2024/02/19 by Ben Zindorf, Zindorf, Ben, Sougato Bose +1 · 1 citation
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Mechanics and Applications #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2402.12356
openalex publication_date 2024/02/19 · openalex created_date 2024/02/21 · openalex updated_date 2026/08/03
Universal gate sets for quantum computation, when single and two qubit operations are accessible, include both Hermitian and non-Hermitian gates. Here we utilize the fact that any single-qubit operator may be implemented as two Hermitian gates, and thus a purely Hermitian universal set is possible. This implementation can be used to prepare high fidelity single-qubit states in the presence of amplitude errors, and helps to achieve a high fidelity single-qubit gate decomposition using four Hermitian gates. An implementational convenience can be that non-identity single-qubit Hermitian gates are equivalent to π rotations up to a global phase. We show that a gate set comprised of π rotations about two fixed axes, along with the CNOT gate, is universal for quantum computation. Moreover, we show that two π rotations can transform the axis of any multi-controlled unitary, a special case being a single CNOT sufficing for any controlled π rotation. These gates simplify the process of circuit compilation in view of their Hermitian nature. We exemplify by designing efficient circuits for a variety of controlled gates, and achieving a CNOT count reduction for the four-controlled Toffoli gate in LNN-restricted qubit connectivity.