Southwest Quantum Information and Technology

Implementing a universal gate set for qudits via optimal control

Presenting Author: Sivaprasad Omanakuttan, University of New Mexico CQuIC
Contributing Author(s): Anupam Mitra Michael J. Martin Ivan H Deutsch

Qudits, the multi-level d>2 generalization of qubits, are considered as one of the potential candidates for universal quantum computation given the potential of storing more information in fewer physical systems and improved threshold for fault tolerance. In this work we design protocols to implement a universal set of qudits with high fidelity. As a physical system, we consider encoding a d=10 dimensional qudit in the I=9/2 nuclear spin of 87Sr atoms, a platform under considerable exploration for quantum information processing. As the generators of SU(d) unitary matrices are not natural physical interactions, we use the well-known techniques of quantum optimal control order to implement these gates. Using rf-control Larmor precession with a time-dependent phase and a tensor light-shift interaction we designed waveforms to create an arbitrary Haar-random SU(10) map with average fidelity = 0.9923, under reasonable experimental conditions including decoherence effects. To complete the universal gate set we also require a two-qudit entangling gate. We augment our toolkit with an entangling Hamiltonian arising from the Van der Waals interaction of two atoms in Rydberg states. In particular, we employ “Rydberg dressing,” which allows us to implement a magneto-Rydberg interaction that can be used to generate any symmetric entangling two-qudit gate such as CPhase. Our techniques can be used to implement entanglers for qudits from d=2 to d=10 encoded in the nuclear spin.

Read this article online: https://arxiv.org/abs/2106.13705, https://arxiv.org/abs/2205.12866

(Session 5 : Thursday from 5:00 pm - 7:00 pm)