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A generic architecture of n-bit quantum operators is proposed forcost-effective transpilation, based on the layouts and the number of n neighborphysical qubits for IBM quantum computers, where n >= 3. This proposedarchitecture is termed "GALA-n quantum operator". The GALA-n quantum operatoris designed using the visual approach of the Bloch sphere, from the visualrepresentations of the rotational quantum operations for IBM native gates(square root of X, X, RZ, and CNOT). In this paper, we also proposed a newformula for the quantum cost, which calculates the total numbers of nativegates, SWAP gates, and the depth of the final transpiled quantum circuits. Thisformula is termed the "transpilation quantum cost". After transpilation, ourproposed GALA-n quantum operator always has a lower transpilation quantum costthan that of conventional n-bit quantum operators, which are mainly constructedfrom costly n-bit Toffoli gates.

GALA-n: Generic Architecture of Layout-Aware n-Bit Quantum Operators for Cost-Effective Realization on IBM Quantum Computers