SHENZHEN, China, Oct. 03, 2025 (GLOBE NEWSWIRE) — MicroCloud Hologram Inc. (NASDAQ: HOLO), (“HOLO” or the “Company”), a technology service provider, conducted in-depth research on the low-cost implementation of quantum channels, revealing the optimization boundaries of C-NOT gate counts by constructing a multi-model quantum circuit framework, providing theoretical support for efficient quantum channel design. The circuit decomposition of quantum channels is the process of transforming abstract quantum state transformations into specific quantum gate sequences, with the core challenge being to minimize the number of C-NOT gates used while ensuring functional correctness. The three quantum circuit models (QCM, RandomQCM, MeasuredQCM) proposed by HOLO build a hierarchical research framework from the perspective of progressively expanding operational degrees of freedom.
The first model is the Quantum Circuit Model (QCM), whose basic structure consists of an ordered sequence of single-qubit gates and C-NOT gates, allowing qubits to be reordered at the end of the gate sequence. This model ensures the deterministic implementation of quantum channels through strict gate operation sequences and qubit routing, but its degree of freedom is limited, relying solely on internal quantum state evolution to complete transformations. The second model (RandomQCM) introduces external classical randomness based on QCM, allowing probabilistic operations in the gate sequence design—for example, controlling the selection of certain gates or qubit routing through classical random numbers. This extension provides new degrees of freedom for reducing C-NOT gate counts, particularly demonstrating advantages in handling probabilistic quantum channels. The third model (MeasuredQCM) further incorporates measurement operations and conditional control, allowing qubits to be measured during circuit execution and subsequent operations to be dynamically adjusted based on measurement outcomes. This “measurement-feedback” mechanism significantly enhances circuit flexibility, creating possibilities for simplified decomposition of complex quantum channels.
Through rigorous proofs of the lower bounds on C-NOT gate counts under the three models, using entanglement entropy analysis in quantum information theory and circuit complexity theory, HOLO demonstrated that for any quantum channel from m qubits to n qubits, there exists a fundamental lower bound on the number of C-NOT gates required for its circuit decomposition. This lower bound is jointly determined by the channel’s entanglement capacity and qubit dimensions. For example, for channels that need to preserve full entanglement properties of quantum states, the lower bound on C-NOT gate counts is positively correlated with the product of m and n; whereas for locally decomposable channels, the lower bound can be significantly reduced.
Building on the proof of the lower bound, the team provided near-optimal circuit decomposition solutions for almost all practical scenarios. In QCM, by optimizing the combination sequence of single-qubit gates and qubit routing strategies, the number of C-NOT gates was controlled within 1.5 times the theoretical lower bound. In RandomQCM, probabilistic optimization of gate sequences using classical randomness further reduced the gap to 1.2 times. In MeasuredQCM, leveraging classical information feedback from measurement operations, a “simplified decomposition” for high-complexity channels was achieved, with the number of C-NOT gates approaching the theoretical lower bound in most scenarios.
HOLO’s research provides a new optimization approach for quantum circuit design. Its core value lies not only in providing specific C-NOT gate count results but also in establishing a circuit design paradigm that integrates “measurement – classical feedback – quantum operations.” This paradigm breaks the limitations of traditional quantum circuits that rely solely on unitary operations, significantly enhancing the resource efficiency of quantum channel implementation through dynamic regulation with classical information.
Of course, this approach still faces challenges in practical applications: the measurement operations in MeasuredQCM introduce quantum state collapse, requiring precise control of measurement timing to avoid destroying critical quantum information; meanwhile, conditional operations demand high real-time performance from classical control logic, potentially increasing the complexity of system engineering implementation. However, with advancements in quantum measurement technology and classical-quantum interface design, these issues are expected to be gradually resolved.
In summary, HOLO, through systematic research on three quantum circuit models, has clarified the C-NOT gate cost boundaries for quantum channel implementation. In particular, the efficient decomposition scheme of MeasuredQCM provides a theoretical basis for low-resource quantum channel design, advancing the process of moving quantum computing from the laboratory to practical applications.
About MicroCloud Hologram Inc.
MicroCloud is committed to providing leading holographic technology services to its customers worldwide. MicroCloud’s holographic technology services include high-precision holographic light detection and ranging (“LiDAR”) solutions, based on holographic technology, exclusive holographic LiDAR point cloud algorithms architecture design, breakthrough technical holographic imaging solutions, holographic LiDAR sensor chip design and holographic vehicle intelligent vision technology to service customers that provide reliable holographic advanced driver assistance systems (“ADAS”). MicroCloud also provides holographic digital twin technology services for customers and has built a proprietary holographic digital twin technology resource library. MicroCloud’s holographic digital twin technology resource library captures shapes and objects in 3D holographic form by utilizing a combination of MicroCloud’s holographic digital twin software, digital content, spatial data-driven data science, holographic digital cloud algorithm, and holographic 3D capture technology. MicroCloud focuses on the development of quantum computing and quantum holography, and plans to invest over $400 million in cutting-edge technology sectors, including Bitcoin-related blockchain development, quantum computing technology development, quantum holography development, and the development of derivatives and technologies in artificial intelligence and augmented reality (AR).
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