MicroCloud Hologram Inc. Studies Three Quantum Circuit Models to Achieve Cost Optimization of Quantum Channels

Rhea-AI Summary

MicroCloud Hologram (NASDAQ: HOLO) on October 3, 2025 reported research defining C-NOT gate cost bounds and near‑optimal decompositions for quantum channels using three circuit models: QCM, RandomQCM, and MeasuredQCM. The study proves lower bounds on C-NOT counts via entanglement‑entropy and circuit complexity, showing bounds scale with qubit dimensions and entanglement needs. HOLO reports practical decompositions: QCM within 1.5× the lower bound, RandomQCM within 1.2×, and MeasuredQCM often approaching the theoretical lower bound. The work proposes a measurement–feedback paradigm to reduce C-NOT resources while noting implementation challenges in measurement timing and classical control.

Insights

Quantum circuit theorist

HOLO proves C-NOT lower bounds across three circuit models and offers near‑optimal decompositions for quantum channels.

What it means: The release presents formal lower bounds on required C-NOT gate counts for any m→n quantum channel using entanglement entropy and circuit complexity arguments, and supplies decomposition schemes within 1.5x, 1.2x, and near‑lower‑bound performance for the QCM, RandomQCM, and MeasuredQCM models respectively.

Why it matters: Lower bounds set provable resource limits; near‑optimal constructions mean the gap between theory and implementable circuits is small, which tightens engineering targets for gate counts and benchmarking. The explicit comparison across models clarifies when adding classical randomness or measurement+feedback yields concrete gate‑count savings.

Monitorable item: The company states plans to invest over $400 million in quantum and related technologies, a trackable commitment.

Quantum systems integration engineer

The proposed MeasuredQCM reduces gate counts by using measurement-feedback but raises practical control challenges.

What it means: Adding measurements and conditional classical control allows decomposition closer to theoretical minima by trading unitary depth for mid-circuit measurement and classical loops; the PR claims this yields near‑bound C‑NOT counts in most scenarios.

Why it matters: Real systems must manage measurement‑induced collapse and sub‑microsecond classical control latency; the release explicitly notes these engineering hurdles and links expected resolution to advances in measurement tech and classical‑quantum interfaces. This frames the result as a provable algorithmic gain that still requires hardware and control improvements to realize.

Monitorable item: Track developments in mid‑circuit measurement fidelity and classical control latency as prerequisites to deploy the MeasuredQCM advantages.

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).
For more information, please visit http://ir.mcholo.com/

Safe Harbor Statement

This press release contains forward-looking statements as defined by the Private Securities Litigation Reform Act of 1995. Forward-looking statements include statements concerning plans, objectives, goals, strategies, future events or performance, and underlying assumptions and other statements that are other than statements of historical facts. When the Company uses words such as “may,” “will,” “intend,” “should,” “believe,” “expect,” “anticipate,” “project,” “estimate,” or similar expressions that do not relate solely to historical matters, it is making forward-looking statements. Forward-looking statements are not guarantees of future performance and involve risks and uncertainties that may cause the actual results to differ materially from the Company’s expectations discussed in the forward-looking statements. These statements are subject to uncertainties and risks including, but not limited to, the following: the Company’s goals and strategies; the Company’s future business development; product and service demand and acceptance; changes in technology; economic conditions; reputation and brand; the impact of competition and pricing; government regulations; fluctuations in general economic; financial condition and results of operations; the expected growth of the holographic industry and business conditions in China and the international markets the Company plans to serve and assumptions underlying or related to any of the foregoing and other risks contained in reports filed by the Company with the Securities and Exchange Commission (“SEC”), including the Company’s most recently filed Annual Report on Form 10-K and current report on Form 6-K and its subsequent filings. For these reasons, among others, investors are cautioned not to place undue reliance upon any forward-looking statements in this press release. Additional factors are discussed in the Company’s filings with the SEC, which are available for review at www.sec.gov. The Company undertakes no obligation to publicly revise these forward-looking statements to reflect events or circumstances that arise after the date hereof.

Contacts
MicroCloud Hologram Inc.
Email: IR@mcvrar.com

FAQ

What did MicroCloud Hologram (HOLO) announce on October 3, 2025 about quantum circuit cost?

HOLO announced proofs of lower bounds on C-NOT gate counts and near‑optimal decompositions across three models (QCM, RandomQCM, MeasuredQCM).

How close are HOLO's decompositions to the theoretical C-NOT lower bound?

HOLO reports QCM within 1.5×, RandomQCM within 1.2×, and MeasuredQCM often approaching the lower bound.

What is MeasuredQCM and why does it matter for HOLO (HOLO) investors?

MeasuredQCM adds in-circuit measurements with classical feedback, which HOLO says reduces C-NOT resources and enables more efficient quantum channel designs.

What technical risks did HOLO cite for implementing MeasuredQCM in practice?

HOLO flagged quantum state collapse risk from measurements and the need for high‑performance classical control for conditional operations.

Does the press release include financial commitments or investment plans by HOLO?

Yes; HOLO states plans to invest over $400 million in advanced technologies, including quantum computing and quantum holography.

How could HOLO's research affect its product roadmap or commercial prospects for HOLO (NASDAQ: HOLO)?

HOLO positions the research as a theoretical basis for low‑resource quantum channel design, which may support future quantum/holography product development and commercialization.