2013/04/01 by A. A. Abdumalikov, J. M. Fink, K. Juliusson +9 · 5 citations
Computer Science · Mathematics · Physics and Astronomy · #Abelian group #Cold Atom Physics and Bose-Einstein Condensates #Gauge theory #Geometric phase #Holonomic #Mathematics #Physics #Pure mathematics #Quantum #Quantum Information and Cryptography #Quantum algorithm #Quantum and electron transport phenomena #Quantum computer #Quantum dissipation #Quantum dynamics #Quantum gate #Quantum mechanics #Quantum phases #Quantum process #Topology (electrical circuits) #quant-ph
paper · pdf · doi:10.1038/nature12010
published as Nature 496 (2013) 482-485 · In press in Nature. Published online on April 17, 2013
openalex publication_date 2013/04/01 · arxiv created 2013/04/18 · arxiv updated 2019/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The geometric aspects of quantum mechanics are underlined most prominently by the concept of geometric phases, which are acquired whenever a quantum system evolves along a closed path in Hilbert space. The geometric phase is determined only by the shape of this path and is -- in its simplest form -- a real number. However, if the system contains degenerate energy levels, matrix-valued geometric phases, termed non-abelian holonomies, can emerge. They play an important role for the creation of synthetic gauge fields in cold atomic gases and the description of non-abelian anyon statistics. Moreover, it has been proposed to exploit non-abelian holonomic gates for robust quantum computation. In contrast to abelian geometric phases, non-abelian ones have been observed only in nuclear quadrupole resonance experiments with a large number of spins and without fully characterizing the geometric process and its non-commutative nature. Here, we realize non-abelian holonomic quantum operations on a single superconducting artificial three-level atom by applying a well controlled two-tone microwave drive. Using quantum process tomography, we determine fidelities of the resulting non-commuting gates exceeding 95 %. We show that a sequence of two paths in Hilbert space traversed in different order yields inequivalent transformations, which is an evidence for the non-abelian character of the implemented holonomic quantum gates. In combination with two-qubit operations, they form a universal set of gates for holonomic quantum computation.