Transition-Aware Decomposition of Single-Qudit Gates

TL;DR

This paper introduces an efficient algorithm for decomposing single-qudit gates into native pulses respecting selection rules, optimizing the number of pulses needed for various qudit platforms, which is crucial for scalable quantum computing.

Contribution

The paper presents a resource-efficient algorithm for decomposing single-qudit gates into minimal pulses, considering specific selection rules of different qudit hardware platforms.

Findings

Maximum of d(d-1)/2 pulses for arbitrary single-qudit operations

Fewer pulses possible for specific operations and platforms

Applicable to various qudit systems like trapped ions and superconducting qudits

Abstract

Quantum computation with $d$-level quantum systems, also known as qudits, benefits from the possibility to use a richer computational space compared to qubits. However, for an arbitrary qudit-based hardware platform, the issue is that a generic qudit operation has to be decomposed into the sequence of native operations $-$ pulses that are adjusted to the transitions between two levels in a qudit. Typically, not all levels in a qudit are simply connected to each other due to specific selection rules. Moreover, the number of pulses plays a significant role, since each pulse takes a certain execution time and may introduce error. In this paper, we propose a resource-efficient algorithm to decompose single-qudit operations into the sequence of pulses that are allowed by qudit selection rules. Using the developed algorithm, the number of pulses is at most $d(d{-}1)/2$ for an arbitrary single-qudit operation. For specific operations, the algorithm could produce even fewer pulses. We provide a comparison of qudit decompositions for several types of trapped ions, specifically $^{171}\text{Yb}^+$, $^{137}\text{Ba}^+$ and $^{40}\text{Ca}^+$ with different selection rules, and also decomposition for superconducting qudits. Although our approach deals with single-qudit operations, the proposed approach is important for realizing two-qudit operations since they can be implemented as a standard two-qubit gate that is surrounded by efficiently implemented single-qudit gates.