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Experimental realization of non-Abelian non-adiabatic geometric gates
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Journal Article
Experimental realization of non-Abelian non-adiabatic geometric gates
2013
Overview
Microwave stimulation of a superconducting artificial three-level atom is used to demonstrate high-fidelity, non-Abelian geometric transformations, the results of which depend on the order in which they are performed.
Gateways to quantum computing
Geometric phases are acquired whenever a quantum system evolves along a path. If the system contains degenerate energy levels, these can take the form of matrix-valued geometric transformations called non-Abelian holonomies. It has been proposed that such holonomies could be exploited for noise-resilient quantum computation. The authors realize non-Abelian holonomic quantum operations on a single superconducting artificial three-level atom. In combination with a non-trivial two-qubit gate, the results may suggest a route to universal holonomic quantum computing.
The geometric aspects of quantum mechanics are emphasized most prominently by the concept of geometric phases, which are acquired whenever a quantum system evolves along a path in Hilbert space, that is, the space of quantum states of the system. The geometric phase is determined only by the shape of this path
1
,
2
,
3
and is, in its simplest form, a real number. However, if the system has degenerate energy levels, then matrix-valued geometric state transformations, known as non-Abelian holonomies—the effect of which depends on the order of two consecutive paths—can be obtained
4
. They are important, for example, for the creation of synthetic gauge fields in cold atomic gases
5
or the description of non-Abelian anyon statistics
6
,
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. Moreover, there are proposals
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,
9
to exploit non-Abelian holonomic gates for the purposes of noise-resilient quantum computation. In contrast to Abelian geometric operations
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, non-Abelian ones have been observed only in nuclear quadrupole resonance experiments with a large number of spins, and without full characterization of the geometric process and its non-commutative nature
11
,
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. Here we realize non-Abelian non-adiabatic holonomic quantum operations
13
,
14
on a single, superconducting, artificial three-level atom
15
by applying a well-controlled, two-tone microwave drive. Using quantum process tomography, we determine fidelities of the resulting non-commuting gates that exceed 95 per cent. We show that two different quantum gates, originating from two distinct paths in Hilbert space, yield non-equivalent transformations when applied in different orders. This provides evidence for the non-Abelian character of the implemented holonomic quantum operations. In combination with a non-trivial two-quantum-bit gate, our method suggests a way to universal holonomic quantum computing.
Publisher
Nature Publishing Group UK,Nature Publishing Group
