The rapid and reliable assembly of defect-free atom arrays poses a fundamental challenge for neutral atom quantum computing. While parallel rearrangement methods using spatial light modulators show promise, they suffer from significant overhead in two sub-tasks: atom-site matching and hologram generation. We propose a framework to address these bottlenecks and enhance the efficiency and fidelity of the assembly process. It features a new optimization objective for atom-site matching that minimizes the longest movement path, and a Fourier U-Net model that integrates Fourier operators with image-to-image translation to enable real-time hologram generation. The model is trained in a fully self-supervised paradigm, leveraging the physical properties of holography to remove the need for costly ground-truth labels. Experimental results show our framework not only significantly outperforms the state-of-the-art supervised CNN-based model but also achieves an inference speed orders of magnitude faster than traditional iterative algorithms, enabling real-time, dynamic atom rearrangement.

Differential equations are essential and popular in science and engineering. Learning-based methods including neural operators, have emerged as a promising paradigm. We explore its quantum counterpart, and propose QuanONet – a quantum neural operator which has not been well studied in literature compared with their counterparts in other machine learning areas. We design a novel architecture as a hardware-efficient ansatz, in the era of noisy intermediate-scale quantum (NISQ). Its circuit is pure quantum. By lying its ground on the operator approximation theorem for its quantum counterpart, QuanONet in theory can fit various differential equation operators. We also propose its modified version TF-QuanONet with ability to adaptively fit the dominant frequency of the problem. The real-device empirical results on problems including anti-derivative operators, Diffusion-reaction Systems demonstrate that QuanONet outperforms peer quantum methods when their model sizes are set akin to QuanONet.

Quantum computing has gained considerable attention, especially after the arrival of the Noisy Intermediate-Scale Quantum (NISQ) era. Quantum processors and cloud services have been made worldwide increasingly available. Unfortunately, jobs on existing quantum processors are often executed in series, and the workload could be heavy to the processor. Typically, one has to wait for hours or even longer to obtain the result of a single quantum job on public quantum cloud due to long queue time. In fact, as the scale grows, the qubit utilization rate of the serial execution mode will further diminish, causing the waste of quantum resources. In this paper, to our best knowledge for the first time, the Quantum Job Scheduling Problem (QJSP) is formulated and introduced, and we accordingly aim to improve the utility efficiency of quantum resources. Specifically, a noise-aware quantum job scheduler (NAQJS) concerning the circuit width, number of measurement shots, and submission time of quantum jobs is proposed to reduce the execution latency. We conduct extensive experiments on a simulated Qiskit noise model, as well as on the Xiaohong (from QuantumCTek) superconducting quantum processor. Numerical results show the effectiveness in both the QPU time and turnaround time.

With the arrival of the Noisy Intermediate-Scale Quantum (NISQ) era, Variational Quantum Algorithms (VQAs) have emerged as popular approaches to obtain possible quantum advantage in the relatively near future. In particular, how to effectively incorporate the common symmetries in physical systems as hard constraints in VQAs remains a critical and open question. In this paper, we revisit the Hamming Weight (HW) preserving ansatz and establish the links from ansatz to various symmetries and constraints, which both enlarges the usage of HW preserving ansatz and provides a coherent solution for constrained VQAs. Meanwhile, we utilize the quantum optimal control theory and quantum overparameterization theory to analyze the capability and expressivity of HW preserving ansatz and verify these theoretical results on unitary approximation problem. We conduct detailed numerical experiments on two well-studied symmetry-preserving problems, namely ground state energy estimation and feature selection in machine learning. The superior performance demonstrates the efficiency and supremacy of the proposed HW preserving ansatz on constrained VQAs.

With the arrival of the Noisy Intermediate-Scale Quantum (NISQ) era, Variational Quantum Algorithms (VQAs) have emerged to obtain possible quantum advantage. In particular, how to effectively incorporate hard constraints in VQAs remains a critical and open question. In this paper, we manage to combine the Hamming Weight Preserving ansatz with a topological-aware parity check on physical qubits to enforce error mitigation and further hard constraints. We demonstrate the combination significantly outperforms peer VQA methods on both quantum chemistry problems and constrained combinatorial optimization problems e.g. Quadratic Assignment Problem. Intensive experimental results on both simulators and superconducting quantum processors are provided to verify that the combination of HWP ansatz with parity check is among the most promising candidates to demonstrate quantum advantages in the NISQ era to solve more realistic problems.

