Efficient Multi-Controlled Gate Implementation in Trapped-Ion Systems

TL;DR

This paper presents optimized pulse-level implementations of multi-controlled gates in trapped-ion quantum systems, reducing resource costs and improving scalability for quantum algorithms.

Contribution

It introduces a novel pulse cancellation technique exploiting sign freedom in RSB pulses and proposes ancilla-free circuits for efficient multi-controlled gates.

Findings

Pulse cancellation reduces gate time and enhances fidelity.

Linear combination of unitaries (LCU) select operator cost is reduced from O(L log L) to O(L).

Ancilla-free circuits enable scalable implementation of N-controlled gates.

Abstract

Multi-controlled gates are essential primitives in quantum algorithms, yet implementing them via standard gate-level decompositions remains resource-intensive. We develop efficient pulse-level implementations of multi-controlled gates in trapped-ion systems using the Cirac-Zoller scheme. We first show that the Cirac-Zoller construction admits a freedom in the sign choice of red-sideband (RSB) pulses, which leaves the logical operation invariant up to a local Pauli-$Z$ correction. By exploiting this freedom, we construct equivalent realizations of multi-controlled gates and develop pulse cancellation for more efficient implementations of successive gates. We perform numerical simulations and show that pulse cancellation reduces the gate time and improves the state fidelity. Furthermore, we propose ancilla-free circuits for general $N$-controlled gates that use a single-controlled gate primitive and $\mathcal{O}(N)$ RSB pulses. As a key application, we apply our pulse cancellation to the linear combination of unitaries (LCU) method for block encoding. We show that the RSB-pulse cost of the select operator over $L$ unitaries can be reduced from $\mathcal{O}(L\log L)$ to $\mathcal{O}(L)$, which improves the efficiency and scalability of LCU-based quantum circuits.