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Physical Review A

Realization of a quantum algorithm using a trapped electron

Giacomo Ciaramicoli, Irene Marzoli, Paolo Tombesi

Published Apr 16, 2001• 24 citations
Publisher

Abstract

We show how a single trapped electron offers the opportunity to realize universal quantum logic gates within the present experimental possibilities. As an example, we propose to implement the Deutsch algorithm by using the quantized cyclotron motion and the electron spin as qubits.
DOI
10.1103/physreva.63.052307

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A constructive scheme has been devised to enable mapping of any quantum computation into a spintronic circuit in which the computation is encoded in a basis that is, in principle, immune to quantum decoherence. The scheme is implemented by an algorithm that utilizes multiple physical spins to encode each logical bit in such a way that collective errors affecting all the physical spins do not disturb the logical bit. The scheme is expected to be of use to experimenters working on spintronic implementations of quantum logic. Spintronic computing devices use quantum-mechanical spins (typically, electron spins) to encode logical bits. Bits thus encoded (denoted qubits) are potentially susceptible to errors caused by noise and decoherence. The traditional model of quantum computation is based partly on the assumption that each qubit is implemented by use of a single two-state quantum system, such as an electron or other spin-1.2 particle. It can be surprisingly difficult to achieve certain gate operations . most notably, those of arbitrary 1-qubit gates . in spintronic hardware according to this model. However, ironically, certain 2-qubit interactions (in particular, spin-spin exchange interactions) can be achieved relatively easily in spintronic hardware. Therefore, it would be fortunate if it were possible to implement any 1-qubit gate by use of a spin-spin exchange interaction. While such a direct representation is not possible, it is possible to achieve an arbitrary 1-qubit gate indirectly by means of a sequence of four spin-spin exchange interactions, which could be implemented by use of four exchange gates. Accordingly, the present scheme provides for mapping any 1-qubit gate in the logical basis into an equivalent sequence of at most four spin-spin exchange interactions in the physical (encoded) basis. The complexity of the mathematical derivation of the scheme from basic quantum principles precludes a description within this article; it must suffice to report that the derivation provides explicit constructions for finding the exchange couplings in the physical basis needed to implement any arbitrary 1-qubit gate. These constructions lead to spintronic encodings of quantum logic that are more efficient than those of a previously published scheme that utilizes a universal but fixed set of gates.
This work tries to model Single, Double and Triple electrons, spins based gates using quantum dot. These gates form universal gates in quantum computation and are building block of all logic circuits based on quantum gates. These spins are based on electrons which now days can be easily confined in quantum dots using a combination of hetero-structure and metal electrodes [5]. The modelling has taken analytical approach (One and Two Electron System [15], [10], [14]) wherever possible and numerical approach (Three Electron System). The spin manipulations in above three system, show us how to implement some of the important gates in quantum computing [NOT, CNOT,TOFFOLI etc.] in spin based quantum dot system. We think the TOFFOLI implementation is a novel architecture for a electron spin based system. We will also comment on the physical aspect of the simulation work wherever possible . We will also workout the aspect of quantum noise of the system which would be based on Davies Master(DM) Equation [8] based on Markovian approximation and Weak Coupling to the surrounding