Automatic quantum architecture search (QAS) has been widely studied across disciplines with different implications. In this paper, beyond a particular domain, we formulate the QAS problem into two basic (and relatively even ideal) tasks: i) arbitrary quantum circuit (QC) regeneration given a target QC; ii) approximating an arbitrary unitary (oracle). The latter can be connected to the setting of various quantum machine learning tasks and other QAS applications. Based on these two tasks, we generate a public QAS benchmark including 900 random QCs and 400 random unitary matrices which is still missing in the literature. We evaluate six baseline algorithms including brute force search, simulated annealing, genetic algorithm, reinforcement learning, hybrid algorithm, and differentiable algorithm as part of our benchmark. One characteristic of our proposed evaluation protocol on the basic tasks is that it deprives the domain-specific designs and techniques as used in existing QAS literature, making a unified evaluation possible and focusing on the vanilla search methods themselves without coupling with domain prior. In fact, the unitary approximation task could be algorithmically more difficult than the specific problems as it needs to explore the whole matrix space to fit the unitary. While specific tasks often only need to fit a partial observation of the unitary as the objective for search. Data and code are available at https://github.com/Lucky-Lance/QAS-Bench.

With the arrival of the Noisy Intermediate-Scale Quantum (NISQ) era and the fast development of machine learning, variational quantum algorithms (VQA) including Variational Quantum Eigensolver (VQE) and quantum neural network (QNN) have received increasing attention with wide potential applications in foreseeable near future. We study the problem of quantum architecture search (QAS) for VQA to automatically design parameterized quantum circuits (PQC). We devise a differentiable searching algorithm based on Gumbel-Softmax in contrast to peer methods that often require numerous circuit sampling and evaluation. Two versions of our algorithm are provided, namely macro search and micro search, where macro search directly searches for the whole circuit like other literature while the innovative micro search is able to infer the sub-circuit structure from a small-scale and then transfer that to a large-scale problem. We conduct intensive experiments on unweighted Max-Cut, ground state energy estimation, and image classification. The superior performance shows the efficiency and capability of macro search, which requires little prior knowledge. Moreover, the experiments on micro search show the potential of our algorithm for large-scale QAS problems.

Learning 3D graph with spatial position as well as node attributes has been recently actively studied, for its utility in different applications e.g. 3D molecules. Quantum computing is known a promising direction for its potential theoretical supremacy for large-scale graph and combinatorial problem as well as the increasing evidence for the availability to physical quantum devices in the near term. In this paper, for the first time to our best knowledge, we propose a quantum 3D embedding ansatz that learns the latent representation of 3D structures from the Hilbert space composed of the Bloch sphere of each qubit. Specifically, the 3D Cartesian coordinates of nodes are converted into rotation and torsion angles and then encode them into the form of qubits. Moreover, Parameterized Quantum Circuit (PQC) is applied to serve as the trainable layers and the output of the PQC is adopted as the final node embedding. Experimental results on two downstream tasks, molecular property prediction and 3D molecular geometries generation, demonstrate the effectiveness of our model. We show the capacity and capability of our model with the evaluation on the QM9 dataset (134k molecules) with very few parameters, and its potential to be executed on a real quantum device.

Combinatorial optimization (CO) on the graph is a crucial but challenging research topic. Recent quantum algorithms provide a new perspective for solving CO problems and have the potential to demonstrate quantum advantage. Quantum Approximate Optimization Algorithm (QAOA) is a well-known quantum heuristic for CO constructed by a parametric quantum circuit. However, QAOA is originally designed for unconstrained problems and the circuit parameters and solutions are jointly solved with time-consuming iterations. In this paper, we propose a novel quantum neural network (QNN) for learning CO problems in a supervised manner to achieve better and faster results. We focus on the Quadratic Assignment Problem (QAP) with matching constraints and the node permutation invariance property. To this end, a quantum neural network called QAP-QNN is devised to translate the QAP into a constrained vertex classification task. Moreover, we study two QAP tasks: Graph Matching and Traveling Salesman Problem on TorchQauntum simulators, and empirically show the effectiveness of our approach.

