Constraint handling is a central challenge for quantum algorithms applied to combinatorial optimization. Standard penalty-based approaches increase problem size, distort energy landscapes, and often degrade performance. Constraint-preserving mixers, such as XY-mixers, restrict quantum evolution to feasible subspaces, but their implementation on gate-based hardware requires Trotterization, which introduces approximation errors. In this work, we systematically investigate the interplay between constraint-preserving XY-mixers and Trotterized Adiabatic Evolution (TAE). We present a theoretical analyses of the origin and scaling of Trotter errors in XY-mixers and show that the dominant contribution depends on the size and structure of individual constraints rather than on the total problem size. Our findings are validated through extensive numerical simulations on three representative problems: Portfolio Optimization, the Multi-Car Paint Shop problem, and a Multi-Commodity Flow problem. For problems with a single global equality constraint spanning all variables, Trotter errors significantly impair XY-mixer performance, making standard Pauli-X mixers more robust under realistic implemen
Sequence and channel mixers, the core mechanism in sequence models, have become the de facto standard in time series analysis (TSA). However, recent studies have questioned the necessity of complex sequence mixers, such as attention mechanisms, demonstrating that simpler architectures can achieve comparable or even superior performance. This suggests that the benefits attributed to complex sequencemixers might instead emerge from other architectural or optimization factors. Based on this observation, we pose a central question: Are common sequence mixers necessary for time-series analysis? Therefore, we propose JustDense, an empirical study that systematically replaces sequence mixers in various well-established TSA models with dense layers. Grounded in the MatrixMixer framework, JustDense treats any sequence mixer as a mixing matrix and replaces it with a dense layer. This substitution isolates the mixing operation, enabling a clear theoretical foundation for understanding its role. Therefore, we conducted extensive experiments on 29 benchmarks covering five representative TSA tasks using seven state-of-the-art TSA models to address our research question. The results show that rep
The realization of universal control in hybrid oscillator-qubit quantum processors enables the systematic design and implementation of quantum algorithms. However, the algorithmic development for such platforms remains at an early stage. While the Quantum Approximate Optimization Algorithm (QAOA) has been extensively studied in both continuous-variable (CV) and discrete-variable (DV) quantum systems, its development in the hybrid CV-DV setting remains limited. In this paper, we propose a hardware-native non-Abelian mixer for QAOA on hybrid CV-DV quantum processors and develop a corresponding hybrid ansatz for the Max-Cut problem. We evaluate the proposed ansatz on unweighted Erdős-Rényi graphs and benchmark it against the standard transverse-field mixer using the approximation ratio and optimal-solution probability. Across all graph sizes and Fock cutoffs in our simulations, the proposed non-Abelian mixer consistently improves both expected solution quality and the probability of sampling an optimal solution relative to the transverse-field mixer. These results indicate that the proposed non-Abelian mixer is a promising building block for QAOA on hybrid oscillator-qubit platforms.
This paper investigates quantum heuristics based on Mixer Hamiltonians, which allow the search to be restricted to a specific subspace and enable warm-start strategies for solving the Traveling Salesman Problem (TSP). Approaches involving Mixer Hamiltonians can be integrated into the Quantum Approximate Optimization Algorithm (QAOA), where the Mixer acts as a mapping function that transforms qubit strings into feasible solution sets. We first introduce a swap-based mixer tailored to the TSP, which ensures that only qubit strings representing valid TSP solutions are explored during the QAOA process. Second, we propose a warm-start technique that initializes QAOA with a solution generated by any classical heuristic, thereby promoting faster convergence. These two contributions are combined into a Warm-Start QAOA framework with a Swap-Based Mixer, leveraging both structural and initialization advantages. Experimental results on a custom TSP instance involving five customers demonstrate the effectiveness of this approach, providing, for the first time, a viable integration of warm-start and swap-based mixers for the TSP within a quantum optimization framework.
