We present Neural Quantum Manifold Forging (NQF), a novel algorithmic paradigm implemented in Rust, designed to overcome the intrinsic limitations of the Variational Quantum Eigensolver (VQE) in the Noisy Intermediate-Scale Quantum (NISQ) era. Unlike static approaches, NQF employs a native auto-differentiation engine and dynamic graphs to heuristically 'forge' the quantum circuit topology in real-time, effectively minimizing circuit depth and decoherence. By leveraging aligned memory allocation (SIMD/AVX-512) and massive parallelism via Rayon, NQF demonstrates up to a 12x processing speedup compared to Python-based frameworks. Validated results from the simulation of the Hydrogen (H2) molecule indicate a massive reduction in logic gate count while maintaining chemical accuracy, establishing NQF as the new standard for scalable quantum simulations.
We present Neural Quantum Manifold Forging (NQF), a novel algorithmic paradigm implemented in Rust, designed to overcome the intrinsic limitations of the Variational Quantum Eigensolver (VQE) in the Noisy Intermediate-Scale Quantum (NISQ) era. Unlike static approaches, NQF employs a native auto-differentiation engine and dynamic graphs to heuristically 'forge' the quantum circuit topology in real-time, effectively minimizing circuit depth and decoherence. By leveraging aligned memory allocation (SIMD/AVX-512) and massive parallelism via Rayon, NQF demonstrates up to a 12x processing speedup compared to Python-based frameworks. Validated results from the simulation of the Hydrogen (H2) molecule indicate a massive reduction in logic gate count while maintaining chemical accuracy, establishing NQF as the new standard for scalable quantum simulations.
The variational quantum eigensolver (VQE) is one of the most representative quantum algorithms in the noisy intermediate-scale quantum (NISQ) era, and is generally speculated to deliver one of the first quantum advantages for the ground-state simulations of some nontrivial Hamiltonians. However, short quantum coherence time and limited availability of quantum hardware resources in the NISQ hardware strongly restrain the capacity and expressiveness of VQEs. In this Letter, we introduce the variational quantum-neural hybrid eigensolver (VQNHE) in which the shallow-circuit quantum Ansatz can be further enhanced by classical post-processing with neural networks. We show that the VQNHE consistently and significantly outperforms the VQE in simulating ground-state energies of quantum spins and molecules given the same amount of quantum resources. More importantly, we demonstrate that, for arbitrary postprocessing neural functions, the VQNHE only incurs a polynomial overhead of processing time and represents the first scalable method to exponentially accelerate the VQE with nonunitary postprocessing that can be efficiently implemented in the NISQ era.
We introduce a general framework called neural-network- (NN) encoded variational quantum algorithms (VQAs), or NNVQA for short, to address the challenges of implementing VQAs on noisy intermediate-scale quantum (NISQ) computers. Specifically, NNVQA feeds input (such as parameters of a Hamiltonian) from a given problem to a neural network and uses its outputs to parameterize an ansatz circuit for the standard VQA. Combining the strengths of NN and parameterized quantum circuits, NNVQA can accelerate the training process of VQAs and handle a broad family of related problems with varying input parameters with the pretrained NN. To concretely illustrate the merits of NNVQA, we present results on a NN variational quantum eigensolver (VQE) for solving the ground state of parameterized XXZ spin models in one and two dimensions. Our results demonstrate that NNVQE is able to estimate the ground-state energies of parameterized Hamiltonians with high precision without fine tuning, and significantly reduce the overall training cost to estimate ground-state properties across the phases of the given Hamiltonian. We also employ an active learning strategy to further increase the training efficiency while maintaining prediction accuracy. These encouraging results demonstrate that NNVQAs offer an alternative hybrid quantum-classical paradigm to utilize NISQ resources for solving more realistic and challenging computational problems.
In the emergent realm of quantum computing, the Variational Quantum Eigensolver (VQE) stands out as a promising algorithm for solving complex quantum problems, especially in the noisy intermediate-scale quantum (NISQ) era. However, the ubiquitous presence of noise in quantum devices often limits the accuracy and reliability of VQE outcomes. This research introduces a novel approach to ameliorate this challenge by utilizing neural networks for zero noise extrapolation (ZNE) in VQE computations. By employing the Qiskit framework, we crafted parameterized quantum circuits using the RY-RZ ansatz and examined their behavior under varying levels of depolarizing noise. Our investigations spanned from determining the expectation values of a Hamiltonian, defined as a tensor product of Z operators, under different noise intensities to extracting the ground state energy. To bridge the observed outcomes under noise with the ideal noise-free scenario, we trained a Feed Forward Neural Network on the error probabilities and their associated expectation values. Remarkably, our model proficiently predicted the VQE outcome under hypothetical noise-free conditions. By juxtaposing the simulation results with real quantum device executions, we unveiled the discrepancies induced by noise and showcased the efficacy of our neural network-based ZNE technique in rectifying them. This integrative approach not only paves the way for enhanced accuracy in VQE computations on NISQ devices but also underlines the immense potential of hybrid quantum-classical paradigms in circumventing the challenges posed by quantum noise. Through this research, we envision a future where quantum algorithms can be reliably executed on noisy devices, bringing us one step closer to realizing the full potential of quantum computing.
