Implementing the Deutsch-Jozsa algorithm with macroscopic ensembles

TL;DR

This paper demonstrates that the Deutsch-Jozsa quantum algorithm can be implemented using macroscopic ensembles, achieving exponential speedup and robustness against decoherence, thus extending quantum computing to larger, more complex systems.

Contribution

It introduces two novel encoding methods for implementing the Deutsch-Jozsa algorithm with macroscopic ensembles, overcoming decoherence issues and maintaining exponential speedup.

Findings

Both methods reproduce the qubit Deutsch-Jozsa algorithm

Implementation is robust under decoherence

Achieves exponential speedup over classical algorithms

Abstract

Quantum computing implementations under consideration today typically deal with systems with microscopic degrees of freedom such as photons, ions, cold atoms, and superconducting circuits. The quantum information is stored typically in low-dimensional Hilbert spaces such as qubits, as quantum effects are strongest in such systems. It has however been demonstrated that quantum effects can be observed in mesoscopic and macroscopic systems, such as nanomechanical systems and gas ensembles. While few-qubit quantum information demonstrations have been performed with such macroscopic systems, a quantum algorithm showing exponential speedup over classical algorithms is yet to be shown. Here we show that the Deutsch-Jozsa algorithm can be implemented with macroscopic ensembles. The encoding that we use avoids the detrimental effects of decoherence that normally plagues macroscopic implementations. We discuss two mapping procedures which can be chosen depending upon the constraints of the oracle and the experiment. Both methods have an exponential speedup over the classical case, and only require control of the ensembles at the level of the total spin of the ensembles. It is shown that both approaches reproduce the qubit Deutsch-Jozsa algorithm, and are robust under decoherence.