MicroCloud Hologram Inc. Develops Approximate Quantum State Preparation and Entanglement-Dependent Complexity Algorithm Technology
SHENZHEN, China, June 25, 2026 (GLOBE NEWSWIRE) — MicroCloud Hologram Inc. (NASDAQ: HOLO), (“HOLO” or the “Company”), a technology service provider, has announced a groundbreaking achievement of great theoretical and engineering significance: its proprietary technology for approximate quantum state preparation alongside an entanglement-dependent complexity algorithm. By systematically restructuring the quantum state preparation workflow, this technology effectively shifts the exponentially growing computational complexity of conventional quantum circuits to classical computing systems. Combined with entanglement structure analysis, the firm has built a controllable-depth approximate state generation framework, which delivers overall performance superior to traditional exact state initialization methods on existing noisy intermediate-scale quantum devices.
Quantum state preparation serves as a fundamental building block in quantum computing. Whether deployed for quantum machine learning, quantum optimization, quantum simulation, or high-dimensional data analysis tasks based on amplitude encoding, all these applications hinge on the critical step of mapping classical data into quantum states. Mathematically, a system of n qubits can span a 2n-dimensional complex vector space, which theoretically enables the encoding of intricate data structures within an exponentially expanded space. Nevertheless, this powerful expressive capability comes with substantial engineering overhead. For any arbitrary unstructured dataset, the exact preparation of its corresponding quantum state generally demands an exponential number of controlled rotation gates and multi-qubit entanglement operations. As a result, circuit depth and total gate counts quickly exceed the operational limits of current-generation quantum hardware.
The technical framework developed by HOLO consists of three tightly coupled layers. To begin with, the classical computing layer executes structural analysis and amplitude rearrangement on input data. The team adopts tensor decomposition to represent datasets, analyzes their inherent low-rank features and correlation distributions, and further identifies the regions that dominate amplitude contributions. When processing high-dimensional image or vector data, this layer leverages matrix and tensor decomposition techniques to extract principal components and generate compressed data representations. Within this workflow, the algorithm introduces an entanglement-dependent complexity metric to quantify the minimum entanglement resources required to construct the target quantum state.
Entanglement-dependent complexity acts as a core theoretical tool underpinning this technology. Conventional quantum state complexity is commonly evaluated based on total gate counts or circuit depth, whereas this newly proposed framework characterizes complexity from the perspective of entanglement structure. Specifically, the bipartite or multipartite entanglement entropy distribution of a target quantum state dictates how many layers of entanglement are necessary for state realization. If a quantum state features locally concentrated or decomposable entanglement distribution, it can be accurately approximated via finite-depth quantum circuits. In contrast, states with highly globally distributed entanglement suffer from an exponential rise in preparation difficulty. HOLO has established a complexity assessment model grounded in the approximation bounds of entanglement entropy, which guides the selection of appropriate approximation strategies deployed on the quantum computing side.
The second layer covers the construction of quantum approximate circuits. Hierarchical parameterized circuit architectures are generated according to analytical outputs from the classical computing layer. Unlike conventional universal amplitude loading schemes, these circuits adopt a modular design, with each module corresponding to a dedicated entanglement subspace. Local rotation gates and controlled entanglement gates are combined to implement block-wise amplitude approximation. All modules are interconnected following constrained connection rules, which prevents the explosive proliferation of global entanglement. The resulting circuit depth increases linearly with the number of core entanglement blocks, rather than scaling exponentially with the overall data dimensionality.
The third optimization layer adopts a hybrid quantum-classical iterative parameter updating mechanism. Distinct from approaches that rely entirely on quantum gradient feedback, this technology first predicts amplitude error distributions on the classical computing side and only conducts fine-tuning on the quantum hardware for critical regions. Quantum measurement results are used to correct local approximation deviations, while most parameter optimization tasks are completed through classical computation. This classical-dominant strategy supplemented by quantum correction drastically cuts down measurement frequency and the operational costs incurred from repeated circuit execution.
For experimental validation, the R&D team carried out tests on multiple groups of random vectors and image datasets spanning different dimensions. Experimental results reveal that, on mainstream superconducting quantum processors currently available, traditional exact amplitude initialization circuits exceed the coherence time limits of quantum hardware once more than a dozen qubits are deployed, leading to a sharp decline in the fidelity of output quantum states. By contrast, the approximate state preparation algorithm reduces circuit depth by over 50%, maintains a tolerable level of amplitude error, and substantially lowers the relative entropy between the measured overall distribution and the target distribution.
Notably, when applied to quantum machine learning scenarios, approximate state preparation not only avoids degradation in model performance but can also enhance generalization ability. HOLO designed comparative image classification experiments, where input data was loaded into quantum feature mapping circuits using both exact and approximate initialization methods. Under noisy operating conditions, the model built with approximate state loading achieved marginally higher classification accuracy on test datasets than its exact-state counterpart. This performance difference can be attributed to improved noise robustness and effective overfitting suppression. While exact state loading delivers complete theoretical information, it tends to magnify minor amplitude errors in noisy environments. By contrast, approximate states undergo smoothing during classical preprocessing, delivering more stable runtime performance in practical hardware deployments.
From an industrialization standpoint, this approximate quantum state preparation technology provides vital technical support for quantum machine learning, quantum data analytics and quantum simulation applications. It can drastically lower operational barriers in fields requiring large-scale data loading, including financial risk evaluation, material simulation and complex network analysis, accelerating the practical commercial adoption of quantum algorithms. Particularly in the current noisy intermediate-scale quantum era, trading modest approximation errors for comprehensive performance gains has emerged as a pragmatic and viable engineering solution.
Moving forward, HOLO will further refine its theoretical model for entanglement-dependent complexity and explore optimal approximate mapping strategies tailored to diverse data structures. The R&D team also plans to deeply integrate this algorithm with quantum neural network architectures to build an end-to-end quantum data processing framework. This innovation not only redefines the standard for measuring complexity in quantum state loading from a theoretical perspective but also verifies through engineering practice that moderate approximation outperforms rigid pursuit of full precision in real-world applications. Given the ongoing immaturity of large-scale quantum hardware, constructing hybrid collaborative computing architectures via reasonable complexity allocation between classical and quantum systems may represent the pivotal pathway to advancing quantum computing toward widespread large-scale industrial deployment.
About MicroCloud Hologram Inc.
MicroCloud Hologram Inc. (NASDAQ: HOLO) is committed to the research and development and application of holographic technology. Its holographic technology services include holographic light detection and ranging (LiDAR) solutions based on holographic technology, holographic LiDAR point cloud algorithm architecture design, technical holographic imaging solutions, holographic LiDAR sensor chip design, and holographic vehicle intelligent vision technology, providing services to customers offering holographic advanced driving assistance systems (ADAS). MicroCloud Hologram Inc. provides holographic technology services to global customers. MicroCloud Hologram Inc. also provides holographic digital twin technology services and owns proprietary holographic digital twin technology resource libraries. Its holographic digital twin technology resource library utilizes a combination of holographic digital twin software, digital content, space data-driven data science, holographic digital cloud algorithms, and holographic 3D capture technology to capture shapes and objects in 3D holographic form. MicroCloud Hologram Inc. focuses on the development of quantum computing and quantum holography. With cash reserves exceeding 390 million USD, the company plans to invest over 400 million USD in blockchain development, quantum computing R&D, quantum holography technology, as well as in the development of derivatives and technologies in cutting-edge fields such as AI, AR, and more. MicroCloud Hologram Inc.’s goal is to become a global leader in quantum holography and quantum computing technologies.
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