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World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering

Quantum Computation Using Two Component Bose-Einstein Condensates

Tim Byrnes

Published Mar 24, 2012• 1 citation
Publisher

Abstract

Quantum computation using qubits made of two component Bose-Einstein condensates (BECs) is analyzed. We construct a general framework for quantum algorithms to be executed using the collective states of the BECs. The use of BECs allows for an increase of energy scales via bosonic enhancement, resulting in two qubit gate operations that can be performed at a time reduced by a factor of N, where N is the number of bosons per qubit. We illustrate the scheme by an application to Deutsch-s and Grover-s algorithms, and discuss possible experimental implementations. Decoherence effects are analyzed under both general conditions and for the experimental implementation proposed.

DOI
10.5281/zenodo.1328697

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Quantum computation using qubits made of two component Bose-Einstein condensates (BECs) is analyzed. We construct a general framework for quantum algorithms to be executed using the collective states of the BECs. The use of BECs allows for an increase of energy scales via bosonic enhancement, resulting in two qubit gate operations that can be performed at a time reduced by a factor of N, where N is the number of bosons per qubit. We illustrate the scheme by an application to Deutsch-s and Grover-s algorithms, and discuss possible experimental implementations. Decoherence effects are analyzed under both general conditions and for the experimental implementation proposed.
We analyze quantum computation using quantum information stored on two component Bose-Einstein condensates (BECs). We construct a general framework for quantum algorithms to be executed using the collective states of the BECs. The use of BECs allows for an increase of energy scales via bosonic enhancement, resulting in two-qubit gate operations that can be performed at a time reduced by a factor of NNN, where NNN is the number of bosons in the BEC. We illustrate the scheme by an application to Grover's algorithm, and discuss possible experimental implementations and decoherence effects.
Abstract Measurement-based quantum computation (MBQC) using two-component Bose–Einstein condensates (BECs) is proposed in this paper. An arbitrary state for one logical qubit is obtained by three-body measurement. Furthermore, a method is proposed for implementing controlled-Z gates for logical qubits in a graph state using BEC qubits and controlled-Z gates for BEC-type encoding. Results showed that the state after a measurement depends on the number of particles. These results pave the way for a novel quantum computing process based on particle control.
Recently, great progress has been made in the creation of a solid-state quantum computer using superconducting qubits on Cooper pairs of charged electrons. However, this approach has met limitations due to decoherence effects caused by the strong Coulomb interaction of the superconducting qubit with the environment. Here, we propose the solution of this problem by switching to another Bose-Einstein condensate (BEC), uncharged long-lived magnons, wherein the magnon BEC qubit can be realized due to the magnon blockade isolating a pair of the magnon condensate energy levels in the mesoscopic and nanoscopic ferromagnetic dielectric sample. We demonstrate the single-qubit gates by operating quantum transition between these states in the external microwave field. We also consider implementation of the two-qubit gates by using the interaction between such magnon BEC qubits due to exchange by virtual photons in a microwave cavity. Finally, we discuss the condition for long-lived magnon BEC qubits, a scalable architecture, and promising advantages of the multiqubit quantum computer based on the magnon qubit.
Two component Bose-Einstein condensates (BECs) have been recently shown to be viable systems for storing and manipulating quantum information. Unlike standard single-particle qubits, the quantum information is duplicated in a large number of identical bosonic particles, thus can be considered to be a macroscopic qubit. The duplication of the quantum information makes them potentially more robust than conventional qubits, where all the quantum information is lost with a single error. It has been shown theoretically and experimentally that such ensembles can be used in many ways the same way as a standard qubit: they can be visualized on the Bloch sphere, and can be manipulated analogously to standard qubits. On the other hand, the BEC qubits do not have genuine interaction between each other and one of the main difficulties with such a system is how to effectively interact them together in order to transfer quantum information and create entanglement. Furthermore, the larger Hilbert space of the macroscopic bosonic system does not allow for unique mapping of standard quantum algorithms. However, in a few past years the main building blocks of quantum information processing and several quantum algorithms were translated to the BEC qubits. In this paper we give a brief colloquium of the current achievements and outline new perspectives of the use of BEC qubits and spin-coherent ensembles for quantum technologies.
The development of ultracold atom technology has enabled precise investigations on the quantum dynamics of quantum gases. Recently, inspired by experimental advancement, the SU(1,1)\text{SU}(1,1)SU(1,1) echo, akin to the well-known SU(2)\text{SU}(2)SU(2) spin echo, was proposed for the single-component Bose-Einstein condensate (BEC). In this paper, we investigate the possibility of quantum echo in the more intricate two-component BEC by fully exploiting its underlying symmetry, which is the Lie group Sp(4,R)\text{Sp}(4,R)Sp(4,R). We demonstrate that quantum echo can occur for the two-component BEC by applying a driving protocol consisting of two steps in each period. The first step can be any Bogoliubov Hamiltonian, while the second step is a Hamiltonian with interactions turned off, which plays a similar role as the $\ensuremath{\pi}$ pulse in spin echo. We confirm our theoretical results with numerical calculations for different examples of the two-component BEC. We further consider the effect of interactions between the excited boson modes on the quantum echo process and discuss the possible experimental implementation of this quantum echo.
We investigate schemes to dynamically create many-particle entangled states of a two-component Bose-Einstein condensate in a very short time proportional to 1/N,1/N,1/N, where N is the number of condensate particles. For small N we compare exact numerical calculations with analytical semiclassical estimates and find very good agreement for N> 50.N>~50.N> 50. We also estimate the effect of decoherence on our scheme, study possible scenarios for measuring the entangled states, and investigate experimental imperfections.