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Realization of Robust Single-Qubit Operations with Purely Geometric Phase Factors

Kenji Toyoda, Kensuke Uchida, Shinsuke Haze, S. Urabe

Published Jan 1, 2011• 0 citations
Publisher

Abstract

Single-qubit operations in a single trapped ion are performed by means of purely geometrical phase factors. Multiple dark states in a four-level (“tripod”) system are manipulated adiabatically to perform the gate operations. Rotation operations along Z and X axes in the Bloch sphere are performed with high fringe visibilities.
DOI
10.1364/iqec.2011.i1059

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With carefully prepared resonant laser-controlled pulses, the two quantum states of a cold ensemble of sodium atoms were manipulated by pure geometric rotations of the Bloch vector around axes 2 and 3 on the Bloch sphere. The fidelity for two geometric rotations was improved to be 90%. A universal single-qubit operation on the ground-state wave function was demonstrated by a pure geometric operation and the phase shift due to the rotation around axis 3 was measured using a geometric atom interferometer.
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Quantum computing leverages fundamental principles of quantum mechanics to perform computations far exceeding classical architectures. At the core of single-qubit quantum state manipulation is the Bloch sphere, a geometric representation mapping the state space of two-level quantum systems onto a three-dimensional unit sphere. This paper presents a comprehensive theoretical framework of qubits, starting from single-qubit geometric state vectors and expanding to rigorous multi-qubit mathematical formulations. Furthermore, it analyzes single-qubit quantum gates as unitary rotations on the Bloch sphere, evaluates multi-qubit system scaling, and explicitly proves state normalization conditions using Born's rule across multi-dimensional Hilbert spaces.