Performing SU(d) Operations and Rudimentary Algorithms in a Superconducting Transmon Qudit for d=3 and d=4

Abstract

Quantum-computation architecture based on d-level systems, or qudits, has attracted considerable attention recently due to their enlarged Hilbert space. Extensive theoretical and experimental studies have addressed aspects of algorithms and benchmarking techniques for qudit-based quantum computation and quantum-information processing. Here, we report a physical realization of a qudit with up to four embedded levels in a superconducting transmon demonstrating high-fidelity initialization, manipulation, and simultaneous multilevel readout. In addition to constructing SU(d) operations and benchmarking protocols for quantum-state tomography, quantum-process tomography, randomized benchmarking, etc., we experimentally carry out these operations for d=3 and d=4. Moreover, we perform prototypical quantum algorithms and observe outcomes consistent with expectations. Our work will hopefully stimulate further research interest in developing manipulation protocols and efficient applications for quantum processors with qudits.