Multi-frequency control and measurement of a spin-7/2 system encoded in a transmon qudit

TL;DR

This paper demonstrates a method for controlling and measuring a high-dimensional spin-7/2 system encoded in a superconducting transmon qudit using multi-frequency drives, enabling efficient arbitrary unitary operations and high-fidelity readout.

Contribution

It introduces a multi-frequency control technique for high-dimensional qudits in superconducting circuits, achieving native arbitrary operations and high-fidelity single-shot readout for all states.

Findings

Achieved single-shot readout of 8 states with 88.3% assignment fidelity.

Realized arbitrary single-qudit unitaries with fidelities from 0.997 to 0.989.

Demonstrated control of a spin-7/2 system in a superconducting transmon.

Abstract

Qudits hold great promise for efficient quantum computation and the simulation of high-dimensional quantum systems. Utilizing a local Hilbert space of dimension d > 2 is known to speed up certain quantum algorithms relative to their qubit counterparts given efficient local qudit control and measurement. However, the direct realization of high-dimensional rotations and projectors has proved challenging, with most experiments relying on decompositions of SU(d) operations into series of rotations between two-level subspaces of adjacent states and projective readout of a small number of states. Here we employ simultaneous multi-frequency drives to generate rotations and projections in an effective spin-7/2 system by mapping it onto the energy eigenstates of a superconducting circuit. We implement single-shot readout of the 8 states using a multi-tone dispersive readout (F_assignment = 88.3%) and exploit the strong nonlinearity in a high EJ/EC transmon to simultaneously address each transition and realize a spin displacement operator. By combining the displacement operator with a virtual SNAP gate, we realize arbitrary single-qudit unitary operations in O(d) physical pulses and extract spin displacement gate fidelities ranging from 0.997 to 0.989 for virtual spins of size j = 1 to j = 7/2. These native qudit operations could be combined with entangling operations to explore qudit-based error correction or simulations of lattice gauge theories with qudits. Our multi-frequency approach to qudit control and measurement can be readily extended to other physical platforms that realize a multi-level system coupled to a cavity and can become a building block for efficient qudit-based quantum computation and simulation.