### Beyond binary quantum information

While most quantum processors encode binary information in two-level systems (qubits, d=2), the transmon circuit intrinsically features higher-level states owing to it’s cosine potential (figure left). Using these excited states, we are developing quantum processors that use many-level systems (qu-*dits*, d>2) as their elementary building block. Our lab recently measured up to 12 levels in a single transmon (d=12) [1] and demonstrated efficient methods for qudit control and readout [2] inspired by large-angular momentum spins.

A qudit processor poses a resource-efficient way to increase the available Hilbert space and strongly reduce the number of required entangling gates (that are typically the most difficult to perform) for a given algorithm. We develop planar qudit processors of coupled transmons, each locally encoding a high-dimensional qudit. A working five-qutrit processor was demonstrated in 2021 at UC Berkeley[3]. On the way to extending these concepts to higher qudit dimension, our lab explores many interesting research questions, including: Can we design a better circuit to encode qudits or is the transmon optimal? Can we employ quantum control techniques, inspired by NMR and quantum optics, to improve single-and mulitple-qudit gates? Can we run quantum computing, simulation -, and sensing protocols that demonstrate a clear qudit advantage over qubits? Is it possible to use a single high-dimensional qudit for quantum error correction?

##### Funded projects

“BE NON-LINEAR: Bosonic Encodings in NOise-resilient circuits with strong Non-LINEARity ”

AFOSR – Young Investigator Program

##### Relevant Publications

**1 – Systematic study of High Ej/Ec transmon qudits up to d = 12**

Z. Wang, R.W. Parker, E. Champion and M.S. Blok

*(submitted, 2024) |* Arxiv:2407.17407

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

E. Champion*, Z. Wang*, R.W. Parker and M.S. Blok

*(submitted, 2024) | Arxiv:2405.15857*

**3 – Quantum Information Scrambling in a Superconducting Qutrit Processor**

M.S. Blok*, V. V. Ramasesh*, T. Schuster, K. O’Brien, J.M. Kreikebaum, D. Dahlen, A. Morvan, B. Yoshida, N. Y. Yao, I. Siddiqi.

Phys. Rev. X **11**, 021010 *(2021)*| Arxiv:2003.03307