Optimizing Quantum Search with a Binomial Version of Grover's Algorithm

TL;DR

This paper introduces a binomial distribution-based partitioning strategy to optimize Grover's quantum search algorithm, reducing iterations and improving efficiency, validated through experiments on Honeywell quantum hardware.

Contribution

It proposes a novel binomial partitioning method to enhance amplitude amplification in Grover's algorithm, allowing for fewer iterations when class information is known or can be estimated.

Findings

Reduced number of iterations when class information is known

Effective partitioning strategy demonstrated on real quantum hardware

Improved quantum search efficiency in structured data scenarios

Abstract

Amplitude Amplification -- a key component of Grover's Search algorithm -- uses an iterative approach to systematically increase the probability of one or multiple target states. We present novel strategies to enhance the amplification procedure by partitioning the states into classes, whose probabilities are increased at different levels before or during amplification. The partitioning process is based on the binomial distribution. If the classes to which the search target states belong are known in advance, the number of iterations in the Amplitude Amplification algorithm can be drastically reduced compared to the standard version. In the more likely case in which the relevant classes are not known in advance, their selection can be configured at run time, or a random approach can be employed, similar to classical algorithms such as binary search. In particular, we apply this method in the context of our previously introduced Quantum Dictionary pattern, where keys and values are encoded in two separate registers, and the value-encoding method is independent of the type of superposition used in the key register. We consider this type of structure to be the natural setup for search. We confirm the validity of our new approach through experimental results obtained on real quantum hardware, the Honeywell System Model H0 trapped-ion quantum computer.