Leveraging quantum walks and spin frustration for computation and error mitigation

I will give an overview of recent work on using quantum walks for solving optimisation problems, and related work on error mitigation. Quantum walks can solve the same problems as adiabatic quantum computing, but the mechanisms are very different, with excited states populated, and many repeats of fast dynamics replacing slow time evolution. For problems such as MAX2SAT and spin glass ground states, the control parameters do not need to be set precisely to obtain an advantage over naive classical algorithms. Heuristic estimates of control parameters are sufficient, making practical applications viable for similar real world problems. However, many open questions remain around the conditions that generate fast dynamics in quantum walks, and the best classical algorithms are still competitive with quantum, especially SAT solvers. Hybrid strategies offer the best route to exploiting quantum solvers, combining different quantum mechanisms with classical solvers for maximum efficiency overall. For larger problems, the fixed precision of hardware control limits how accurately the problem can be represented. Using copies connected with anti-ferromagnatic links can increase the effective precision by counteracting errors and inhibiting error propagation. Hardware graphs with triangles that can natively display frustration are thus a desirable feature for future hardware design.