"progress swiftly" is correct and usable in written English.
It means to move or develop quickly and smoothly. You can use it in any situation where you want to convey that something is happening rapidly and efficiently. Example: With the help of advanced technology, the construction of the new bridge is expected to progress swiftly and be completed ahead of schedule.
Genie's progress swiftly reversed, perhaps never to be recovered.
The AI revolution will have two engines — China and the United States — pushing its progress swiftly forward.
Time, and the progress swiftly made by him and his supporters, are a vindication of all that he worked and yearned for.
The work had to progress swiftly, for an object not grabbed immediately could be lost forever to the speedy cleanup, headed for burial at the landfill or for the metal recycling scrapyards.
The Department for Transport is developing plans under the codename "Operation Brock" to handle queues of thousands of trucks, should freight be unable to progress swiftly through the ports when the UK leaves the EU – possibly from March next year.
They progressed swiftly through the stages of their relationship: moving in together, planning marriage and discussing starting a family.
To their delight, romantic sparks continued to fly over dinner and from that point on, things progressed swiftly.
From roughly 1960 onward the developed world's railroads, pressed hard by highway and air competition, progressed swiftly into a new technological age.
The cost of storing images is dropping, and new software algorithms for mining, matching and scrutinizing the flood of visual data are progressing swiftly.
This supports the mechanism that we propose in Fig. 1, with the CE progressing swiftly along the wire once a segment is transformed.
For example, CMV retinitis presents with large areas of necrotizing retinitis that progresses swiftly, requiring immediate initiation of antiviral treatment, APMPPE presents with diffuse placoid lesions that are self limiting, and Birdshot chorioretinopathy presents with multiple depigmented lesions that require prompt immunosuppression.
