Environment-assisted holonomic quantum maps

Abstract

Holonomic quantum computation uses non-Abelian geometric phases to realize error resilient quantum gates. Nonadiabatic holonomic gates are particularly suitable to avoid unwanted decoherence effects, as they can be performed at high speed. By letting the computational system interact with a structured environment, we show that the scope of error resilience of nonadiabatic holonomic gates can be widened to include systematic parameter errors. Our scheme maintains the geometric properties of the evolution and results in an environment-assisted holonomic quantum map that can mimic the effect of a holonomic gate. We demonstrate that the sensitivity to systematic errors can be reduced in a proof-of-concept spin-bath model.

arXiv commentNew figure added. Journal reference added

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Cited by in corpus (26)

• Experimental Realization of Nonadiabatic Holonomic Single-Qubit Quantum Gates\\ with Optimal Control in a Trapped Ion
• Fast holonomic quantum computation on superconducting circuits with optimal control
• General approach for constructing Hamiltonians for nonadiabatic holonomic quantum computation
• Dynamical-decoupling-protected nonadiabatic holonomic quantum computation
• Super-robust nonadiabatic geometric quantum control
• Dynamically Corrected Nonadiabatic Holonomic Quantum Gates
• Superrobust Geometric Control of a Superconducting Circuit
• Experimental Realization of Nonadiabatic Holonomic Single-Qubit Quantum Gates with Two Dark Paths in a Trapped Ion
• Rabi-error and Blockade-error-resilient All-Geometric Rydberg Quantum Gates
• Realizing nonadiabatic holonomic quantum computation beyond the three-level setting
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• Unidirectional acoustic metamaterials based on nonadiabatic holonomic quantum transformations
• Scalable nonadiabatic holonomic quantum computation on a superconducting qubit lattice
• Nonadiabatic holonomic quantum computation based on commutation relation
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• Implementing conventional and unconventional nonadiabatic geometric quantum gates via SU(2) transformations
• Error-Resilient Floquet Geometric Quantum Computation
• Non-adiabatic holonomic quantum operations in continuous variable systems
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