Fermionic quantum approximate optimization algorithm

Quantum computers are expected to accelerate solving combinatorial optimization problems, including algorithms such as Grover adaptive search and quantum approximate algorithm (QAOA). However, many problems involve constraints which, when imposed soft in the cost function, can negatively impact performance of algorithm. In this paper, we propose fermionic (FQAOA) for with constraints. Specifically FQAOA tackle constrains issue by using fermion particle number preservation intrinsically impose them throughout QAOA. We provide a systematic guideline designing driver Hamiltonian given problem The initial state be chosen superposition states satisfying constraint ground Hamiltonian. This property is important since reduced adiabatic computation large limit circuit depth p improved performance, even shallow circuits optimizing parameters starting from fixed-angle determined Trotterized evolution. perform an extensive numerical simulation demonstrates that proposed provides substantial advantage against existing approaches portfolio problems. Furthermore, design useful not only QAOA, but also phase estimation solve Since software tools systems have been developed computational chemistry both noisy intermediate-scale fault-tolerant computers, allows us apply these constrained