) OTOCs to (classical) decorrelators. We, thus, discover a series of exact relations, connecting quantities in RUC and (quantum or classical) RPCs. Our results indicate that, despite the fundamental differences between quantum and classical systems, their many-body dynamics exhibits remarkably similar behaviors. Published by the American Physical Society 2025

Fractal dimension and the counting rule of the Goldstone modes

Abstract It is argued that there are a set of orthonormal basis states, which appear as highly degenerate ground states arising from spontaneous symmetry breaking with a type-B Goldstone mode, and they are scale-invariant, with a salient feature that the entanglement entropy S(n) scales logarithmically with the block size n in the thermodynamic limit. As it turns out, the prefactor is half the number of type-B Goldstone modes N B . This is achieved by performing an exact Schmidt decomposition of the orthonormal basis states, thus unveiling their self-similarities in the real space—the essence of a fractal. Combining with a field-theoretic prediction (Castro-Alvaredo and Doyon 2012 Phys. Rev. Lett. 108 120401), we are led to the identification of the fractal dimension d f with the number of type-B Goldstone modes N B for the orthonormal basis states in quantum many-body systems undergoing spontaneous symmetry breaking.

Anticoncentration and State Design of Random Tensor Networks.

We investigate quantum random tensor network states in which the dimension of the bond scales polynomially with the size of the system N. Specifically, we examine the delocalization properties of random matrix product states (RMPS) in the computational basis by deriving an exact analytical expression for the inverse participation ratio (IPR) of any degree, applicable to both open and closed boundary conditions. For bond dimensions χ∼γN, we determine the leading order of the associated overlaps probability distribution and demonstrate its convergence to the Porter-Thomas distribution, characteristic of Haar-random states, as γ increases. Additionally, we provide numerical evidence for the frame potential, measuring the 2-distance from the Haar ensemble, which confirms the convergence of random MPS to Haar-like behavior for χ≫sqrt[N]. We extend this analysis to two-dimensional systems using random projected entangled pair states, where we similarly observe the convergence of IPRs to their Haar values for χ≫sqrt[N]. These findings demonstrate that random tensor networks with bond dimensions scaling polynomially in the system size are fully Haar anticoncentrated and approximate unitary designs, regardless of the spatial dimension.

Time-bin entangled Bell state generation and tomography on thin-film lithium niobate

Optical quantum communication technologies are making the prospect of unconditionally secure and efficient information transfer a reality. The possibility of generating and reliably detecting quantum states of light, with the further need of increasing the private data-rate is where most research efforts are focusing. The physical concept of entanglement is a solution guaranteeing the highest degree of security in device-independent schemes, yet its implementation and preservation over long communication links is hard to achieve. Lithium niobate-on-insulator has emerged as a revolutionising platform for high-speed classical telecommunication and is equally suited for quantum information applications owing to the large second-order nonlinearities that can efficiently produce entangled photon pairs. In this work, we generate maximally entangled quantum states in the time-bin basis using lithium niobate-on-insulator photonics at the fibre optics telecommunication wavelength, and reconstruct the density matrix by quantum tomography on a single photonic integrated circuit. We use on-chip periodically-poled lithium niobate as source of entangled qubits with a brightness of 242 MHz/mW and perform quantum tomography with a fidelity of 91.9 ± 1.0 %. Our results, combined with the established large electro-optic bandwidth of lithium niobate, showcase the platform as perfect candidate to realise fibre-coupled, high-speed time-bin quantum communication modules that exploit entanglement to achieve information security.

Cluster Configurations in Li Isotopes in the Variation of Multi-Bases of the Antisymmetrized Molecular Dynamics

Abstract We investigate the cluster configurations in Li isotopes, which are described in the optimization of the multi-Slater determinants of the antisymmetrized molecular dynamics. Each Slater determinant in the superposition is determined simultaneously in the variation of the total energy. The configurations of the excited states are obtained by imposing the orthogonal condition onto the ground-state configurations. In Li isotopes, various cluster configurations are confirmed and are related to the thresholds of the corresponding cluster emissions. For $^5$Li, we predict the $^3$He+$d$ clustering in the excited state as well as the mirror state of $^5$He with $^3$H+$d$. For $^{6-9}$Li, various combinations of the clusters are obtained in the ground and excited states, and the superposition of these basis states reproduces the observed energy spectra. For $^9$Li, we predict the linear-chain states consisting of various cluster configurations at excitation energy levels of 10–13 MeV.

