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arXiv:1501.01932 · Physical Review B

Long-distance entanglement of soliton spin qubits in gated nanowires

Paweł Szumniak, Jarosław Pawłowski, Stanisław Bednarek, Daniel Loss

Published Jul 2, 2015• 15 citations
arXivHTMLPDF

Abstract

We investigate numerically the charge, spin, and entanglement dynamics of two electrons confined in a gated semiconductor nanowire. The electrostatic coupling between electrons in the nanowire and the induced charge on the metal electrodes leads to a self-trapping of the electrons, which results in solitonlike properties. We show that the interplay of an all-electrically controlled coherent transport of the electron solitons and of the exchange interaction can be used to realize ultrafast SWAP and entangling $\sqrt{\text{SWAP}}$ gates for distant spin qubits. We demonstrate that the latter gate can be used to generate a maximally entangled spin state of spatially separated electrons. The results are obtained by quantum-mechanical time-dependent calculations with exact inclusion of electron-electron correlations.

DOI
10.1103/physrevb.92.035403

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We investigate numerically the charge, spin, and entanglement dynamics of two electrons confined in a gated semiconductor nanowire. The electrostatic coupling between electrons in the nanowire and the induced charge on the metal electrodes leads to a self-trapping of the electrons, which results in solitonlike properties. We show that the interplay of an all-electrically controlled coherent transport of the electron solitons and of the exchange interaction can be used to realize ultrafast SWAP and entangling SWAP\sqrt{\text{SWAP}}SWAP​ gates for distant spin qubits. We demonstrate that the latter gate can be used to generate a maximally entangled spin state of spatially separated electrons. The results are obtained by quantum-mechanical time-dependent calculations with exact inclusion of electron-electron correlations.
A nanodevice capable of separating spins of two electrons confined in a quantum dot formed in a gated semiconductor nanowire is proposed. Two electrons confined initially in a single quantum dot in the singlet state are transformed into the system of two electrons confined in two spatially separated quantum dots with opposite spins. In order to separate the electrons' spins we exploit transitions between the singlet and the triplet state, which are induced by resonantly oscillating Rashba spin-orbit coupling strength. The proposed device is all electrically controlled and the electron spin separation can be realized within tens of picoseconds. The results are supported by solving numerically the quasi-one-dimensional time-dependent Schroedinger equation for two electrons, where the electron-electron correlations are taken into account in the exact manner.
We propose and analyze a scheme for performing a long-range entangling gate for qubits encoded in electron spins trapped in semiconductor quantum dots. Our coupling makes use of an electrostatic interaction between the state-dependent charge configurations of a singlet-triplet qubit and the edge modes of a quantum Hall droplet. We show that distant singlet-triplet qubits can be selectively coupled, with gate times that can be much shorter than qubit dephasing times and faster than decoherence due to coupling to the edge modes. Based on parameters from recent experiments, we argue that fidelities above 9999%99 could in principle be achieved for a two-qubit entangling gate taking as little as 20 ns.
The electron spin is a natural two-level system that allows a qubit to be encoded.When localized in a gate-defined quantum dot, the electron spin provides a promising platform for a future functional quantum computer.The essential ingredient of any quantum computer is entanglement-for the case of electronspin qubits considered here-commonly achieved via the exchange interaction.Nevertheless, there is an immense challenge as to how to scale the system up to include many qubits.In this paper, we propose a novel architecture of a large-scale quantum computer based on a realization of long-distance quantum gates between electron spins localized in quantum dots.The crucial ingredients of such a long-distance coupling are floating metallic gates that mediate electrostatic coupling over large distances.We show, both analytically and numerically, that distant electron spins in an array of quantum dots can be coupled selectively, with coupling strengths that are larger than the electron-spin decay and with switching times on the order of nanoseconds.
We propose a setup for universal and electrically controlled quantum information processing with hole spins in Ge/Si core/shell nanowire quantum dots (NW QDs). Single-qubit gates can be driven through electric-dipole-induced spin resonance, with spin-flip times shorter than 100 ps. Long-distance qubit-qubit coupling can be mediated by the cavity electric field of a superconducting transmission line resonator, where we show that operation times below 20 ns seem feasible for the entangling iSWAP\sqrt{i\text{SWAP}}iSWAP​ gate. The absence of Dresselhaus spin-orbit interaction (SOI) and the presence of an unusually strong Rashba-type SOI enable precise control over the transverse qubit coupling via an externally applied, perpendicular electric field. The latter serves as an on-off switch for quantum gates and also provides control over the ggg factor, so single- and two-qubit gates can be operated independently. Remarkably, we find that idle qubits are insensitive to charge noise and phonons, and we discuss strategies for enhancing noise-limited gate fidelities.
We consider an electron confined in a gated nanowire quantum dot (NQD) with arbitrarily strong spin-orbit coupling (SOC) and weak static magnetic field, and treat the latter as a perturbation to seek the maximal spin-motion entangled states with the exact general solutions of the perturbed equations. From the boundedness and self-consistent conditions of the general solutions we find two corrected energies to any n level of the unperturbed system with ground state n = 0, which are much less than the unperturbed level-difference and corresponds to a spin-orbit qubit. We demonstrate the metastability of the two-level states and the decoherence-averse effect of SOC, and suggest an alternative scheme to perform the qubit control, simply by adjusting the orientation of magnetic field for any fixed SOC. Such a adjustment can lead to the spin flipping of the state vector and the position exchanging of the probability-density wavepackets which can be proposed as the non-Abelian quasiparticles. The results could be directly extended to a weakly coupled array of NQDs for coherently encoding the robust spin-orbit qubits.
A two-electron system confined in two coupled semiconductor quantum dots is investigated as a candidate for performing quantum logic operations with spin qubits. We study different processes of swapping the electron spins by a controlled switching on and off of the exchange interaction. The resulting spin swap corresponds to an elementary operation in quantum-information processing. We perform direct simulations of the time evolution of the two-electron system. Our results show that, in order to obtain the full interchange of spins, the exchange interaction should change smoothly in time. The presence of jumps and spikes in the time characteristics of the confinement potential leads to a considerable increase of the spin-swap time. We propose several mechanisms to modify the exchange interaction by changing the confinement potential profile and discuss their advantages and disadvantages.