Performing SU($d$) operations and rudimentary algorithms in a superconducting transmon qudit for $d=3$ and $d=4$

TL;DR

This paper demonstrates the physical realization and control of qudits with up to four levels in a superconducting transmon, including high-fidelity operations and algorithms, advancing qudit-based quantum computing.

Contribution

It presents the first experimental implementation of SU(d) operations and algorithms for d=3 and 4 in a superconducting transmon qudit system, with high-fidelity control and measurement.

Findings

Successful high-fidelity initialization and manipulation of qudits with up to 4 levels.

Implementation of SU(d) operations and benchmarking protocols for d=3 and 4.

Prototypical quantum algorithms performed with outcomes matching theoretical expectations.

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 qudit with upto 4 embedded levels in a superconducting transmon, demonstrating high-fidelity initialization, manipulation, and simultaneous multi-level readout. In addition to constructing SU($d$) operations and benchmarking protocols for quantum state tomography, quantum process tomography, and 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.