Constructing vortex functions and basis states of Chern insulators: Ideal condition, inequality from index theorem, and coherentlike states on the von Neumann lattice

Constructing vortex functions and basis states of Chern insulators: Ideal condition, inequality from index theorem, and coherentlike states on the von Neumann lattice

Quantum Speed Limit in Quantum Sensing.

Quantum sensors capitalize on advanced control sequences for maximizing sensitivity and precision. However, protocols are not usually optimized for temporal resolution. Here, we establish the limits for time-resolved sensing of dynamical signals using qubit probes. We show that the best possible time resolution is closely related to the quantum speed limit (QSL), which describes the minimum time needed to transform between basis states. We further show that a composite control sequence consisting of two phase-shifted pulses reaches the QSL. Practical implementation is discussed based on the example of the spin-1 qutrit of a nitrogen-vacancy center in diamond.

On Deadlock Analysis and Characterization of Labeled Petri Nets with Undistinguishable and Unobservable Transitions

This work addresses the analysis and characterization of deadlocks in discrete-event systems modeled by labeled Petri nets (LPNs) with undistinguishable and unobservable transitions. To provide a solution for the notorious problem, it is essential to present an effective characterization in such a way that deadlock control and synthesis are technically and methodologically possible. To this end, we introduce the notion of dangerous implicit vectors (DIVs), which implicitly threaten the system deadlock-freedom. The set of dead markings is divided into two subsets: dead basis markings (DBMs) and dangerous implicit markings (DIMs). An algorithm is designed to compute the sets of DIVs and DIMs at a given basis state of a system. Moreover, by virtue of linear algebraic equations, we formulate sufficient conditions for identifying the existence of blocking markings in an LPN. Finally, an algorithm is developed to construct an observed graph that is a compendious presentation of the reachability graph of a net system, with respect to the existence of dead reaches. At the end of this paper, experiment results that illustrate the correctness and effectiveness of the reported solution are presented.

A qubit-efficient variational selected configuration-interaction method

Abstract Finding the ground-state energy of molecules is an important and challenging computational problem for which quantum computing can potentially find efficient solutions. The variational quantum eigensolver (VQE) is a quantum algorithm that tackles the molecular groundstate problem and is regarded as one of the flagships of quantum computing. Yet, to date, only very small molecules were computed via VQE, due to high noise levels in current quantum devices. Here we present an alternative variational quantum scheme that requires significantly less qubits than VQE. The reduction in the qubit number allows for shallower circuits to be sufficient, rendering the method more resistant to noise. The proposed algorithm, termed variational quantum selected-configuration-interaction (VQ-SCI), is based on: (a) representing the target groundstate as a superposition of Slater determinant configurations, encoded directly upon the quantum computational basis states; and (b) selecting a-priory only the most dominant configurations. This is demonstrated through a set of groundstate calculations of the H2, LiH, BeH2, H2O, NH3 and C2H4 molecules in the sto-3g basis set, performed on IBM quantum devices. We show that the VQ-SCI reaches the full configuration interaction energy within chemical accuracy using the lowest number of qubits reported to date. Moreover, when the SCI matrix is generated ‘on the fly’, the VQ-SCI requires exponentially less memory than classical SCI methods. This offers a potential remedy to a severe memory bottleneck problem in classical SCI calculations. Finally, the proposed scheme is general and can be straightforwardly applied for finding the groundstate of any Hermitian matrix, outside the chemical context.

Qubit analog with polariton superfluid in an annular trap.

We report on the experimental realization and characterization of a qubit analog with semiconductor exciton-polaritons. In our system, a polaritonic condensate is confined by a spatially patterned pump laser in an annular trap that supports energy-degenerate vortex states of the polariton superfluid. Using temporal interference measurements, we observe coherent oscillations between a pair of counter-circulating vortex states coupled by elastic scattering of polaritons off the laser-imprinted potential. The qubit basis states correspond to the symmetric and antisymmetric superpositions of the two vortex states. By engineering the potential, we tune the coupling and coherent oscillations between the two circulating current states, control the energies of the qubit basis states, and initialize the qubit in the desired state. The dynamics of the system is accurately reproduced by our theoretical two-state model, and we discuss potential avenues to implement quantum gates and algorithms with polaritonic qubits analogous to quantum computation with standard qubits.