Quasi-Shor Algorithms for Global Benchmarking of Universal Quantum Processors

This work generalizes Shor’s algorithm into quasi-Shor algorithms by replacing the modular exponentiation with alternative unitary operations. By using the quantum circuits to generate Bell states as the unitary operations, a specific example called the Bell–Shor algorithm was constructed. The system density matrices in the quantum circuits with four distinct input states were calculated in ideal conditions and illustrated through chromatic graphs to witness the evolution of quantum states in the quantum circuits. For the real part of the density matrices, it was revealed that the number of zero elements dramatically declined to only a few points after the operation of the inverse quantum Fourier transformation. Based on this property, a protocol constituting a pair of error metrics Γa and Γb is proposed for the global benchmarking of universal quantum processors by looking at the locations of the zero entries and normalized average values of non-zero entries. The protocol has polynomial resource requirements with the scale of the quantum processor. The Bell–Shor algorithm is capable of being a feasible setting for the global benchmarking of universal quantum processors.