Nonadiabatic holonomic multiqubit controlled gates

Abstract

Previous schemes of nonadiabatic holonomic quantum computation were focused mainly on realizing a universal set of elementary gates. Multiqubit controlled gates could be built by decomposing them into a series of the universal gates. In this article, we propose an approach for realizing nonadiabatic holonomic multiqubit controlled gates in which a $(n+1)$-qubit controlled-$(\mathrm{n}\cdot \sigma )$ gate is realized by $(2n-1)$ basic operations instead of decomposing it into the universal gates, whereas an $(n+1)$-qubit controlled arbitrary rotation gate can be obtained by combining only two such controlled-$(\mathrm{n}\cdot \sigma )$ gates. Our scheme greatly reduces the operations of nonadiabatic holonomic quantum computation.

6 pages, 2 figures

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• High-fidelity geometric quantum gates with short paths on superconducting circuits
• One-step implementation of a multi-target-qubit controlled-phase gate with photonic qubits encoded via eigenstates of the photon-number parity operator
• Nonadiabatic holonomic quantum computation based on commutation relation
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• Dark path holonomic qudit computation
• Error-Resilient Floquet Geometric Quantum Computation
• Time optimal holonomic quantum computation
• Mitigation of systematic amplitude error in nonadiabatic holonomic operations
• Speeding up adiabatic holonomic quantum gates via $\pi$-pulse modulation