arXiv subjects

Carter M. Gustin

Publications and source records attributed to Carter M. Gustin.

5 recordsLinked to original sources

arXiv2026

Second-order effective renormalized Hamiltonian of Quantum Chromodynamics

The effective Hamiltonian of quantum chromodynamics in the front form of Hamiltonian dynamics is calculated and renormalized. The renormalization group procedure for effective particles up to the second order in the coupling constant is used. Small gluon mass is used to regulate infrared singularities of the theory. The counterterms necessary to renormalize the theory are determined by computing matrix elements of the effective Hamiltonian. The effective Hamiltonians are well-defined symmetric forms on a dense subspace of the Fock space. The zero modes are cut off but, once ultraviolet renormalization is performed, no divergences are found in the color singlet subspace in the limit of the gluon mass approaching zero. A major result is that the interplay between self-energy terms and gluon exchange effective terms generates a term proportional to the quadratic SU(3) Casimir operator times the logarithm of the gluon mass. Therefore, the matrix elements are logarithmically divergent in the color nonsinglet subspace, but finite in the color singlet subspace, because the Casimir operator vanishes in the color singlet subspace. The effective Hamiltonians are suitable for nonperturbative numerical calculations using either classical or quantum computers.

hep-ph↗

arXiv2025

Ladder Operator Block-Encoding

We describe and analyze LOBE (Ladder Operator Block-Encoding), a framework for block-encoding ladder operators that act upon fermionic and bosonic modes. In this framework, we achieve efficient block-encodings by applying the desired action of the operator onto the quantum state and pushing any undesired effects outside of the encoded subspace. This direct approach avoids any overhead caused by expanding the operators in another basis. We numerically benchmark these constructions using models arising in quantum field theories including the quartic harmonic oscillator, and $ϕ^4$ and Yukawa Hamiltonians on the light front. These benchmarks show that LOBE often produces block-encodings with fewer non-Clifford operations, fewer block-encoding ancillae and overall number of qubits, and lower rescaling factors for various operators as compared to frameworks that expand the ladder operators in the Pauli basis. LOBE constructions also demonstrate favorable scaling with respect to key parameters, including the maximum occupation of bosonic modes, the total number of fermionic and bosonic modes, and the locality of the operators. LOBE is implemented as an open-source python package to enable further applications.

quant-ph↗

arXiv2025

Second-order renormalized Hamiltonian of Yukawa theory

Using the renormalization group procedure for effective particles (RGPEP) we calculate the effective Hamiltonians in the theory of a fermion field coupled to a scalar field via the Yukawa interaction. The theory is renormalized by the addition of counterterms. Necessary counterterms are determined by computing matrix elements of the effective Hamiltonian. All calculations are performed up to the second order in the expansion in powers of the coupling constant. Renormalized effective Hamiltonians are well-defined symmetric forms acting in the Fock space as opposed to the renormalized bare Hamiltonian, which is not well-defined without regularization. We introduce computational techniques that should streamline higher-order calculations and may be of independent interest.

hep-ph↗

arXiv2025

The Renormalized Yukawa Hamiltonian: Spectrum, Parton Distribution Functions, and Resource Estimates for Quantum Simulation

We apply the Renormalization Group Procedure for Effective Particles (RGPEP) to the front form Yukawa Hamiltonian, yielding a renormalized (effective) Hamiltonian, accurate up to second order in the coupling strength. Subsequently, we examine the spectrum and parton distribution functions produced by the renormalized Hamiltonian, and show that the addition of counterterms leads to finite results. Resource estimates for quantum simulation are calculated for a single `Ladder Operator Block Encoding' (LOBE), and show that the cost to block encode the renormalized Hamiltonian is comparable to block encoding the bare Hamiltonian.

hep-th↗

arXiv2023

Generalized Parton Distribution Functions via Quantum Simulation of Quantum Field Theory in Light-front Coordinates

Quantum simulation of quantum field theories offers a new way to investigate properties of the fundamental constituents of matter. We develop quantum simulation algorithms based on the light-front formulation of relativistic field theories. The process of quantizing the system in light-cone coordinates will be explained for a Hamiltonian formulation, which becomes block diagonal, each block approximating the Fock space with a certain harmonic resolution K. We analyze a QCD theory in 2+1D. We compute the analogue of parton distribution functions, the generalized parton distribution functions for mesonic composite particles, like hadrons, in these theories. The dependence of such analyses on the scaling of the number of qubits is compared with other schemes and conventional computations. There is a notable advantage to the light-front formulation.

hep-th↗