Quantum information theory: Trading classical for quantum computation using indirection

Modular exponentiation is the most expensive portion of Shor’s algorithm. We show that it is possible to reduce the number of quantum modular multiplications necessary by a factor of ω, at a cost of adding temporary storage space and associated machinery for a table of 2^ωentries, and performing 2^ωtimes as many classical modular multiplications. The storage space may be a quantum-addressable classical memory, or pure quantum memory. With classical computation as much as 10¹³times as fast as quantum computation, values of ω from 2 to 30 seem attractive; physically feasible values depend on the implementation of the memory.