Realization of a Quantum Streaming Algorithm on Long-lived Trapped-ion Qubits

TL;DR

This paper demonstrates a quantum streaming algorithm implemented on a long-lived trapped-ion quantum computer, showing that quantum advantage in space can be maintained even with fault-tolerance overheads.

Contribution

It experimentally realizes a quantum streaming algorithm on a trapped-ion platform with long-lived qubits, and confirms the persistence of quantum space advantage under fault-tolerance.

Findings

Successful implementation of quantum pair sketch on trapped-ion qubits.

Quantum space advantage persists with fault-tolerant encoding.

Demonstration of solving Hidden Matching problem with quantum advantage.

Abstract

Large classical datasets are often processed in the streaming model, with data arriving one item at a time. In this model, quantum algorithms have been shown to offer an unconditional exponential advantage in space. However, experimentally implementing such streaming algorithms requires qubits that remain coherent while interacting with an external data stream. In this work, we realize such a data-streaming model using Quantinuum Helios trapped-ion quantum computer with long-lived qubits that communicate with an external server. We implement a quantum pair sketch, which is the primitive underlying many quantum streaming algorithms, and use it to solve Hidden Matching, a problem known to exhibit a theoretical exponential quantum advantage in space. Furthermore, we compile the quantum streaming algorithm to fault-tolerant quantum architectures based on surface and bivariate bicycle codes and show that the quantum space advantage persists even with the overheads of fault-tolerance.