arXiv subjects

Guorui Zhu

Publications and source records attributed to Guorui Zhu.

9 recordsLinked to original sources

arXiv2026

Three-Loop Five-Point CK-Dual Amplitudes and UV Structure in N=4 SYM and N=8 SUGRA

We construct the complete full-color three-loop five-point integrand of N=4 super-Yang--Mills theory in a representation that manifestly satisfies color--kinematics duality. Its double copy gives the corresponding N=8 supergravity integrand. For four-dimensional external states, we evaluate the ultraviolet poles of both amplitudes in the critical dimension, Dc=6. Extending the external-state dependence to D dimensions is subtle. We consider a candidate replacement of the four-dimensional prefactors by expressions built from D-dimensional tree amplitudes. It reproduces the open-string prediction for the SYM pole with generic D-dimensional external states, whereas the corresponding gravity expression differs from the string-inspired one by an evanescent term.

hep-th↗

arXiv2026

Structure-Aware Compilation for Scalable Neutral-Atom Quantum Computing

We study the compilation of structured quantum gate families on two-dimensional neutral-atom arrays, aiming to reduce addressing and transport overhead under realistic hardware constraints. For single-qubit gates, we exploit the algebraic structures of gate families at the matrix level, enabling efficient rank-one decompositions over appropriate algebraic structures and thereby reducing the number of addressing layers. For controlled-Z (C-Z) gates, we formulate the transport scheduling problem using graph-theoretic models, leading to efficient compilation algorithms under realistic transport constraints. We provide provable performance guarantees for the proposed methods and validate them through extensive numerical experiments. Across representative single-qubit gate families, our methods reduce the number of addressing layers by up to a factor of two compared with na\"ive row- or column-wise implementations. For C-Z gates, our scheduling strategy reduces the required number of atom transport operations by approximately 50\%. When applied to QAOA circuits for MaxCut, the proposed framework reduces transport cost by more than 30\% on average. These results show that the physical constraints of neutral-atom hardware can be converted into algebraic and graph-theoretic structure, turning a hardware-level scheduling bottleneck into tractable decomposition and coloring problems.

quant-ph↗

arXiv2026

Dyeing form factors as amplitudes

The double copy of form factors has revealed a striking feature: poles that are spurious from the gauge-theory perspective become physical propagators in gravity. At the same time, form factors obey hidden factorization relations on the kinematics of these poles. We explain both phenomena by introducing a dyeing procedure, which promotes the color-singlet operator, or the Higgs particle representing it, to an adjoint massive state. The original form factor is recovered by the inverse bleaching operation, realized as a $U(1)$ decoupling of the dyed leg. In the dyed theory, these apparent spurious poles turn into ordinary physical propagators of colored amplitudes, and the hidden factorization relations follow from standard BCJ relations. Applying this framework to multiple operator insertions gives a systematic double-copy construction for multi-Higgs amplitudes and, as a byproduct, reveals scalar-ordering sectors. We also discuss higher-length scalar operators and fermionic operators, including the dyed vector construction for $\bar{\psi}\gamma^{\mu}\psi$, as well as a loop-level example.

hep-th↗

arXiv2026

Double copy of form factors with multiple operator insertions

Extending the double copy of scattering amplitudes to more general physical quantities involving local gauge-invariant operators is a central open question. While progress has been made in the double copy of form factors (FFs) with a single-operator insertion, it has led to two intriguing features: poles that are spurious from the FF viewpoint become physical propagators in gravity, and FFs obey hidden factorization relations on these poles. This picture is difficult to generalize to FFs with multiple operator insertions due to even more complicated spurious pole structures. We resolve this problem by introducing a "dyeing" procedure that promotes color-singlet operators to adjoint colored states, while the original FF is recovered by the inverse "bleaching" (U(1) decoupling) operation. In this new picture, the spurious poles are propagators of the dyed state, and the hidden factorization relations follow from BCJ relations of the dyed amplitudes. For multiple operator insertions, this framework uncovers a new scalar-ordering structure that survives the double copy to gravity.

hep-th↗

arXiv2025

AI for Pattern Hunter: Application in Wilson Loop of 2D Lattice Yang-Mills Theory

