Quantum Algorithm for Simulating Coupled Classical Oscillators - IPAM at UCLA

Explore a quantum algorithm for simulating the classical dynamics of 2^n coupled oscillators in this 57-minute lecture presented by Rolando Somma of Google at IPAM's Quantum Algorithms for Scientific Computation Workshop. Delve into the algorithm's foundation, which maps the Schrödinger equation to Newton's equations for harmonic potentials, enabling the encoding of classical oscillators' kinetic and potential energies in quantum state amplitudes. Discover the algorithm's polynomial complexity in n, near-linear scaling with evolution time, and sublinear dependence on sparsity. Examine an application estimating oscillator kinetic energy, proven to be BQP-complete, and learn about an oracular problem where this quantum approach exponentially outperforms classical computers. Investigate the algorithm's potential for efficiently simulating general classical harmonic systems with 2^n modes, while also considering its limitations and real-world applications with significant speedups.