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

A generic architecture of n-bit quantum operators is proposed for cost-effective transpilation, based on the layouts and the number of n neighbor physical qubits for IBM quantum computers, where n >= 3. This proposed architecture is termed "GALA-n quantum operator". The GALA-n quantum operator is designed using the visual approach of the Bloch sphere, from the visual representations of the rotational quantum operations for IBM native gates (square root of X, X, RZ, and CNOT). In this paper, we also proposed a new formula for the quantum cost, which calculates the total numbers of native gates, SWAP gates, and the depth of the final transpiled quantum circuits. This formula is termed the "transpilation quantum cost". After transpilation, our proposed GALA-n quantum operator always has a lower transpilation quantum cost than that of conventional n-bit quantum operators, which are mainly constructed from costly n-bit Toffoli gates.Comment: 27 pages, 22 figure

Algorithms for the Optimization of Quantum Circuits

This thesis investigates techniques for the automated optimization of quantum circuits. In the first part we develop an exponential time algorithm for synthesizing minimal depth quantum circuits. We combine this with effective heuristics for reducing the search space, and show how it can be extended to different optimization problems. We then use the algorithm to compute circuits over the Clifford group and T gate for many of the commonly used quantum gates, improving upon the former best known circuits in many cases. In the second part, we present a polynomial time algorithm for the re-synthesis of CNOT and T gate circuits while reducing the number of phase gates and parallelizing them. We then describe different methods for expanding this algorithm to optimize circuits over Clifford and T gates

Synthesis and testing of reversible Toffoli circuits

xii, 82 leaves : ill. ; 29 cmRecently, researchers have been interested in reversible computing because of its ability to dissipate nearly zero heat and because of its applications in quantum computing and low power VLSI design. Synthesis and testing are two important areas of reversible logic. The thesis first presents an approach for the synthesis of reversible circuits from the exclusive- OR sum-of-products (ESOP) representation of functions, which makes better use of shared functionality among multiple outputs, resulting in up to 75% minimization of quantum cost compared to the previous approach. This thesis also investigates the previous work on constructing the online testable circuits and points out some design issues. A simple approach for online fault detection is proposed for a particular type of ESOP-based reversible circuit, which is also extended for any type of Toffoli circuits. The proposed online testable designs not only address the problems of the previous designs but also achieve significant improvements of up to 78% and 99% in terms of quantum cost and garbage outputs, respectively