Platonic dynamical decoupling sequences for qudits

• URL: http://arxiv.org/abs/2409.04974v1
• Date: Sun, 8 Sep 2024 04:52:12 GMT
• Title: Platonic dynamical decoupling sequences for qudits
• Authors: Colin Read, Eduardo Serrano-Ensástiga, John Martin,
• Abstract summary: We use a generalization of the Majorana representation for Hamiltonians to develop a simple framework that establishes the decoupling properties of each Platonic sequence. These sequences are universal in their ability to cancel any type of interaction with the environment for single qudits with up to 6 levels. They are capable of decoupling up to 5-body interactions in an ensemble of interacting qubits with only global pulses.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In the NISQ era, where quantum information processing is hindered by the decoherence and dissipation of elementary quantum systems, developing new protocols to extend the lifetime of quantum states is of considerable practical and theoretical importance. A prominent method, called dynamical decoupling, uses a carefully designed sequence of pulses applied to a quantum system, such as a qudit (a d-level quantum system), to suppress the coupling Hamiltonian between the system and its environment, thereby mitigating dissipation. While dynamical decoupling of qubit systems has been widely studied, the decoupling of qudit systems has been far less explored and often involves complex sequences and operations. In this work, we design efficient decoupling sequences composed solely of SU(2) rotations and based on tetrahedral, octahedral, and icosahedral point groups, which we call Platonic sequences. We use a generalization of the Majorana representation for Hamiltonians to develop a simple framework that establishes the decoupling properties of each Platonic sequence and show its efficiency on many examples. These sequences are universal in their ability to cancel any type of interaction with the environment for single qudits with up to 6 levels, and they are capable of decoupling up to 5-body interactions in an ensemble of interacting qubits with only global pulses, provided that the interaction Hamiltonian has no isotropic component, with the exception of the global identity. We also discuss their inherent robustness to finite pulse duration and a wide range of pulse errors, as well as their potential application as building blocks for dynamically corrected gates.

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