As large-scale quantum computers become a reality, they will likely exist as centralized cloud resources accessible to a broad user base. Securely delegating private quantum computations to untrusted servers is therefore a foundational challenge. This requires rigorous guarantees of privacy (blindness), correctness (completeness), and integrity against malicious actions (verifiability). This paper presents an integrated architectural framework for noise-aware distributed quantum computation. The framework combines three technical components into a unified system: (1) a distributed stabilizer code backbone to encode and store quantum states across multiple server nodes, with security analyzed under non-communication and bounded collusion assumptions; (2) a two-level error management structure, where each server node can locally handle errors based on its specific noise model; and (3) a trap-based verification protocol to detect malicious deviations with probability controlled by a security parameter. We provide a security analysis showing that, under the stated assumptions, the framework achieves completeness, blindness, and verifiability with respect to the permitted leakage. Our work provides an architectural blueprint for trustworthy distributed quantum computation under explicitly stated assumptions, paving the way for further development of secure quantum cloud services.
Structured pure dephasing can produce coherence revival, but a predictive reduced description must also identify the physically admissible parameter domain and connect observables obtained under different control protocols. We study a constrained memory kernel composed of a short-memory broadband term and a finite-linewidth damped-oscillatory term, the minimal background-plus-resonance member of a hierarchy for spectra dominated by one isolated finite-linewidth feature. Although their difference defines a single scalar Volterra kernel, independent calibration of the broadband sector makes the constrained decomposition a testable low-dimensional parametrization. Starting from the second-order Born pure-dephasing equation, we establish the scalar-kernel normalization and derive an exact four-dimensional state-space realization. The associated rational transfer function yields a quartic characteristic equation, explicit Routh–Hurwitz stability conditions, and a pole-residue criterion for observable revival. Complete positivity is certified independently through the necessary and sufficient condition |G(t)|≤ 1 . For ideal longitudinal toggling, we define a controlled extension of the effective-kernel model and obtain the Hahn-echo response by piecewise matrix-exponential propagation using the same parameters as the Ramsey dynamics, without a Gaussian cumulant approximation, an infinitely narrow spectral line, or a protocol-dependent amplitude. Dimensionless maps separate completely positive revival, spectrally stable but non-CP dynamics, and spectral instability. A synthetic cross-protocol benchmark further shows that restricted one-component kernels fitted to Ramsey data can reproduce the overall free-induction decay while failing to predict the corresponding echo response. The framework therefore connects structured environmental scales, modal dynamics, physical admissibility, and controlled-coherence prediction within a unified analytically tractable model.
We present a demonstration of converting a microwave field to an optical field via three-wave mixing (TWM) in the cold atoms, where the microwave field carries orbital angular momentum (OAM). We show that the conversion allows the structural information of the microwave field to be coherently transferred to the optical field. With the current energy level scheme, we achieve a high-similarity transfer of the intensity and phase information. Our proposed scheme provides a way to realize OAM transmission and spiral phase regulation in cold atoms, and may find some applications in Quantum Information Processing.
Grover’s search algorithms, including various partial Grover searches (PGS), experience scaling problems when multiple solutions are sought, as the number of iterations increases with the number of solutions or marked states, making implementation more computationally expensive. Inspired by recent PGS algorithms for multi-solution searchers, this article proposes a scalable Grover quantum search algorithm, referred to as Bi-directional Multi-solution scalable Grover Search (BMGS), to efficiently search for an arbitrary number of solutions from an unstructured database. We introduced a novel multi-segment bidirectional search tactic with PGS across multiple equal segments of each state, starting from an initial state and multiple marked states in parallel, obviating the need for merge operations. We have shown in this work that for each solution our novel approach requires at most √(𝒩)( 1- √(1/b^⌊r/dk⌋)) iterations (here, 𝒩=2^r elements, k=log _2 b , d is the number of equal segments on r qubits, and b is the branching factor). Our proposed BMGS algorithm is benchmarked against state-of-the-art Depth-First Grover Search (DFGS) and PGS implementations for an arbitrary number of solutions, ranging from 2 to 20 qubits, as a proof of concept. We also show that our BMGS requires fewer iterations for shallow quantum circuits and achieves an optimal 𝒪 ( √(s𝒩) ) average complexity for s solutions, when dk < r . The Qiskit Python implementation of the proposed BMGS algorithm is available on GitHub ( https://github.com/hafeezzwiz21/Multi-Solution-DFGS-BMGS ).