Cryptocurrency users increasingly rely on obfuscation techniques such as mixers, swappers, and decentralised or no-KYC exchanges to protect their anonymity. However, at the same time, these services are exploited by criminals to conceal and launder illicit funds. Among obfuscation services, mixers remain one of the most challenging entities to tackle. This is because their owners are often unwilling to cooperate with Law Enforcement Agencies, and technically, they operate as 'black boxes'. To better understand their functionalities, this paper proposes an approach to analyse the operations of mixers by examining their address-transaction graphs and identifying topological similarities to uncover common patterns that can define the mixer's modus operandi. The approach utilises community detection algorithms to extract dense topological structures and clustering algorithms to group similar communities. The analysis is further enriched by incorporating data from external sources related to known Exchanges, in order to understand their role in mixer operations. The approach is applied to dissect the Blender.io mixer activities within the Bitcoin blockchain, revealing: i) consistent str
4D point cloud videos capture rich spatial and temporal dynamics of scenes which possess unique values in various 4D understanding tasks. However, most existing methods work in the spatiotemporal domain where the underlying geometric characteristics of 4D point cloud videos are hard to capture, leading to degraded representation learning and understanding of 4D point cloud videos. We address the above challenge from a complementary spectral perspective. By transforming 4D point cloud videos into graph spectral signals, we can decompose them into multiple frequency bands each of which captures distinct geometric structures of point cloud videos. Our spectral analysis reveals that the decomposed low-frequency signals capture more coarse shapes while high-frequency signals encode more fine-grained geometry details. Building on these observations, we design Spatio-Temporal-Spectral Mixer (STS-Mixer), a unified framework that mixes spatial, temporal, and spectral representations of point cloud videos. STS-Mixer integrates multi-band delineated spectral signals with spatiotemporal information to capture rich geometries and temporal dynamics, while enabling fine-grained and holistic under
A wide array of sequence models are built on a framework modeled after Transformers, comprising alternating sequence mixer and channel mixer layers. This paper studies a unifying matrix mixer view of sequence mixers that can be conceptualized as a linear map on the input sequence. This framework encompasses a broad range of well-known sequence models, including the self-attention of Transformers as well as recent strong alternatives such as structured state space models (SSMs), and allows understanding downstream characteristics such as efficiency and expressivity through properties of their structured matrix class. We identify a key axis of matrix parameterizations termed sequence alignment, which increases the flexibility and performance of matrix mixers, providing insights into the strong performance of Transformers and recent SSMs such as Mamba. Furthermore, the matrix mixer framework offers a systematic approach to developing sequence mixers with desired properties, allowing us to develop several new sub-quadratic sequence models. In particular, we propose a natural bidirectional extension of the Mamba model (Hydra), parameterized as a quasiseparable matrix mixer, which demons
The Grover mixer quantum alternating operator ansatz (GM-QAOA) employs the Grover mixer to confine the quantum evolution to the feasible subspace defined by the problem. Its mixing unitary, however, requires a global multi-controlled phase-shift gate acting on all qubits, resulting in substantial circuit overhead on near-term quantum devices. In this work, we propose locally acting Grover mixers tailored to initial states that admit a product structure over disjoint qubit subsystems, which may be obtained by encoding only a subset of problem constraints into the initial state preparation. The proposed method preserves the search space defined by the initial state while significantly lowering implementation cost, as the global multi-controlled phase-shift gate is replaced with local operations on disjoint subsystems. Numerical simulations on the exact-cover problem and the traveling salesman problem (TSP) demonstrate that the proposed method achieves convergence behavior comparable to that of the original GM-QAOA, while using shallower circuits with fewer gates. We further compare two constraint encoding strategies for the TSP, encoding only a subset of constraints versus all constr
The Quantum Approximate Optimization Algorithm (QAOA) is a quantum algorithm proposed for Noisy Intermediate-Scale Quantum (NISQ) devices and is regarded as a promising approach to combinatorial optimization problems, with potential applications in the financial sector. In this study, we apply QAOA to the portfolio optimization problem, which is one of the central challenges in financial engineering. A portfolio consists of a combination of multiple assets, and the portfolio optimization problem aims to determine the optimal asset allocation by balancing expected return and risk. In the context of quantum optimization, portfolio optimization is often formulated using discrete variables. Unlike conventional binary formulations, we consider a ternary portfolio optimization problem that accounts for three states-holding, not holding, and short selling-and compare its performance using different mixer operators. Specifically, we implement QAOA with the standard mixer and several XY Mixers (XY Ring, XY Parity Ring, XY Full, and QAMPA), and conducted simulations using real data based on the German stock index (DAX 30) for portfolios consisting of 5 and 8 assets. Furthermore, we introduce
Sequential recommendation, a critical task in recommendation systems, predicts the next user action based on the understanding of the user's historical behaviors. Conventional studies mainly focus on cross-behavior modeling with self-attention based methods while neglecting comprehensive user interest modeling for more dimensions. In this study, we propose a novel sequential recommendation model, Pyramid Mixer, which leverages the MLP-Mixer architecture to achieve efficient and complete modeling of user interests. Our method learns comprehensive user interests via cross-behavior and cross-feature user sequence modeling. The mixer layers are stacked in a pyramid way for cross-period user temporal interest learning. Through extensive offline and online experiments, we demonstrate the effectiveness and efficiency of our method, and we obtain a +0.106% improvement in user stay duration and a +0.0113% increase in user active days in the online A/B test. The Pyramid Mixer has been successfully deployed on the industrial platform, demonstrating its scalability and impact in real-world applications.
