arXiv subjects

Mark S. Gordon

Publications and source records attributed to Mark S. Gordon.

8 recordsLinked to original sources

arXiv2026

An Agentic Workflow for Legacy HPC Modernization: Converting the Two-Electron-Integral Core of GAMESS

Modernizing legacy Fortran is a problem of volume: the transformations are individually routine, but the codebases can be enormous, and across much of computational science the work simply goes undone. We propose an agentic workflow that takes this work on at production scale, and we set out to measure how far such delegation can reach. In this work, three prompt-specialized agent roles operate under a version-controlled specification that the agents themselves authored and revised, while humans hold a small number of gates. The arrangement is kept safe by an exact verification oracle inherited from the domain, and the boundary of safe delegation lies exactly where that oracle stops seeing. We apply the proposed workflow in a case study, converting the two-electron-integral routines of GAMESS (General Atomic and Molecular Electronic Structure System), a mature quantum-chemistry package with a 48-year development history, from fixed-form Fortran 77 to free-form Fortran 2008. The scope of this work was twelve source files, 56,448 lines, and 225 subroutines for computing electron repulsion integrals. The agents ran as three Claude Code roles in isolated worktrees, and the work spanned four Claude model generations. Because the GAMESS group ships a standard test suite whose printed energies its user community treats as canonical, we could adopt bit-for-bit reproduction of those energies as the merge criterion, where a deviation in the twelfth decimal place counts as a failure rather than drift. All twelve source files pass a 51-test validation battery comprising the 49 standard GAMESS tests and two additional calculations, and across 612 test runs the number of chemistry-relevant differences is zero, and every file also passes the Jenkins tests that are used for continuous integration.

cs.AI↗

arXiv2025

Fragmentation of Virtual Orbitals for Quantum Computing: Reducing Qubit Requirements through Many-Body Expansion

We introduce quantum virtual-orbital fragmentation (Q-FVO), a systematic method for reducing the largest active space in correlated quantum-chemistry calculations. The complete occupied space is retained, the localized virtual space is partitioned into chemically motivated fragments, and the correlation energy is recovered through an inclusion-exclusion many-body expansion. Across six molecular benchmarks, the largest one-body Q-FVO calculations reduce the qubit requirement by 46 to 66 percent, while two-body calculations reduce it by approximately 31 to 42 percent relative to the corresponding unfragmented spaces. Two-body expansions recover most of the correlation energy, with errors of 0.9 to 7.5 kcal/mol; three-body expansions are below 1 kcal/mol for all CCSD tests and remain below 2 kcal/mol at CCSD(T). Illustrative statevector UCCSD calculations also reduce implementation-reported circuit depth while retaining accuracy below 1 kcal/mol. Q-FVO can be nested inside Q-EFMO real-space fragmentation and, in turn, the resulting cluster can be embedded in a Q-EFP environment. The hierarchy therefore reduces quantum-resource growth along three complementary dimensions: environment, molecular fragments, and virtual-orbital space.

quant-ph↗

arXiv2025

A Verified Compiler for Quantum Simulation

Hamiltonian simulation is a central application of quantum computing, with significant potential in modeling physical systems and solving complex optimization problems. Existing compilers for such simulations typically focus on low-level representations based on Pauli operators, limiting programmability and offering no formal guarantees of correctness across the compilation pipeline. We introduce QBlue, a high-level, formally verified framework for compiling Hamiltonian simulations. QBlue is based on the formalism of second quantization, which provides a natural and expressive way to describe quantum particle systems using creation and annihilation operators. To ensure safety and correctness, QBlue includes a type system that tracks particle types and enforces Hermitian structure. The framework supports compilation to both digital and analog quantum circuits and captures multiple layers of semantics, from static constraints to dynamic evolution. All components of QBlue, including its language design, type system, and compilation correctness, are fully mechanized in the Rocq proof framework, making it the first end-to-end verified compiler for second-quantized Hamiltonian simulation.