Let R be finite non-chain rings 𝔽_q^2m+u𝔽_q^2m , where 𝔽_q^2m is a finite field with q^2m elements, q is an odd prime power, m is a positive integer, u is an indeterminate with u^2=1. In this paper, we firstly define a class of Gray maps, which changes Hermitian dual-containing property of linear codes over R into the Hermitian dual-containing property of linear codes over 𝔽_q^2m . Applying Hermitian construction, a class of q^m -ary quantum codes are obtained from Hermitian constacyclic dual-containing codes over R. Moreover, a family of q-ary primitive quantum BCH codes are determined via the Hermitian construction from the subfield subcodes of Gray images of Hermitian dual-containing u-constacyclic codes over R. Finally, we define another class of maps, which changes the Hermitian dual-containing property of linear codes over R into the trace dual-containing property of linear codes over 𝔽_q^2m . Using Symplectic construction, another class of q^m -ary quantum codes are obtained from Hermitian dual-containing u-constacyclic codes over R.
Quantum-state discrimination provides a fundamental framework for extracting information from nonorthogonal quantum states. In this work, we present an operational formulation of wave–particle complementarity in the low-gain Zou–Wang–Mandel (ZWM) induced-coherence interferometer. In this regime, each photon pair is emitted by one of two nonlinear crystals, preparing nonorthogonal conditional idler states that encode which-crystal information and define a binary quantum hypothesis-testing problem. We analyze which-crystal inference using both unambiguous state discrimination (Ivanovic–Dieks–Peres, IDP) and minimum-error discrimination (Helstrom bound). We identify a correspondence between the signal visibility and the optimal inconclusive probability of unambiguous discrimination, while the Helstrom bound characterizes the optimal success probability for source identification. The Helstrom and IDP interpretations developed here apply specifically to the low-gain binary single-pair sector. At arbitrary parametric gain, idler-seeded emission produces unequal signal intensities and modifies the ordinary fringe visibility; the appropriate all-gain formulation instead involves normalized first-order coherence and a correlation-based distinguishability. This formulation provides an operational perspective on complementarity in induced coherence, emphasizing the role of measurement in determining accessible which-crystal information. We further extend the analysis to thermal noise in the object arm, where the idler states become mixed, leading to reduced visibility and distinguishability consistent with mixed-state-discrimination limits. The approach is general and applicable to two-path interferometers with marker degrees of freedom.
The choice of a given encoding scheme for the problem variables, represented by a set of input qubits of a quantum circuit, substantially influences its design, as well as the quantity and nature of quantum resources (qubits and gates) employed by it. Quantum programmers have access to a variety of encoding strategies, such as one-hot, binary, Gray, amplitude encoding, or Schmidt decomposition, but each of them allows encoding just a single value for each problem variable. This article introduces a novel encoding scheme based on one-hot encoding, termed Multi-Unary, which enables the representation of multiple values within the input qubits, hence the descriptor ‘dense encoding scheme.’ The application of Multi-Unary is demonstrated in the context of the graph coloring problem using Grover’s algorithm, although its applicability extends to a broader class of quantum algorithms. By increasing the informational density on the input qubits, the multi-unary encoding offers potential advantages in terms of circuit compactness and resource efficiency, while at the same time enables an output value to contain more than one solution to a problem. Given its simple implementation, it can even replace the one-hot encoding scheme.
Long-distance quantum communication requires architectures that withstand photon loss and operational noise without relying on two-way classical signalling that incurs round-trip latency. Motivated by recent hybrid designs combining photonic trees with small stabilizer codes, we benchmark the Steane code [[7, 1, 3]] against the standard five-qubit [[5, 1, 3]] baseline within a tree-assisted repeater architecture. Unlike the saturated five-qubit code, which is constrained by a fully populated syndrome space, our implementation exploits the Steane code’s underpopulated syndrome space to correct all single-qubit erasures and additionally a subset of two-qubit errors. Consequently, the Steane code demonstrates superior robustness at realistic re-encoding error rates ( ϵ _r≥ 0.05% ), maintaining higher message qubit transmission success rates than the baseline. Notably, at ϵ _r=0.2% , the Steane-based repeater maintains a competitive cost threshold up to 5000 km, significantly exceeding the 800 km limit of the five-qubit code. These results suggest that the Steane code’s capacity for erasure correction offers a practical advantage for one-way repeaters, outweighing the overhead of its larger block size.
