Applications of Multi-Valued Quantum Algorithms

Abstract

This paper generalizes both the binary Deutsch-Jozsa and Grover algorithms to $n$-valued logic using the quantum Fourier transform. Our extended Deutsch-Jozsa algorithm is not only able to distinguish between constant and balanced Boolean functions in a single query, but can also find closed expressions for classes of affine logical functions in quantum oracles, accurate to a constant term. Furthermore, our multi-valued extension of the Grover algorithm for quantum database search requires fewer qudits and hence a substantially smaller memory register, as well as fewer wasted information states, to implement. We note several applications of these algorithms and their advantages over the binary cases.

12 pages, 4 figures; updated version of paper for ISMVL 2007; contains new proof of multi-valued Grover algorithm time complexity, with typos corrected

References in corpus (3)

• Multi-valued Logic Gates for Quantum Computation
• Grover's Algorithm: Quantum Database Search
• Generalization of the Deutsch algorithm using two qudits

Cited by in corpus (8)

• Qudits and high-dimensional quantum computing
• Arithmetic Circuits for Multilevel Qudits Based on Quantum Fourier Transform
• Asymptotically Improved Circuit for $d$-ary Grover's Algorithm with Advanced Decomposition of $n$-qudit Toffoli Gate
• Efficient classical simulation of the Deutsch-Jozsa and Simon's algorithms
• Emulating two qubits with a four-level transmon qudit for variational quantum algorithms
• One-Dimensional Lazy Quantum walk in Ternary System
• QuDiet: A Classical Simulation Platform for Qubit-Qudit Hybrid Quantum Systems
• A Generalization of Bernstein-Vazirani Algorithm to Qudit Systems