A Rigorous Framework for a Hadronic Quantum Computer Based on Protons

This paper presents a rigorous theoretical framework for a novel type of quantum computer, termed a Hadronic Quantum Computer (HQC), which utilizes protons as its fundamental qubits. The core advantage of this approach is the exceptional intrinsic stability of the proton, which offers a robust physical substrate for quantum information and a potential solution to the decoherence and scalability challenges that limit current quantum computing platforms. The proposed architecture consists of a proton lattice with inter-nucleon separations on the order of one femtometer. This precise arrangement is maintained by a sophisticated hybrid system combining a linear Paul trap for macroscopic confinement and highly focused optical tweezers to create deep potential wells, ensuring stability against quantum mechanical zero-point energy fluctuations. Quantum control is achieved through well-established physics. Single-qubit gates are implemented by manipulating the proton's spin using external magnetic fields, governed by the Rabi Hamiltonian. Multi-qubit entanglement is mediated by the strong nuclear force. The framework provides a detailed analysis of this interaction, moving beyond the simple one-pion exchange (OPE) potential to include crucial short-range corrections from heavier meson exchanges, which are significant at the proposed operational distances. A key innovation is the proposed non-destructive readout mechanism. As direct measurement of a single proton's spin is experimentally prohibitive, the paper details a quantum logic spectroscopy scheme. An auxiliary "logic" ion (e.g., Calcium-40) is co-trapped near the proton lattice. The spin state of a proton qubit is first mapped to its motional state, which is then coherently transferred to the logic ion via Coulomb coupling. The state of the logic ion can then be measured with near-perfect fidelity using standard fluorescence techniques. To perform computations, the framework integrates a Variational Quantum Eigensolver (VQE) with a custom-designed, hardware-efficient ansatz. This approach is tailored to prepare complex hadronic ground states and simulate QCD processes. The validity of this computational strategy is demonstrated through high-precision numerical simulations using the QuTiP library, which achieved a relative error of approximately 10⁻⁹ for a two-qubit proxy Hamiltonian. The primary application of the HQC would be the first-principles simulation of lattice QCD, a grand challenge in physics. This would enable unprecedented calculations in hadron physics and simulations of high-energy events. Further, the paper suggests novel applications in drug discovery and materials science. In conclusion, the HQC paradigm offers a promising, albeit technologically challenging, path toward fault-tolerant quantum computation by leveraging the fundamental stability of baryonic matter.