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Hyperloop One is in the early stages of making the technology commercially viable after completing a full-scale test in Las Vegas.
In the system, passengers and cargo will be loaded into a pod, and accelerated gradually via electric propulsion through a low-pressure tube.
Virgin Hyperloop has so far listed three main routes in plans to build in the UK.
A route from London to Edinburgh is expected to take 50 minutes, as will the route from Cardiff to Glasgow.
It was unveiled by Elon Musk in 2013, who at the time said it could take passengers the 380 miles (610km) from LA to San Francisco in 30 minutes - half the time it takes a plane.
Hyperloop One and Richard Branson, founder of Virgin, are yet to respond to the paper.
In total, they would cross 53 urban centres and span a total of 4,121 miles (6,600 km), connecting almost 150 million people.
The firm, which Elon Musk is not associated with, plans to have three of the routes up and running in a commercial capacity by 2021.
But the paper adds that building underground 'would have a significant impact on capital costs and would make maintenance and emergency evacuation more difficult.'Another issue raised in the paper is whether the radical nature of Hyperloop will raise some issues around passenger acceptance.
The paper adds: 'It will be critical for the success of the systems to demonstrate to passengers that Hyperloop systems will operate with the highest levels of safety and reliability.