The efficiency of information reconciliation in quantum key distribution (QKD) is significantly constrained by the dynamic, time-varying nature of quantum channels. Conventional post-processing schemes relying on fixed parameters suffer from bandwidth inefficiency during periods of low error rates and face a high risk of link outages when error rates spike. To address these issues, we propose a dual-adaptive post-processing framework utilizing IEEE 802.11n standard QC-LDPC codes. First, we introduce a dynamic parameter-estimation strategy based on channel confidence. This approach adapts the check ratio while maintaining a fixed statistical confidence target. Second, we implement a rate-compatible error correction scheme employing puncturing and shortening techniques to accommodate substantial channel fluctuations. The check-ratio, QBER-threshold, and rate selections are validated through a constrained policy-grid search, realistic-channel LDPC-level decoding experiments and a separate QBER-anomaly-detection test. In the stable low-QBER scenario, the safety-constrained policy with check ratios {8%,12%,32%} and rates {0.56,0.52,0.33} achieves a total normalized SKR of 146.360± 2.951 , corresponding to an 11.34%± 0.21% gain over the fixed benchmark, while maintaining 99.59%± 0.10% decoding availability. With n_sift=10^5 , the security-anomaly test gives zero no-attack false alarms, 100% detection for tested sustained attacks with QBER at least 8% , and 100% abort probability for tested attacks with QBER at least 11% . These results show that the proposed architecture provides a controllable trade-off between efficiency, robustness, and security-aware parameter estimation in dynamic quantum channels.
Quantum image processing exploits quantum mechanical phenomena such as superposition and entanglement to achieve computational advantages over classical methods. This paper presents a comprehensive framework for quantum image filtering based on the Flexible Representation of Quantum Images (FRQI). We develop four quantum filters targeting fundamental image processing tasks. First, a quantum thresholding filter (QTF) employs Grover’s amplitude amplification to identify pixels exceeding an intensity threshold with quadratic speedup 𝒪(√(N/M)) over classical linear search, where N is the total number of pixels and M is the number of marked pixels. Second, a quantum object recognition filter (QORF) combines SWAP-test fidelity estimation with Grover search to perform template matching, achieving 𝒪(√(M/L)) query complexity for identifying L matching patches among M candidates. Third, a quantum Hadamard edge detection (QHED) algorithm extracts horizontal, vertical and diagonal edges with 𝒪(log N) gate complexity. Fourth, a quantum blur filter (QBF) performs low-pass filtering using the Walsh–Hadamard transform with only 𝒪(log N) quantum gates, compared to 𝒪(N log N) for classical FFT-based convolution. For each filter, we provide rigorous mathematical formulations, explicit quantum circuit constructions and complexity analyses. We also discuss practical limitations including FRQI state preparation overhead, measurement complexity and NISQ hardware constraints. This paper establishes a unified quantum image processing framework that bridges theoretical quantum speedups with implementable circuit designs, providing a foundation for future developments in quantum-enhanced computer vision.
We obtain uniform phase sensitivity of 1/√(⟨ N⟩) using spin coherent light. It is shown that two-mode non-classicality is essential for uniform phase sensitivity in the standard quantum limit. Spin coherent light is realised by detecting N photons sequentially in a time-differential manner from a coherent light source. The coherence of the spin coherent state is seen to be retained even while using inefficient detectors and in the presence of quantum-limited loss in the interferometer. The working principle is demonstrated experimentally in a Mach–Zehnder interferometer and a polarisation interferometer for the choice of N = 400 using a commercially available 632.8 nm laser source. The 1/√(N) scaling in phase sensitivity is checked for other values of N. Non-classicality of the detected photons is experimentally demonstrated.
Quantum Fisher Information (QFI), which sets the fundamental bound on parameter estimation precision via the quantum Cramér-Rao inequality, is investigated for a general single-mode Gaussian state before and after teleportation. Using a two-mode squeezed vacuum state as a shared entanglement resource between Alice and Bob, we analyze the teleportation protocol under environmental noise, focusing on diffusion and dissipation induced by a thermal bath. By comparing QFI for several parameters of the input state before and after teleportation, we evaluate the effectiveness of QFI transfer. We find that increasing the squeezing of the shared state enhances QFI preservation. Notably, under certain conditions, environmental interactions can help maintain QFI, particularly for shared states with high frequency, suggesting a subtle interplay between system dynamics and decoherence.
