Implementing the Deutsch-Jozsa algorithm with macroscopic ensembles

Abstract

General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available: http://www.bristol.ac.uk/pure/about/ebr-terms PHYSICAL REVIEW A 93, 052302 (2016) Implementing the Deutsch-Jozsa algorithm with macroscopic ensembles 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.

Error suppression in adiabatic quantum computing with qubit ensembles

“…The sensitivity of qubit ensemble states have already been investigated in numerous works, see for example Refs. [50,[55][56][57]. The main point here is that the fragility of the quantum states is state dependent: while Schrodinger cat states are extremely sensitive, spin coherent states are generally quite robust.…”

Remote state preparation of two-component Bose-Einstein condensates

“…[51] overcame this limitation by using two auxiliary ensembles to produce correlations in more spin directions, to achieve teleportation for any state on the Bloch sphere. This makes the 2A2S squeezed states potentially a better candidate from a quantum information perspective [52][53][54][55], which have in the past mainly considered 1A2S squeezed states.…”

Classical realization of the quantum Deutsch algorithm

“…Though simple, the Deutsch-Jozsa algorithm encompasses all the main ingredients typically found in most quantum algorithms: all quantum computations are just more complex variations of it 2 . This explains its importance in the field of quantum computation, leading hitherto to an uncountable number of experimental realizations in a variety of physical systems such as nuclear spins 3 , ion traps 4 , quantum dots 5 , superconducting devices 6 , electronic spins 7 , photonic degrees of freedom 8 and macroscopic ensembles 9 , to name a few. Despite the fact that the algorithm is composed by a small number of elementary logical gates, such implementations can be highly involved, depending on which physical system is being used for the experimental realization.…”