Simulating Quantum Information Processing using Heisenberg Spin Chains with Finite Size Effects

Qubit computing leverages qubit entanglement and superposition to perform complex computations. Spin-1/2 A key component of hardware simulation based on qubits is Heisenberg models. In this work, we model gate operations and memory switching in spin chains. Energy spectra and spin gaps are extracted using diagonalization techniques. We compare simulated dynamics with experimental results from materials such as Sr₂Cu(PO₄)₂. Our findings are consistent with gap and experimental susceptibility data. Various J₂/J₁ ratios are used to assess finite-length effects. We describe critical gap behaviour, memory transitions, and freezing behaviour. Scalable architectures using low-dimensional spin systems are guided by these results. Additionally, the results support theories proposed in recent work on quantum hardware (Bishop et al., 2008; Belik et al., 2005). We introduce reversible pulse-controlled retention mechanism in Heisenberg spin chains; a feature not explored in earlier models.