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Shor's factoring algorithm uses two quantum registers. By introducing moreregisters we show that the measured numbers in these registers which are of thesame pre-measurement state, should be equal if the original Shor's complexityargument is sound. This contradicts the argument that the second register has$r$ possible measured values. There is an anonymous comment which argues thatthe states in these registers are entangled. If so, the entanglement involvingmany quantum registers can not be interpreted by the mechanism of EPR pairs andthe like. In view of this peculiar entanglement has not yet been mentioned andinvestigated, we think the claim that the Shor's algorithm runs in polynomialtime needs more physical verifications. We also discuss the problem to certifyquantum computers.

On Shor's Factoring Algorithm with More Registers and the Problem to Certify Quantum Computers