Single qudit realization of the Deutsch algorithm using superconducting many-level quantum circuits

TL;DR

This paper proposes a method to implement the Deutsch quantum algorithm using a single five-level superconducting qudit, avoiding the need for multiple qubits by manipulating a single high-dimensional quantum system.

Contribution

It introduces a novel approach for realizing quantum algorithms with noncomposite systems, specifically demonstrating a single qudit implementation of the Deutsch algorithm with superconducting circuits.

Findings

Successful design of a single qudit realization of the Deutsch algorithm.

Demonstration of universal gate set implementation using a five-level system.

Potential for scalable quantum computing with noncomposite systems.

Abstract

Design of a large-scale quantum computer has paramount importance for science and technologies. We investigate a scheme for realization of quantum algorithms using noncomposite quantum systems, i.e., systems without subsystems. In this framework, $n$ artificially allocated "subsystems" play a role of qubits in $n$-qubits quantum algorithms. With focus on two-qubit quantum algorithms, we demonstrate a realization of the universal set of gates using a $d=5$ single qudit state. Manipulation for an ancillary level in the systems allows effective implementation of operators from ${\rm U}(4)$ group via operators from ${\rm SU}(5)$ group. Using a possible experimental realization of such systems through anharmonic superconducting many-level quantum circuits, we present a blueprint for a single qudit realization of the Deutsch algorithm, which generalizes previously studied realization based on the virtual spin representation [A.R. Kessel et al., Phys. Rev. A 66, 062322 (2002)].