This letter presents an experimental characterization technique for assessing the performance of terahertz harmonic mixers across a wide frequency range. The total signal transfer loss of three mixers was measured in both up- and down-conversion configurations, and the conversion loss was determined through the solution of a linear system of equations. The proposed method uses LO signals with a frequency offset to ensure single sideband measurements, thereby eliminating the need for image-reject filters. The three-mixer method was verified by measurements of millimeter-wave mixers, which matched the traditional characterization method using a calibrated source and power meter. Given this successful millimeter-wave demonstration, we characterized three WM-86 Schottky diode x4-harmonic mixers from 2.2 to 3 THz. This technique presents a notable advantage for conducting broadband mixer characterizations, particularly in the terahertz frequency regime which lacks tunable, wide-band sources.
Recently, MLP structures have regained popularity, with MLP-Mixer standing out as a prominent example. In the field of computer vision, MLP-Mixer is noted for its ability to extract data information from both channel and token perspectives, effectively acting as a fusion of channel and token information. Indeed, Mixer represents a paradigm for information extraction that amalgamates channel and token information. The essence of Mixer lies in its ability to blend information from diverse perspectives, epitomizing the true concept of "mixing" in the realm of neural network architectures. Beyond channel and token considerations, it is possible to create more tailored mixers from various perspectives to better suit specific task requirements. This study focuses on the domain of audio recognition, introducing a novel model named Audio Spectrogram Mixer with Roll-Time and Hermit FFT (ASM-RH) that incorporates insights from both time and frequency domains. Experimental results demonstrate that ASM-RH is particularly well-suited for audio data and yields promising outcomes across multiple classification tasks. The models and optimal weights files will be published.
We introduce a zero-knowledge cryptocurrency mixer framework that allows groups of users to set up a mixing pool with configurable governance conditions, configurable deposit delays, and the ability to refund or confiscate deposits if it is suspected that funds originate from crime. Using a consensus process, group participants can monitor inputs to the mixer and determine whether the inputs satisfy the mixer conditions. If a deposit is accepted by the group, it will enter the mixer and become untraceable. If it is not accepted, the verifiers can freeze the deposit and collectively vote to either refund the deposit back to the user, or confiscate the deposit and send it to a different user. This behaviour can be used to examine deposits, determine if they originate from a legitimate source, and if not, return deposits to victims of crime.
Graph neural networks have achieved remarkable success in learning graph representations, especially graph Transformer, which has recently shown superior performance on various graph mining tasks. However, graph Transformer generally treats nodes as tokens, which results in quadratic complexity regarding the number of nodes during self-attention computation. The graph MLP Mixer addresses this challenge by using the efficient MLP Mixer technique from computer vision. However, the time-consuming process of extracting graph tokens limits its performance. In this paper, we present a novel architecture named ChebMixer, a newly graph MLP Mixer that uses fast Chebyshev polynomials-based spectral filtering to extract a sequence of tokens. Firstly, we produce multiscale representations of graph nodes via fast Chebyshev polynomial-based spectral filtering. Next, we consider each node's multiscale representations as a sequence of tokens and refine the node representation with an effective MLP Mixer. Finally, we aggregate the multiscale representations of nodes through Chebyshev interpolation. Owing to the powerful representation capabilities and fast computational properties of MLP Mixer, we
Constructing an optimal mixer for Quantum Approximate Optimization Algorithm (QAOA) Hamiltonian is crucial for enhancing the performance of QAOA in solving combinatorial optimization problems. We present a systematic methodology for constructing the QAOA tailored mixer Hamiltonian, ensuring alignment with the inherent symmetries of classical optimization problem objectives. The key to our approach is to identify an operator that commutes with the action of the group of symmetries on the QAOA underlying Hilbert space and meets the essential technical criteria for effective mixer Hamiltonian functionality. We offer a construction method specifically tailored to the symmetric group $S_d$, prevalent in a variety of combinatorial optimization problems. By rigorously validating the required properties, providing a concrete formula and corresponding quantum circuit for implementation, we establish the viability of the proposed mixer Hamiltonian. Furthermore, we demonstrate that the classical mixer $B$ commutes only with a subgroup of $S_d$ of significantly smaller order than the group itself, enhancing the efficiency of the proposed approach. To evaluate the effectiveness of our methodolo
