Breaking Through the Classic Computing Power Bottleneck: Weiyun Holography (NASDAQ: HOLO) Conformal Truncated Quantum Simulation Analysis

In the field of numerical solutions for strongly coupled quantum field theories, conformal truncation offers a purely field-theoretic approach that does not rely on lattice regularization, providing a new perspective for tackling complex problems such as quantum chromodynamics and condensed matter systems. However, even this optimized method faces computational bottlenecks on classical computers—when the truncation space’s dimension is high, matrix operations become increasingly complex, and calculations can take days. MicroHolo (NASDAQ: HOLO) focuses on this challenge, exploring how quantum algorithms and quantum devices can accelerate conformal truncation calculations, revealing the unique advantages of quantum computing in simulating strongly coupled field theories.

The core of conformal truncation involves leveraging conformal symmetry to efficiently compress degrees of freedom. In quantum field theory, conformal symmetry requires the system to remain invariant under scale transformations, translations, rotations, and other operations. This property allows projecting the infinite-dimensional Hilbert space of the field theory onto a finite subspace spanned by conformal eigenstates. Specifically, the process includes: first identifying the conformal symmetry group (such as the Virasoro algebra in two-dimensional theories), then selecting conformal eigenstates with energies below a certain cutoff as basis vectors, and constructing an effective Hamiltonian within this truncated space. Solving for the eigenvalues and eigenstates of this Hamiltonian approximates physical observables of the original theory—such as particle masses and interaction strengths. Compared to lattice methods, this purely field-theoretic framework avoids discretization errors in spacetime, enabling more precise descriptions of low-energy physics in continuous theories. The trade-off is that the dimension of the truncated space grows rapidly with the energy cutoff, posing a significant challenge for classical computation.

The integration of quantum computing with conformal truncation stems from a deep mathematical compatibility. MicroHolo’s research finds that solving for the effective Hamiltonian in conformal truncation is highly similar to eigenvalue problems in molecular Hamiltonian calculations in quantum chemistry—both involve linear algebra in high-dimensional Hilbert spaces, with Hamiltonians often being sparse (having few non-zero matrix elements). This similarity allows the direct transfer of mature quantum simulation techniques from quantum chemistry—such as variational algorithms and quantum phase estimation—to the conformal truncation setting. More importantly, renormalization group (RG) theory provides a theoretical framework for this transfer: the energy cutoff in conformal truncation essentially acts as an ultraviolet (UV) renormalization, and quantum bit encoding in quantum simulations naturally corresponds to the low-energy degrees of freedom after RG flow. Quantum entanglement efficiently encodes correlations within the field theory, overcoming the dimensionality limitations faced by classical methods.

Focusing on two-dimensional quantum chromodynamics (2D QCD), MicroHolo has validated multiple quantum simulation approaches both theoretically and experimentally. The theoretical design involves mapping the 2D QCD Hamiltonian via conformal truncation into a finite-dimensional effective matrix, which is then encoded as a Hamiltonian evolution operator in a quantum circuit. Specific methods include: adiabatic state preparation—gradually tuning the initial Hamiltonian (such as a product state) to the target Hamiltonian using the adiabatic theorem; variational quantum eigensolvers (VQE)—generating trial states with parameterized quantum circuits and optimizing classical algorithms to minimize energy expectation values, achieving a variational estimate of the 2D QCD ground state energy on IBM’s 16-qubit quantum simulator with errors under 5%; imaginary time evolution—simulating exponential evolution of the Hamiltonian to generate thermal states for studying phase transitions at finite temperature; and quantum Lanczos algorithms—using quantum phase estimation to efficiently compute the lowest eigenvalues of the Hamiltonian, providing data for hadron spectrum calculations. These methods share the common feature of leveraging quantum parallelism to process all basis states in the truncated space simultaneously, greatly reducing computational complexity and enhancing efficiency.

MicroHolo’s research deepens the understanding of the relationship between quantum computing and quantum field theory. Their work demonstrates that the quantum Church-Turing thesis holds in the realm of strongly coupled theories—any computable physical quantity in such theories can be efficiently simulated via quantum algorithms. Looking ahead, as the number of qubits increases and coherence times extend, quantum simulation of conformal truncation is expected to expand to more complex systems such as three-dimensional QCD and gauge/gravity dualities, addressing the limitations of traditional methods.