We employ the Transformer to learn patterns in two-dimensional lattice Yang-Mills theory. Specifically, we represent both Wilson loops and their expectation values as tokenized sequences. Taking the shape of Wilson loops as input, the model successfully predicts expectation values with high accuracy, indicating a meaningful connection between loop geometry and physical results. Our study differs from prior machine learning applications in lattice QCD by emphasizing analytical structures rather than numerical computations. We explore model performance under varying hyperparameters, training data sizes, and sequence lengths. This work serves as a first step toward extending such methods to higher dimensions and inspiring rigorous analytical derivations.

hep-th↗

arXiv2025

State-Specific Orbital Optimization for Enhanced Excited-States Calculation on Quantum Computers

We propose a state-specific orbital optimization scheme for improving the accuracy of excited states of the electronic structure Hamiltonian for the use on near-term quantum computers, which can be combined with any overlap-based excited-state quantum eigensolver. We derived the gradient of the overlap term between different states generated by different orbitals with respect to the orbital rotation matrix and use the gradient-based optimization methods to optimize the orbitals. This scheme allows for more flexibility in the choice of orbitals. We implement the state-specific orbital optimization scheme with the variational quantum deflation (VQD) algorithm, and show that it achieves higher accuracy than the state-averaged orbital optimization scheme on various molecules including H4 and LiH.

quant-ph↗

arXiv2025

Bootstrapping SU(3) Lattice Yang-Mills Theory

We apply the positivity bootstrap approach to SU(3) lattice Yang-Mills (YM) theory, extending previous studies of large N and SU(2) theories by incorporating multiple-trace Wilson loop operators. By utilizing Hermitian and reflection positivity conditions, alongside Schwinger-Dyson (SD) loop equations, we compute rigorous bounds for the expectation values of plaquette Wilson loops in 2D, 3D, and 4D YM theories. Our results exhibit clear convergence and are consistent with known analytic or numerical results. To enhance the approach, we introduce a novel twist-reflection positivity condition, which we prove to be exact in 2D YM theory. Additionally, we propose a dimensional-reduction truncation, where Wilson loop operators are effectively restricted to a lower-dimensional subplane, significantly simplifying computations. SD equations for double-trace Wilson loops are also derived in detail. Our findings suggest that the positivity bootstrap method is broadly applicable to higher-rank gauge theories beyond single-trace cases, providing a solid foundation for further non-perturbative investigations of gauge theories using positivity-based methods.

hep-th↗

arXiv2025

Quantum Circuit for Non-Unitary Linear Transformation of Basis Sets

This paper introduces a novel approach to implementing non-unitary linear transformations of basis on quantum computational platforms, a significant leap beyond the conventional unitary methods. By integrating Singular Value Decomposition (SVD) into the process, the method achieves an operational depth of $O(n)$ with about $n$ ancilla qubits, enhancing the computational capabilities for analyzing fermionic systems. The non-unitarity of the transformation allows us to transform a wave function from one basis to another, which can span different spaces. By this trick, we can calculate the overlap of two wavefunctions that live in different (but non-distinct Hilbert subspaces) with different basis representations. This provides the opportunity to use state specific ansatzes to calculate different energy eigenstates under orbital-optimized settings and may improve the accuracy when computing the energies of multiple eigenstates simultaneously in VQE or other framework. It allows for a deeper exploration of complex quantum states and phenomena, expanding the practical applications of quantum computing in physics and chemistry.

quant-ph↗

arXiv2024

Applying Color-Kinematics Duality in Pure Yang-Mills at Three Loops

We present the first application of color-kinematics (CK) duality at the three-loop level in non-supersymmetric pure Yang-Mills (YM) theory. Building on the minimal deformation approach introduced in \cite{Li:2023akg}, we extend its use to the three-loop Sudakov form factor. Although three classes of unitarity cuts fail under the globally off-shell CK-dual ansatz, a compact and elegant solution is achieved by deforming a single master numerator. The final numerators exhibit Lorentz invariance in $d$ dimensions and take a local form. This method harnesses CK duality's full potential by enforcing a subset of off-shell dual Jacobi identities for the deformation, offering a promising path toward constructing three-loop amplitudes in non-supersymmetric YM theory and gravity through CK duality and double copy.

hep-th↗