Heuristics for Shuttling Sequence Optimization for a Linear Segmented Trapped-Ion Quantum Computer

TL;DR

The present work provides an implementation of an algorithm that produces sequences proved to be optimal for circuits with a quantum Fourier transform-like structure, and shows that multiple zones for gate interactions can reduce the amount of qubit register reordering.

Abstract

An algorithm for the generation of shuttling sequences is necessary for the operation of a linear segmented ion-trap quantum computer. The present work provides an implementation of an algorithm that produces sequences proved to be optimal for circuits with a quantum Fourier transform-like structure. Such optimality was proved in previous work of our group. We first present an approach for qubit mapping, i.e. determining the initial ordering of the ions, termed the common ion order, and develop a heuristic algorithm for its implementation. We explain how this heuristic is integrated in the shuttling sequence generation algorithm described in the previous work. The results show the increased performance of the heuristic in terms of reducing the number of required shuttling operations. The number of ion displacements required exhibits a polynomial increase in terms of the number of qubits, such that these operations become the main contribution to the overall resource cost. Furthermore, we show that multiple zones for gate interactions can reduce the amount of qubit register reordering.

Figures (14)

• Figure 1: Architecture of the linear segmented ion trap quantum computers and operations. Segmented traps are depicted in orange, the LIZ in green, and ions in red. Operations: a) Laser interaction in the LIZ, b) crystal displacement, c) crystal splitting, and d) crystal rotation.
• Figure 2: Illustration of an ion exchange. This figure can be either looked at from top to bottom or from bottom to top. The purple ion is exchanged with the green ion. A total of 3 merge and 3 split operations are involved.
• Figure 3: Circuits used for testing the algorithm proposed herein. Squares represent one-qubit gates, while in Toffoli gates the filled circles correspond to the control qubits and the empty circles to the controlled qubits. The number of qubits in the circuits shown differ from one circuit to another; these numbers are not important, they were chosen just for the purpose of making the circuit structures clearly visible.
• Figure 4: Results comparing the CIO and OAI initial ordering algorithms in terms of the circuit fit metric for the circuits considered.
• Figure 5: Evolution of the crystal distance between ions participating in two-qubit gates while shuttling proceeds. Note that for clarity, the graphs for the QFT and Yoyo circuits only show the first 50 gates since the oscillatory behavior is the same for the entire graph up to their full number of gates.