Speaker
Description
The leading approach to increase the computational capabilities of an ion-trap quantum computer is to increase the number of ions in the device. Employing multi-level systems, however, also significantly increases the Hilbert space dimension but with less hardware overhead. In trapped ions, multi-level systems can be made, for example, by using more atomic states or by harnessing the harmonic modes of motion of the chain. The multiple levels can be treated either as one large base-$d$ register (known as qudits) or as multiple base-2 qubits (known as polyqubits or virtual qubits).$^1$ While the two interpretations are equivalent, the theoretical and experimental study of qubits is much more mature than that of qudits. Interpreting each ion as multiple qubits might provide more insight and intuition.
Manipulating a multi-level system is technically challenging. Driving gates within a single multi-level system requires control of multiple tones: at least $d-1$ tones are needed to address a $d$-level system. Generating these tones is experimentally complex, especially in certain use cases where they must be phase-locked to each other. The tones are usually driven sequentially, and switching between them exposes the system to errors that don't appear in qubit devices.$^2$ Each pair of states within the polyqubit must remain phase coherent with its driving tone, so any phase that is accrued while that transition is not addressed must be tracked and corrected.
We present a novel approach to driving individual qubits in a polyqubit that addresses the sources of error inherent to single-tone gate schemes. We also provide an implementation of this gate in a polyqbuit with two qubits stored in a single $^{137}$Ba$^+$ ion across the ground $S_{1/2}$ and metastable $D_{5/2}$ levels. Our multi-tone technique directly drives single-qubit gates with one pulse, compared to single-tone schemes which use multiple two-qubit gates to construct single-qubit gates. In our polyqubit gate, all tones are driven at the same time, creating a closed-contour interaction$^{3,4}$. The tones interfere with each other to create the desired dynamics that drive a single-qubit gate. Choosing whether to drive one qubit versus the other can be done in software by simply updating the relative phases of the tones. This technique leverages the unique features of multi-level systems instead of using techniques originally developed for two-level systems to create a more native polyqubit gate.
References
[1] Shivam et al., arXiv:2406.19332 (2024).
[2] A. Vazquez-Brennan, PhD thesis. Manuscript in preparation (2026).
[3] Buckle et al., Optica Acta: International Journal of Optics, 33(9), 1129–1140 (1986).
[4] Barfuss et al., Nat. Phys. Volume 14, 1087–109 (2018).
| Academic level | PhD student |
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