How did Russia know how to build an H-bomb in 1953 when the US was inventing it in 1952?

Answer 1

It had been in reasearch since the 1930's and the arms race began well before the 1950's. Neither the US or Russia wanted the other to have the weapon first so both were working on it.

The Soviet 1953 "hydrogen bomb" was not a staged hydrogen bomb like the US 1952 & 1954 hydrogen bombs. It was just a Lithium Deuteride boosted fission bomb. Its only advantage was it was a deliverable megaton range yield boosted fission bomb one year before the US got deliverable multimegaton range yield teller-ulam staged fusion bombs.

The Soviets only declared it a "type of hydrogen bomb" because some of the yield was from fusion, most was still from Plutonium fission. The design was sometimes referred to as the Layer Cake as it used a more or less conventional Plutonium implosion mechanism, but the Plutonium core was alternately layered with concentric shells of Lithium Deuteride instead of being just Plutonium.

The US had considered such a design in ~ 1950, but never pursued it as it was considered a dead end. Computing resources were better spent on better designs.

Answer 2

It is believed that Soviet spies obtained information about the design and development of the H-bomb from the United States during the Cold War, which accelerated Russia's progress in building their own hydrogen bomb. This espionage allowed the Soviet Union to rapidly catch up with the US in nuclear weapons technology.