The security of models based on new architectures such as MLP-Mixer and ViTs needs to be studied urgently. However, most of the current researches are mainly aimed at the adversarial attack against ViTs, and there is still relatively little adversarial work on MLP-mixer. We propose an adversarial attack method against MLP-Mixer called Maxwell's demon Attack (MA). MA breaks the channel-mixing and token-mixing mechanism of MLP-Mixer by controlling the part input of MLP-Mixer's each Mixer layer, and disturbs MLP-Mixer to obtain the main information of images. Our method can mask the part input of the Mixer layer, avoid overfitting of the adversarial examples to the source model, and improve the transferability of cross-architecture. Extensive experimental evaluation demonstrates the effectiveness and superior performance of the proposed MA. Our method can be easily combined with existing methods and can improve the transferability by up to 38.0% on MLP-based ResMLP. Adversarial examples produced by our method on MLP-Mixer are able to exceed the transferability of adversarial examples produced using DenseNet against CNNs. To the best of our knowledge, we are the first work to study adv
Recently, Hadfield et al. proposed the quantum alternating operator ansatz algorithm (QAOA+), an extension of the quantum approximate optimization algorithm (QAOA), to solve constrained combinatorial optimization problems (CCOPs). Compared with QAOA, QAOA+ enables the search for optimal solutions within a feasible solution space by encoding problem constraints into the mixer Hamiltonian, thereby reducing the search space and eliminating the possibility of yielding infeasible solutions. However, QAOA+ may incur high overall gate costs when the mixer is applied to all qubits in each layer, and each mixer is costly to implement. To address this challenge, an adaptive mixer allocation strategy is tailored for QAOA+. The resulting algorithm, which integrates this strategy into the original QAOA+ framework, is referred to as AMA-QAOA+. Unlike QAOA+, AMA-QAOA+ adaptively applies the mixer to a subset of qubits in each layer of the mixer unitary operator based on an evaluation function. The performance of AMA-QAOA+ is evaluated on the maximum independent set problem. Numerical simulation results show that, under the same number of optimization runs, AMA-QAOA+ achieves better solution quali
As one of the most fundamental functionalities of microwave photonics, microwave frequency mixing plays an essential role in modern radars and wireless communication systems. However, the commonly utilized intensity modulation in the systems often leads to inadequate spurious-free dynamic range (SFDR) for many sought-after applications. Quantum microwave photonics technique offers a promising solution for improving SFDR in terms of higher-order harmonic distortion. In this paper, we demonstrate two types of quantum microwave photonic mixers based on the configuration of the intensity modulators: cascade-type and parallel-type. Leveraging the nonlocal RF signal encoding capability, both types of quantum microwave photonic mixers not only exhibit the advantage of dual-channel output but also present significant improvement in SFDR. Specifically, the parallel-type quantum microwave photonic mixer achieves a remarkable SFDR value of 113.6 dB.Hz1/2, which is 30 dB better than that of the cascade-type quantum microwave photonic mixer. When compared to the classical microwave photonic mixer, this enhancement reaches a notable 53.6 dB at the expense of 8 dB conversion loss. These results h
We have demonstrated three 4x2 hot electron bolometer (HEB) mixer arrays for operation at local oscillator (LO) frequencies of 1.46, 1.9 and 4.7 THz, respectively. They consist of spiral antenna coupled NbN HEB mixers combined with elliptical lenses. These are to date the highest pixel count arrays using a quasi-optical coupling scheme at supra-THz frequencies. At 1.4 THz, we measured an average double sideband mixer noise temperature of 330 K, a mixer conversion loss of 5.7 dB, and an optimum LO power of 210 nW. The array at 1.9 THz has an average mixer noise temperature of 420K, a conversion loss of 6.9 dB, and an optimum LO power of 190 nW. For the array at 4.7 THz, we obtained an average mixer noise temperature of 700 K, a conversion loss of 9.7 dB, and an optimum LO power of 240 nW. We found the arrays to be uniform regarding the mixer noise temperature with a standard deviation of 3-4%, the conversion loss with a standard deviation of 7-10%, and optimum LO power with a standard deviation of 5-6%. The noise bandwidth was also measured, being 3.5 GHz for the three arrays. These performances are comparable to previously reported values in the literature for single pixels and als
We studied the effect of the NbN/Au contact on the sensitivities of a NbN hot electron bolometer (HEB) mixer by measuring the double sideband (DSB) receiver noise temperature (T_rec_DSB) at three local oscillator frequencies of 1.6, 2.5 and 5.3 THz. The HEB has cleaned contact structures with a thick Au layer. We demonstrated low mixer noise temperatures (T_mixer_DSB) of 240 K and 290 K at 1.6 and 2.5 THz, respectively. The latter reach roughly 3 times the quantum noise at their frequencies. The mixer is developed for the proposed OASIS and SALTUS (concept) missions. The enhanced T_mixer_DSB are more than 30 % better in comparison with published NbN HEB mixers. The improvement can reduce the integration time of a heterodyne instrument roughly by a factor of 2. The T_mixer^DSB of the same HEB has shown limited improvement at 5.3 THz, which is partly due to non-optimized antenna geometry. Besides, the results also help to understand device physics of a wide HEB (4 um) at high frequencies.