NP-hard but no longer hard to solve? Using quantum computing to tackle optimization problems

In the last decade, public and industrial research funding has moved quantum computing from the early promises of Shor's algorithm through experiments to the era of noisy intermediate scale quantum devices (NISQ) for solving real-world problems. It is likely that quantum methods can efficiently solve certain (NP-)hard optimization problems where classical approaches fail. In our perspective, we examine the field of quantum optimization where we solve optimization problems using quantum computers. We demonstrate this through a proper use case and discuss the current quality of quantum computers, their solver capabilities, and benchmarking difficulties. Although we show a proof-of-concept rather than a full benchmark, we use the results to emphasize the importance of using appropriate metrics when comparing quantum and classical methods. We conclude with discussion on some recent quantum optimization breakthroughs and the current status and future directions

Developing spontaneous coherence in incoherently-driven Tavis Cummings system

This work examines the possibility of developing spontaneous coherence in a driven-dissipative hybrid quantum system composed of a superconducting resonator coupled to a solid-state spins ensemble. Previous theoretical studies, involving microcavity polaritons for example, use an effective fermionic pump to generate the collective coherence and condensation of the quasi-particles. Instead of a phenomenological approach, this work develops a microscopic theory by means of a nonequilibrium cavity system with the addition of an incoherent bosonic (optical) pump. This prompts the use of Schwinger-Keldysh technique to analyse the system dynamics. The optical driving mechanism is equivalent to adding non-Markovian noise to the cavity, which causes an effective spin-spin interaction mediated by photons. Most importantly, this mechanism is present on the mean-field level. The form of its distribution function has a strong effect on the condensation behaviour which is shown in various phase diagrams that compare the cavity system with and with without the optical drive. For specific ranges of the fermionic pump strength (a mathematical construct that does not exist in the hybrid system), the phase diagrams show novel exotic behaviour that may be caused by the effective spin-spin interactions. It is plausible that the optical driving can develop spontaneous coherence in the cavity, but this is still inconclusive and needs to be studied further. Although these nonequilibrium quantum optics systems potentially find use in quantum information processing as quantum memories, they may also double as a quantum simulator, allowing further exploration into the nonequilibrium phase transitions of solid-state devices