cs.PL↗

arXiv2025

Quantum Simulation Programming via Typing

Quantum simulations are designed to model quantum systems, and many compilation frameworks have been developed for executing such simulations on quantum computers. Most compilers leverage the capabilities of digital and analog quantum computers by representing quantum particle systems with Pauli strings or digital quantum circuits, making it challenging for users in physics, chemistry, and biology to program simulations effectively. QBLUE is proposed as the first programming language for describing the behaviors of quantum systems in terms of second quantization Hamiltonians. Within QBLUE, a novel type system is proposed to clearly define states across different quantum systems and treat quantum computers as quantum particle systems of specific types. The type system is compatible with the compilation of quantum simulations expressed in QBLUE for digital and analog quantum computers. With QBLUE, users can specify the desired quantum particle system and model the system on quantum computers.

quant-ph↗

arXiv2018

Nodal Variational Principle for Excited States

It is proven that the exact excited-state wave function and energy may be obtained by minimizing the energy expectation value of trial wave functions that are constrained only to have the correct nodes of the state of interest. This excited-state nodal minimum principle has the advantage that it requires neither minimization with the constraint of wave-function orthogonality to all lower eigenstates nor the antisymmetry of the trial wave functions. It is also found that the minimization over the entire space can be partitioned into several interconnected minimizations within the individual nodal regions, and the exact excited-state energy may be obtained by a minimization in just one or several of these nodal regions. For the proofs of the theorem, it is observed that the many-electron eigenfunction (excited state as well as ground state), restricted to a nodal region, is equivalent to a ground-state wave function of one electron in a higher-dimensional space; and, alternatively, an explicit excited-state energy variational expression is utilized by generalizing the Jacobi method of multiplicative variation. In corollaries, error functions are constructed for cases for which the nodes are not necessarily exact. The exact nodes minimize the energy error functions with respect to nodal variations. Simple numerical illustrations of the error functions are presented.

quant-ph↗

arXiv2017

An efficient MPI/OpenMP parallelization of the Hartree-Fock method for the second generation of Intel Xeon Phi processor

Modern OpenMP threading techniques are used to convert the MPI-only Hartree-Fock code in the GAMESS program to a hybrid MPI/OpenMP algorithm. Two separate implementations that differ by the sharing or replication of key data structures among threads are considered, density and Fock matrices. All implementations are benchmarked on a super-computer of 3,000 Intel Xeon Phi processors. With 64 cores per processor, scaling numbers are reported on up to 192,000 cores. The hybrid MPI/OpenMP implementation reduces the memory footprint by approximately 200 times compared to the legacy code. The MPI/OpenMP code was shown to run up to six times faster than the original for a range of molecular system sizes.

cs.DC↗

arXiv2007

New symmetric families of silicon quantum dots and their conglomerates as a tunable source of photoluminescence in nanodevices

We propose a new variety of silicon quantum dots containing fullerene-derived hollows of nearly arbitrary symmetry. Conglomerate structures are designed by connecting the quantum dots through two kinds of junctions. The quantum confinement effect is investigated using semiempirical quantum-mechanical method. It is shown that within each family of quantum dots, the band gap and the stability are inversely proportional to the particle effective size. Quantum dots inherit a wide variety of structural and symmetry properties from their parent fullerenes. The conglomerates confine electrons like quasi-molecules with a peculiar electronic structure related to the junctions. Quantum dots and their conglomerates can host guest atoms in their hollows and therefore present a new promising type of tunable photoluminescent nanomaterials.

cond-mat.mtrl-sci↗

arXiv2007

Multiterminal Nanowire Junctions of Silicon: A Theoretical Prediction of Atomic Structure and Electronic Properties

Using empirical scheme, atomic structure of a new exotic class of silicon nanoclusters was elaborated upon the central icosahedral core (Si-IC) and pentagonal petals (Si-PP) growing from Si-IC vertexes. It was shown that Si-IC/Si-PP interface formation is energetically preferable. Some experimental observations of silicon nanostructures can be explained by presence of the proposed objects. The Extended Huckel Theory electronic structure calculations demonstrate an ability of the proposed objects to act as nanoscale tunnel junctions.

cond-mat.mtrl-sci↗