Experimental Study of Forrelation in Nuclear Spins

TL;DR

This paper experimentally investigates Forrelation functions in nuclear spins, demonstrating that quantum algorithms can efficiently determine Forrelations with potential implications for quantum supremacy, despite experimental noise.

Contribution

It provides the first experimental implementation of Forrelation in nuclear spins, showcasing the feasibility of quantum algorithms for complex correlation functions.

Findings

Quantum algorithms can determine Forrelations accurately in nuclear spins.

Optimized GRAPE pulses effectively control spin fluctuations.

Results support potential for demonstrating quantum supremacy.

Abstract

Correlation functions are often employed to quantify the relationships among interdependent variables or sets of data. Recently, a new class of correlation functions, called Forrelation, has been introduced by Aaronson and Ambainis for studying the query complexity of quantum devices. It was found that there exists a quantum query algorithm solving 2-fold Forrelation problems with an exponential quantum speedup over all possible classical means, which represents essentially the largest possible separation between quantum and classical query complexities. Here we report an experimental study probing the 2-fold and 3-fold Forrelations encoded in nuclear spins. The major experimental challenge is to control the spin fluctuation to within a threshold value, which is achieved by developing a set of optimized GRAPE pulse sequences. Overall, our small-scale implementation indicates that the quantum query algorithm is capable of determine the values of Forrelations within an acceptable accuracy required for demonstrating quantum supremacy, given the current technology and in the presence of experimental noise.