At the beginning of December last year, a committee set up by the U.S. National Academies of Sciences, Engineering, and Medicine said it had come to the conclusion a viable quantum computer with the ability to break ciphers based on today's encryption algorithms is a decade or more away, but they are coming. Committee chair Mark Horowitz said he and his colleagues could see no fundamental reason, in principle, why a functional quantum computer could not ever be built.
When they do finally arrive, quantum computers pose a number of problems for computer scientists when it comes to determining whether they work as expected. Quantum computers can make use of the property of superposition: where the bits in a register in the machine do not exist in a single known state, but in a combination of states. Each state has a finite probability of being the one recorded when the register is read and the superposition collapses.
"... to factor the large primes ..." -- I don't think even a quantum computer will ever be able to do that.
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