Quantum Information Processing
A lattice-based quantum algorithm is presented to model the non-linear Schrödinger-like equations in 2 + 1 dimensions. In this lattice-based model, using only 2 qubits per node, a sequence of unitary collide (qubit-qubit interaction) and stream (qubit translation) operators locally evolve a discrete field of probability amplitudes that in the long-wavelength limit accurately approximates a non-relativistic scalar wave function. The collision operator locally entangles pairs of qubits followed by a streaming operator that spreads the entanglement throughout the two dimensional lattice. The quantum algorithmic scheme employs a non-linear potential that is proportional to the moduli square of the wave function. The model is tested on the transverse modulation instability of a one dimensional soliton wave train, both in its linear and non-linear stages. In the integrable cases where analytical solutions are available, the numerical predictions are in excellent agreement with the theory.
Original Publication Citation
Yepez, J., Vahala, G., & Vahala, L. (2005). Lattice quantum algorithm for the Schrödinger wave equation in 2+1 dimensions with a demonstration by modeling soliton instabilities. Quantum Information Processing, 4(6), 457-469. doi: 10.1007/s11128-005-0008-8
Yepez, Jeffrey; Vahala, George; and Vahala, Linda L., "Lattice Quantum Algorithm for the Schrodinger Wave Equation in 2+1 Dimensions With a Demonstration by Modeling Soliton Instabilities" (2005). Electrical & Computer Engineering Faculty Publications. 44.