A Computational Framework for Quantum Mechanics

Burigede Liu, M. Ortíz, Fehmi Cirak

Ed Gerck

We present a proposal addressing the foundational question of whether quantum mechanics can be reformulated in a computable way. Using a rational, and deterministic framework based on arbitrary-length integers and algebra. Departing from traditional models that rely on real numbers, complex amplitudes, and probabilistic interpretations, we propose a rational-number-based formulation of quantum mechanics. We demonstrate this approach through the exact eigenvalue formulation of the Schrödinger equation, a harmonization of general relativity with QM, and a reworking of Shor's algorithm using only finite, rational arithmetic (ISA). Our results suggest that quantum theory can be grounded in exact, computable logic that aligns with physical measurement, quantum computing, and existing digital hardware.

Ed Gerck

We present a proposal addressing the foundational question of whether quantum mechanics can be reformulated in a computable way. Using a rational, and deterministic framework based on arbitrary-length integers and algebra. Departing from traditional models that rely on real numbers, complex amplitudes, and probabilistic interpretations, we propose a rational-number-based formulation of quantum mechanics. We demonstrate this approach through the exact eigenvalue formulation of the Schrödinger equation, a harmonization of general relativity with QM, and a reworking of Shor's algorithm using only finite, rational arithmetic (ISA). Our results suggest that quantum theory can be grounded in exact, computable logic that aligns with physical measurement, quantum computing, and existing digital hardware.

Burcin Temel

Bart D’Hooghe, Jarosław Pykacz

Joseph C. R. Thacker, Mateusz Meller, Alberto Popescu +4 more

We present a multiscale workflow for coupling quantum computing algorithms for quantum chemical calculations with conventional high-performance computing (HPC) software. The resulting embedding framework, implemented in the multiscale computational chemistry environment ChemShell, combines a generic N-layer subtractive quantum mechanics/molecular mechanics (QM/MM) scheme and selection of an active orbital space for the quantum algorithm region. We have benchmarked the embedding models for gas phase and solvated molecules to understand the performance, benefits and current limitations of embedding quantum computing algorithms within a QM/MM model. We compare the performance of simulated quantum phase estimation (QPE) calculations on an HPC cluster using graphical processing units (GPUs) and central processing units (CPUs).