Quantum algorithm for reducing amplitudes in order to search and filter data (2504.16634v1)

Abstract: The method is introduced for fast data processing by reducing the probability amplitudes of undesirable elements. The algorithm has a mathematical description and circuit implementation on a quantum processor. The idea is to make a quick decision (down to a single iteration) based on the correspondence between the data and the desired result, with a probability proportionate to this correspondence. Our approach allows one to calibrate the circuit to control specified proportions.

Quantum Algorithm for Reducing Amplitudes in Order to Search and Filter Data

The paper “Quantum Algorithm for Reducing Amplitudes in Order to Search and Filter Data” by Karina Zakharova, Artem Chernikov, and Sergey Sysoev presents a novel quantum algorithm designed to efficiently process data by modulating the probability amplitudes of undesired elements in a quantum array. Unlike traditional quantum search algorithms that primarily aim to amplify the probability of desirable outcomes, this approach focuses on diminishing the amplitude of undesired results, allowing for an effective filtering process.

Methodology and Implementation

The core of the algorithm is its ability to find values closest to a specified target, denoted as $B$, within an array $A$ using a unique amplitude reduction technique. This process commences by loading the data into a quantum register $C$, facilitated by a counter formed of qubits or qudits that enable superposition over $M$ states. The algorithm iterates over possible states of $C$, shifting probability amplitudes based on proximity to $B$.

A rotation matrix, central to this amplitude adjustment, alters the amplitude of each potential state $|D_i\rangle$, contingent upon the differences between $C_i$ and $B$. The algorithm circumvents the typical requirement for labeled data elements inherent in Grover's algorithm, facilitating application without preexisting knowledge of matches within the dataset or the proximity of values to $B$.

Numerical Results and Analysis

The paper presents simulation results demonstrating the algorithm’s implementation on quantum circuits to validate its functionality. For instance, the probability redistribution, following controlled rotations, leads to the attenuation of the amplitudes corresponding to less relevant data—a process confirmed through numerous empirical tests. Notably, the maximum enhancement of wanted amplitudes per single execution is sustained at a factor of two.

In cases involving duplicate element values, challenges arise due to amplitude cancellations. The authors propose leveraging decoherence—specifically intermediate measurements—to mitigate these effects and maintain amplitude integrity.

Theoretical and Practical Implications

The proposed algorithm suggests a shift in approach from conventional quantum searches by introducing a methodology that optimally attenuates irrelevant data, thus focusing computational resources on meaningful targets. Practically, this bears implications for data filtering applications where speed and accuracy are paramount, given that the algorithm achieves results analogous to $O(1)$ complexity.

Additionally, the utility of null elements as amplitude buffers underscores a potential avenue for increasing amplitude management efficiency in situations demanding exact data matches. Consequently, the algorithm holds promise for fine-tuning quantum systems to maximize desired outcomes, aligning nicely with the concept of quantum amplitude equalization across a diverse dataset spectrum.

Considerations for Future Research

The authors recognize challenges, including amplitude enhancement limits and data entanglement complexity. Future research may explore refining amplitude transitions through iterative design, addressing the amplitude limit and extending the algorithm's utility to broader types of data processing tasks. Similarly, optimizing matrix constraints to cater to larger datasets is identified as a critical area for ongoing development.

Overall, this work expands the practical repertoire for quantum data processing algorithms, presenting alternative strategies for filtering and searching data that warrant further investigation and development within the broader quantum computing research community.