Learning of network embedding with vector-based node representation has attracted wide attention over the decade. It differs from the general setting of graph node embedding whereby the node attributes are also considered and yet may incur privacy issues. In this paper, we depart from the classic CPU/GPU architecture to consider the well-established network alignment problem based on network embedding, and develop a quantum machine learning approach with a low qubit cost for its near-future applicability on Noisy Intermediate-Scale Quantum (NISQ) devices. Specifically, our model adopts the discrete-time quantum walk (QW) and conducts the QW on the tailored merged network to extract structure information from the two aligning networks without the need for quantum state preparation which otherwise requires high quantum gate cost. Then the quantum states from QW are fed to a quantum embedding ansatz (i.e., parameterized circuit) to learn the latent representation of each node. The key part of our approach is to connect these two quantum modules to achieve a pure quantum paradigm without involving classical modules. To our best knowledge, there has not been any classic-quantum hybrid approach to network embedding, let alone a pure quantum paradigm being free from the bottleneck of communication between classic devices and quantum devices, which is still an open problem. Experimental results on two real-world datasets show the effectiveness of our quantum embedding approach in comparison with classical embedding approaches. Our model is readily and efficiently implemented in Python with a full-amplitude simulation of the QW and the quantum circuit. Therefore, our model can be readily deployed on an existing NISQ device with all the circuits provided, and only 13 qubits are needed in the experiments, which is rarely attained in existing quantum graph learning works.

Graph representation learning has been extensively studied, and recent models can well incorporate both node features and graph structures. Despite these progress, the inherent scalability challenge for classical computers of processing graph data and solving the downstream tasks (many are NP-hard) is still a bottleneck for existing classical graph learning models. On the other hand, quantum computing is known a promising direction for its theoretically verified scalability as well as the increasing evidence for the access to physical quantum machine in near-term. Different from many existing classical-quantum hybrid machine learning models on graphs, in this paper we take a more aggressive initiative for developing a native quantum paradigm for (attributed) graph representation learning, which to our best knowledge, has not been fulfilled in literature yet. Specifically, our model adopts the well-established theory and technique in quantum computing e.g. quantum random walk, and adapt it to the attributed graph. Then the node attribute quantum state sequence is fed into a quantum recurrent network to obtain the final node embedding. Experimental results on three public datasets show the effectiveness of our quantum model which also outperforms a classical learning approach GraphRNA notably in terms of efficiency even on a classical computer. Though it is still restricted to the classical loss-based learning paradigm with gradient descent for model parameter training, while our computing scheme is compatible with quantum computing without involving classical computers. This is in fact largely in contrast to many hybrid quantum graph learning models which often involve many steps and modules having to be performed on classical computers.

Influence Maximization (IM) problem is to select influential users to maximize the influence spread, which plays an important role in many real-world applications such as product recommendation, epidemic control, and network monitoring. Nowadays multiple kinds of information can propagate in online social networks simultaneously, but current literature seldom discuss about this phenomenon. Accordingly, in this article, we propose Multiple Influence Maximization (MIM) problem where multiple information can propagate in a single network with different propagation probabilities. The goal of MIM problems is to maximize the overall accumulative influence spreads of different information with the limit of seed budget . To solve MIM problems, we first propose a greedy framework to solve MIM problems which maintains an -approximate ratio. We further propose parallel algorithms based on semaphores, an inter-thread communication mechanism, which significantly improves our algorithms efficiency. Then we conduct experiments for our framework using complex social network datasets with 12k, 154k, 317k, and 1.1m nodes, and the experimental results show that our greedy framework outperforms other heuristic algorithms greatly for large influence spread and parallelization of algorithms reduces running time observably with acceptable memory overhead.