This study presents improved quantum-inspired artificial bee colony algorithm based on the Bloch sphere for multi-objective optimization with particular application to wireless communication security. Firstly, an innovative quantum-inspired artificial bee colony framework for multi-objective optimization is proposed, whose encoding is adopted on the Bloch sphere instead of a quantum bit to extend the feasible solution space, under the control of two development strategies to enhance the accuracy and efficiency of the search. Secondly, tailored updating mechanisms are implemented for different swarm stages, which have undergone enhancements by elite class, alternating search, and adaptive guidance. The quantum rotation angles compatible with this algorithm are designed to accelerate the optimization to improve the overall performance. Furthermore, the proposed algorithm is designed to solve the optimization problem of the wireless communication model in the presence of an intelligent reflective surface with multi objectives. The security and performance are jointly improved through the simultaneous optimization of the security rate and base station beamforming. Experimental comparisons with classical multi-objective algorithms on benchmark test suites demonstrate that the algorithm can consistently converge to the Pareto-optimal frontier and shows significant advantages in GD, Spread, IGD, and run time. It achieves an average improvement of 15.6
We study the one-dimensional frustrated J_1-J_2 Heisenberg spin-1/2 model under periodic boundary conditions, focusing on quantum criticality induced by competing interactions and parity-dependent frustration. Using quantum discord (QD) and global quantum discord (GQD), we analyze phase transitions in mixed and first excited states, revealing clear parity effects: even-length chains show a single energy level crossing and a sharp derivative anomaly near the singular point, which extrapolates to the thermodynamic infinite-order Berezinskii–Kosterlitz–Thouless phase transition point λ _c(∞ )≈ 0.241 ( λ =J_2/J_1 ) marking the Luttinger liquid to dimerized phase transition; odd-length chains exhibit two crossings but no abrupt transition. This smoothing effect is physically rooted in the true geometric frustration inherent to a periodic ring with an odd number of sites, which prohibits perfect dimerization and drives a comprehensive spectral reorganization and state hybridization among the low-lying excited states under low-energy state truncation. The resulting thermal stability of QD and GQD in odd-length chains, valid within the low-temperature regime, offers insights for the design of quantum memory platforms in frustrated systems. Our results highlight QD and GQD as effective probes of parity-resolved quantum phase transitions in frustrated low-dimensional systems.
In this paper, we introduce the variational quantum Kolmogorov–Arnold network (VQKAN), a novel framework for quantum machine learning that uses measurement results of qubits as neurons and quantum gates as synapses. VQKAN is applied to multi-dimensional function fitting and binary classification tasks, where it shows reduced overfitting and competitive accuracy compared to a baseline quantum neural network (QNN) under the conditions tested. We also evaluate VQKAN on a Fourier partial differential equation; on that task, VQKAN does not surpass QNN, QCNN, TTN, or LSTM baselines, and we report this negative result and discuss its implications. Empirically, the per-iteration computation time grows sub-cubically with the number of qubits over the tested range N_q∈ [2,8] (best fit T∝ N_q^2.5 , R^2=0.99 ); a pure logarithmic fit is rejected ( R^2=0.78 ). Within this practical regime, VQKAN offers a favourable trade-off between accuracy and gate count. A key empirical strength of VQKAN is reduced overfitting on the tested fitting tasks compared to QNN, allowing for better generalization even with limited data. Additionally, we present a modified compact ansatz that further enhances accuracy on the regression benchmark; on the classification benchmark, this ansatz is more expressive but more expensive and is not competitive with the canonical ansatz under MAE, a negative result we report alongside the positive one. All numerical experiments use noiseless statevector simulation; we further provide a finite-shot study (256–4096 shots), showing that the test-MAE remains within ∼ 0.06 of the infinite-shot value down to 4096 shots on the regression task, with no systematic degradation at lower shot counts, indicating moderate shot-noise robustness. Hardware (depolarizing / decoherence) noise was not modelled and is left to future work. These contributions establish VQKAN as a promising tool for advancing quantum machine learning and optimization techniques on tasks where edge-wise function approximations are natural.
