A Generalization of Bernstein-Vazirani Algorithm to Qudit Systems

TL;DR

This paper extends the Bernstein-Vazirani quantum algorithm from qubits to qudit systems, demonstrating how quantum advantage can be achieved in higher-dimensional quantum systems.

Contribution

It introduces a generalized version of the Bernstein-Vazirani algorithm applicable to qudit systems, broadening the scope of quantum algorithms beyond qubits.

Findings

Quantum advantage demonstrated in qudit systems

Generalization of the algorithm to higher dimensions

Potential for more efficient quantum computations

Abstract

A quantum algorithm to solve the parity problem is better than its most efficient classical counter- part with a separation that is polynomial in the number of queries. This was shown by E. Bernstein and U. Vazirani and was one of the earliest indications that the quantum information processing can outperform the classical one by a significant margin. The problem and its solution both is usually stated for a 2-level system since we generally work with bits/qubits. However, many works have been done generalizing known quantum computing techniques to higher level systems. Following this, we look at a generalization of the Bernstein-Vazirani algorithm implemented on a general qudit system.