I am not an expert on china, but I am an economic historian. China also has a lot in common with the soviet union, which i do know quite a bit about and can draw some parallels.

The honest answer is we don't really know. The overall trend of growth since the 1800's has been divergence rather than convergence, in other words, the rich countries get richer and the poor poorer. Few countries have been able to overcome this, Russia, China, the east Asian tigers are the most notable exceptions, but it is not a hotly contested issue among economic historians. If you come up with an answer there is probably a nobel prize in economics waiting for you.

There is evidence that economies under authoritarian rule or centralized planning are able to industrialize much quicker than their democratic counterparts. This due to the ability of technocrats within the government to force investment into heavy industry, like steel and coal production at the expense of consumer goods and agriculture. These investment were not profitable, due to a lack of demand, but are vital to having a modern economy. Therefore, it is necessary for an entity like the state to invest in heavy industry because they do are not necessarily concerned with profit. The Chinese government continues to invest heavily in new industries which it deems relevant to progress.

Secondly, China in 1949 when Mao took power was a highly backwards country. With a large part of the population working as sustenance farmers. The chinese government did not start measuring GDP till 1985 but estimates have been around 150 yuan per head in the 50's. With such low GDP any attempt at industrialization and subsequent technology transfer would result in substantial growth.

The massive amount of labor available to the Chinese economy played a large role. In the USSR and China people worked for sustenance or slightly below sustenance wages. Both countries used slave labor in order to complete difficult projects and millions died. Free or almost free labor allows for the saved capital to be invested in other industries, which is largely what happened.

The real growth began after began after reforms began in 1982. Central planning was greatly reduced and the allocation of resources was left to the market, china began to open to trade and exports increased roughly 5% a year in the 1980s, foreign investment poured into china (with strict capital controls) and GDP fucking sky rocketed. Since 1978 to the present annual growth in GDP has been almost 10% which is ridiculously high almost to the point of being unbelievable.

sources http://www.imf.org/external/pubs/ft/weo/2012/02/weodata/index.aspx Robert allen's Farm to Factory https://www.fas.org/sgp/crs/row/RL33534.pdf http://en.wikipedia.org/wiki/Convergence_(economics) (i know its wikipedia but the article is quite good and I can't link the original paper as its in a jstor like site)

There was economic reform that allowed a factory to sell extra unit of something for profit. A factory would have to make ten units of steel, but if they made the 11th it was extra money in someone's hands. This allowed the state to still control production and introduced capitalism.

Also the planned economy has been very effective and building infrastructure. As of 1990, The PuDong district was marshland. Now, it is an industrial powerhouse of one of most important cities in China. The government invested a lot to make that happen. A guide book from 1999 would list just two subway lines. There are now 16 in what is the largest subway by total km. Not many places are committed to building that level of infrastructure. For the last 15 years has been trying to get western access to the main airport. There still isn't western access to the airport today.