Reference-frame-independent quantum key distribution (RFI-QKD) has the advantage of tolerating the slow varied reference frame. Two remote communication parties can share secret keys in the case of unknown and drifted reference frames. However, in the practical QKD system, the drift of reference frames will inevitably compromise the performance of the QKD system, resulting in the reduction of the secret key rate and transmission distance. In this paper, we attempt to improve the performance of RFI-QKD and RFI measurement-device-independent QKD (RFI MDI-QKD) based on the two-way local operations and classical communications (TW-LOCC) classical post-processing method. We focus on the iterative B-step-optimized TW-LOCC due to its immediate experimental feasibility. The simulation results show that the TW-LOCC method can significantly improve the transmission distance and secret key rate of RFI-QKD and RFI MDI-QKD by optimizing the number of executions B steps, and the maximum safe transmission distance is increased by 92 and 60 km, respectively. Our work provides a new idea for the post-processing of RFI-QKD protocols and further enhances the practicability and robustness of RFI-QKD.
Quantum computing offers novel paradigms for data representation and signal processing, yet traditional Quantum Image Representation (QIP) models often face significant challenges regarding qubit resources and state preparation complexity. This paper introduces a hybrid quantum-classical framework that utilizes Discrete-Time Quantum Walks (DTQW) as a generative mechanism for construction of classical dictionary learning. The core contribution of this work lies in the spectral and informational characterization of the quantum-generated basis. A comparative analysis against industry-standard benchmarks, including the Discrete Cosine Transform (DCT) and Haar Wavelet Transform (WAV), reveals that the DTQW basis operates in a high-entropy representational regime, achieving a maximum normalized Shannon entropy ( H/H_max≈ 1.0 ). This property facilitates a delocalized or “holographic” distribution of signal energy across the entire coefficient spectrum. Furthermore, we show that applying unitary quantum operator to the position register enables visually interpretable image transformations through a computationally efficient coefficient reuse mechanism. This research shifts the focus from traditional compression-centric imaging toward a robustness-centric quantum-assisted paradigm, offering promising applications in secure communication and resilient image representation.
We investigate the information transmission capabilities of a dissipative three-mode bosonic quantum system by analyzing its associated quantum channel. The study focuses on the evaluation of coherent information and entanglement-assisted classical capacity under both pure and mixed input states. The system dynamics are modeled using a Lindblad master equation, allowing us to capture the effects of environmental decoherence and dissipation. For pure states, the two capacity measures exhibit close agreement, while for mixed states a clear separation emerges due to the contribution of input entropy. The results further reveal a nontrivial dependence on evolution time and Hilbert space dimension, highlighting the competing roles of coherent interactions and noise. These findings provide insight into the fundamental limits of information transmission in realistic open quantum systems.
Preserving quantum correlations in noisy environments is fundamental for advancing quantum technologies. We investigate the interplay between channel memory and indefinite causal order in protecting bipartite correlations—coherence, entanglement, and discord—between two qutrits. Our analysis covers amplitude damping channels with V-type and Λ -type transitions, as well as trit flip, phase flip, and depolarizing channels. We show that memory effects in correlated channels not only delay entanglement sudden death but also enhance the resilience of quantum correlations against decoherence. Strikingly, the quantum switch of amplitude damping and bit-flip channels offers a significant advantage over their memoryless counterparts, demonstrating that indefinite causal order can amplify the benefits of channel memory. Fidelity analysis further confirms that correlations in two-qutrit states remain substantially more robust in correlated channels across all scenarios studied. These findings highlight the potential of combining channel memory and causal indefiniteness as powerful resources for reliable quantum communication and information processing.
The Quantum Fisher Information Matrix (QFIM) quantifies how sensitive parameterized quantum states are to changes in their parameters. Recently, it has been used to improve variational quantum algorithm optimization through geometry-aware techniques. However, estimating the QFIM—particularly its off-block-diagonal elements—requires substantial resources. To address this, we introduce a novel protocol that efficiently computes these elements for commuting-block variational circuits. Our approach reduces the number of quantum state preparations from O(m^2) to O(L^2) , where m is the number of parameters and L the number of circuit layers. This also lowers classical measurement and post-processing requirements, improving computational efficiency.
