Optically controlled logic gates for two spin qubits in vertically coupled quantum dots

Abstract

We describe an interaction mechanism between electron spins in a vertically-stacked double quantum dot that can be used for controlled two-qubit operations. This interaction is mediated by excitons confined within, and delocalized over, the double dot. We show that gates equivalent to the √ SWAP gate can be obtained in times much less than the exciton relaxation time and that the negative effects of hole-mixing and spontaneous emission do not seriously affect these results.PACS numbers: 78.67.Hc, 03.67.LxThe spin of an electron confined in a quantum dot (QD) is one of the leading candidates for the realization of a practical qubit. Since the work of Loss and DiVincenzo [1], there have been a number of proposals on how best to achieve the precise manipulations of such spins required for the operation of quantum logic. See, for example, [2,3,4,5].Whilst interest in electrostatic gating remains strong, the use of lasers has several advantages in this role, most notably speed and control. Despite significant theoretical advances in this direction, there has, as yet, been no experimental demonstration of optically-controlled gating between electron spins in QDs.In this paper, we describe an interaction mechanism to achieve just this. This qubit-qubit interaction is mediated by interdot tunnelling of photo-excited carriersan area which has been the subject of significant recent experimental advances [6,7]. Our results are of explicit relevance to the current generation of vertically-stacked self-assembled InAs QDs, but are also easily adaptable to the other dots, including horizontally-coupled ones.The interaction we describe has its origin in the so-called optical-RKKY effect, in which two electron spins are coupled via their exchange interactions with optically-generated excitons in the semiconductor bulk [8]. The coupling effect of these bulk excitons between two electron spins in a double QD was examined in Ref.[9]. Here we consider an interaction mediated, not by bulk excitons, but by a single exciton confined in the same double QD structure. We describe a situation in which the excitonic electron is able to tunnel between the dots and form delocalized 'molecular' states. It is the exchange interaction between this electron and the resident qubit electrons that leads to an optically controlled gating. This gate, although not one of the standard quantum computation (QC) gates, can be used to form a controlled-Z operation when used twice in conjunction with single qubit rotations, and is, in this way, similar to the √ SWAP gate. The main factor limiting the speed with which oper- The lowest electron levels in each dot (labeled 1 and 2) are the two qubit levels and an electron permanently resides in each of them. Laser illumination is tuned such that it creates an exciton in the excited levels of dot A only (levels 3). (c) Due to a tunnel coupling τ34 between the dots and a resonance condition met through the tuning of the gate voltage Vg, the excitonic electron can tunnel back-and-forth. The exchange interaction be...

Geometric Phase in a Tunneling-Coupled Quantum Dot Molecule

“…From the density plots Fig. 2a and b, it can be seen that the Berry phase changes rapidly in the vicinity of δ 1 + ω 21 Fig. 2c, which is confirmed by Fig.…”

Quantum computing by optical control of electron spins

“…In two-qubit operations [64, 68-71, 73-76, 173], the intermediate states are excitons with two excess electrons. The effective exchange interaction between two spins may be induced by the virtual excitation of one exciton tunneling back and forth between two dots, which is similar to the RKKY process and is dubbed optical RKKY interaction to indicate the role of the optical excitation [73][74][75]. Alternatively, even if there is no tunneling between QDs, the interplay between Coulomb interaction and the spin blocking effect would induce effective interaction between two separated spins when two excitons are (virtually) excited in two dots [68][69][70][71]173].…”

“…To implement two-qubit quantum gates, optically induced RKKY interaction (ORKKY) between electrons doped in QDs has been proposed to couple two spins, laterally via continuum excitons [73,74] or vertically via discrete states [75]. The ORKKY interaction mediated by continuum excitons [73,74], due to the extension nature of the continuum states, is less controllable in selectively coupling certain spins.…”

“…The ORKKY interaction mediated by continuum excitons [73,74], due to the extension nature of the continuum states, is less controllable in selectively coupling certain spins. The ORKKY interaction between QDs vertically stacked [75], on the other hand, is not applicable to a scalable system with a planar layout. For the sake of scalability, we consider to employ the discrete excited states in laterally coupled QDs to induce the ORKKY interaction, which, as described below, can be controlled to selectively couple spins in designated adjacent QDs.…”

“…75 As, 69 Ga and 71 Ga in GaAs). The interaction can be separated as "diagonal" terms which involve only the spin vector components along the field (z) We show by explicitly examining Shor's algorithm the crucial role of quantum non-demolition measurement for quantum computation to be scalable.…”