A longstanding computational challenge is the accurate simulation of many-body particle systems. Especially for deriving key characteristics of high-impact but complex systems such as battery materials and high entropy alloys (HEA). While simple models allow for simulations of the required scale, these methods often fail to capture the complex dynamics that determine the characteristics. A long-theorized approach is to use quantum computers for this purpose, which allows for a more efficient encoding of quantum mechanical systems. In recent years, the field of quantum computing has become significantly more mature. Furthermore, the rise in integration of machine learning with quantum computing further pushes to a near-term advantage. In this work we aim to improve the well-established quantum computing method for calculating the inter-atomic potential, the variational quantum eigensolver, by presenting an auto-encoded VQE with neural-network predictions: NN-AE-VQE. We apply a quantum autoencoder for a compressed quantum state representation of the atomic system, to which a naive circuit ansatz is applied. This reduces the number of circuit parameters to optimize, while still minimal reduction in accuracy. Additionally, we train a classical neural network to predict the circuit parameters to avoid computationally expensive parameter optimization. We demonstrate these methods on a H2 molecule, achieving chemical accuracy. We believe this method shows promise of efficiently capturing highly accurate systems while omitting current bottlenecks of variational quantum algorithms. Finally, we explore options for exploiting the algorithm structure and further algorithm improvements.
The convergence of quantum computing and machine learning offers significant potential for processing complex data distributions. However, the realization of this potential in the Noisy Intermediate-Scale Quantum (NISQ) era is constrained by physical hardware limitations, particularly restricted qubit counts and system noise. This thesis addresses the challenge of the ”Representation Bottleneck” by establishing a framework for resource-efficient quantum representation learning. The research demonstrates that effective learning on near-term devices can be achieved by optimizing circuit architectures and objective functions to align with hardware constraints. First, to address resource limitations in high-dimensional visual recognition, we propose the Multi-Gate Quantum Convolutional Neural Network (MG-QNN). By employing a Multi-Gate strategy, this architecture optimizes the utilization of quan tum resources within the circuit design. Empirical evaluations on face recognition benchmarks indicate that this approach maintains competitive recognition accuracy while reducing the qubit requirement compared to standard quantum convolutional methods. Second, extending the framework to non-Euclidean data, we introduce the Single-Qubit Graph Neural Network (sQGNN). Utilizing Discrete-Time Quantum Walks, this method encodes graph topologies and relational patterns onto a single qubit. This approach circumvents the need for multi-qubit entangling gates, thereby reducing the computational overhead and noise sensitivity typically associated with processing graph-structured data. Third, in the domain of generative modeling, we present the Single-Qubit Quan tum Convolutional Variational Autoencoder (QCVAE). Addressing the difficulty of generative tasks on constrained devices, this model integrates the Information Bottleneck principle with efficient data re-uploading techniques. The study demonstrates that a single qubit possesses sufficient expressivity to model and reconstruct image distributions effectively when guided by appropriate information theoretic constraints. Finally, to resolve the fundamental limitations of classical loss functions in quantum learning, we establish the Hilbert-Schmidt Information Bottleneck (HSIB). We identify that standard Euclidean metrics often fail to respect the geometric structure of the Hilbert space. The HSIB framework employs the Hilbert Schmidt distance as a tractable geometric measure, providing a learning objective that maximizes information retention while adhering to the intrinsic geometry of quantum states. Collectively, these contributions illustrate that practical quantum machine learning advantage in the NISQ era does not rely solely on scaling hardware, but on the strategic design of resource-efficient architectures and geometrically valid metrics.
Developing robust and high performance quantum software is challenging due to the dynamic nature of existing Python-based frameworks, which often suffer from runtime errors and scalability bottlenecks. In this work, we present LogosQ, a high performance backend agnostic quantum computing library implemented in Rust that enforces correctness through compile time type safety. Unlike existing tools, LogosQ leverages Rust static analysis to eliminate entire classes of runtime errors, particularly in parameter-shift rule gradient computations for variational algorithms. We introduce novel optimization techniques, including direct state-vector manipulation, adaptive parallel processing, and an FFT optimized Quantum Fourier Transform, which collectively deliver speedups of up to 900 times for state preparation (QFT) and 2 to 5 times for variational workloads over Python frameworks (PennyLane, Qiskit), 6 to 22 times over Julia implementations (Yao), and competitive performance with Q sharp. Beyond performance, we validate numerical stability through variational quantum eigensolver (VQE) experiments on molecular hydrogen and XYZ Heisenberg models, achieving chemical accuracy even in edge cases where other libraries fail. By combining the safety of systems programming with advanced circuit optimization, LogosQ establishes a new standard for reliable and efficient quantum simulation.