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arXiv:1404.5420 · Physical Review B

Capacitative coupling of singlet-triplet qubits in different interqubit geometries

Tuukka Hiltunen, Ari Harju

Published Sep 5, 2014• 7 citations
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Abstract

In the singlet-triplet qubit architecture, the two-qubit interactions required in universal quantum computing can be implemented by capacitative coupling, by exploiting the charge distribution differences of the singlet and triplet states. The efficiency of this scheme is limited by decoherence, that can be mitigated by stronger coupling between the qubits. In this paper, we study the capacitative coupling of singlet-triplet qubits in different geometries of the two-qubit system. The effects of the qubit-qubit distance and the relative orientation of the qubits on the capacitative coupling strength are discussed using an accurate microscopic model and exact diagonalization of it. We find that trapezoidal quantum dot formations allow strong coupling with low charge distribution differences between the singlet and triplet states. The analysis of geometry on the capacitative coupling is also extended to the many-qubit case and the creation of cluster states.

DOI
10.1103/physrevb.90.125303

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In the singlet-triplet qubit architecture, the two-qubit interactions required in universal quantum computing can be implemented by capacitative coupling, by exploiting the charge distribution differences of the singlet and triplet states. The efficiency of this scheme is limited by decoherence, that can be mitigated by stronger coupling between the qubits. In this paper, we study the capacitative coupling of singlet-triplet qubits in different geometries of the two-qubit system. The effects of the qubit-qubit distance and the relative orientation of the qubits on the capacitative coupling strength are discussed using an accurate microscopic model and exact diagonalization of it. We find that trapezoidal quantum dot formations allow strong coupling with low charge distribution differences between the singlet and triplet states. The analysis of geometry on the capacitative coupling is also extended to the many-qubit case and the creation of cluster states.
We investigate a method for entangling two singlet-triplet qubits in adjacent double quantum dots via capacitive interactions. In contrast to prior work, here we focus on a regime with strong interactions between the qubits. The interplay of the interaction energy and simultaneous large detunings for both double dots gives rise to the ``double charge resonant'' regime, in which the unpolarized (1111) and fully polarized (0202) four-electron states in the absence of interqubit tunneling are near degeneracy, while being energetically well separated from the partially polarized (0211 and 1102) states. A rapid controlled-phase gate may be realized by combining time evolution in this regime in the presence of intraqubit tunneling and the interqubit Coulomb interaction with refocusing $\ensuremath{\pi}$ pulses that swap the singly occupied singlet and triplet states of the two qubits via, e.g., magnetic gradients. We calculate the fidelity of this entangling gate, incorporating models for two types of noise---charge fluctuations in the single-qubit detunings and charge relaxation within the low-energy subspace via electron-phonon interaction---and identify parameter regimes that optimize the fidelity. The rates of phonon-induced decay for pairs of GaAs or Si double quantum dots vary with the sizes of the dipolar and quadrupolar contributions and are several orders of magnitude smaller for Si, leading to high theoretical gate fidelities for coupled singlet-triplet qubits in Si dots. We also consider the dependence of the capacitive coupling on the relative orientation of the double dots and find that a linear geometry provides the fastest potential gate.
We consider a system of two purely capacitively coupled singlet-triplet qubits and numerically simulate the energy structure of four electrons in two double quantum dots with a large potential barrier between them. We calculate the interqubit coupling strength using an extended Hund-Mulliken approach which includes excited orbitals in addition to the lowest-energy orbital for each quantum dot. We show the coupling strength as a function of the qubit separation as well as plotting it against the detunings of the two double quantum dots and show that the general qualitative features of our results can be captured by a potential-independent toy model of the system.
We analyze and give estimates for the long-distance coupling via floating metallic gates between different types of spin qubits in quantum dots made of different commonly used materials. In particular, we consider the hybrid, the singlet-triplet, and the spin-12\frac{1}{2}21​ qubits, and the pairwise coupling between each type of these qubits with another hybrid qubit in GaAs, InAs, Si, and Si0.9Ge0.1{\mathrm{Si}}_{0.9}{\mathrm{Ge}}_{0.1}Si0.9​Ge0.1​. We show that hybrid qubits can be capacitively coupled strongly enough to implement two-qubit gates, as long as the distance of the dots from the metallic gates is small enough. Thus, hybrid qubits are good candidates for scalable implementations of quantum computing in semiconducting nanostructures.
We report coherent operation of a singlet-triplet qubit controlled by the spatial arrangement of two confined electrons in an adjacent double quantum dot that is electrostatically coupled to the qubit. This four-dot system is the specific device geometry needed for two-qubit operations of a two-electron spin qubit. We extract the strength of the capacitive coupling between qubit and adjacent double quantum dot and show that the present geometry allows fast conditional gate operation, opening pathways toward implementation of a universal set of gates for singlet-triplet spin qubits.
In the semiconductor double quantum dot singlet-triplet qubit architecture, the decoherence caused by the qubit's charge environment poses a serious obstacle towards large scale quantum computing. The effects of the charge decoherence can be mitigated by operating the qubit in the so-called sweet spot regions where it is insensitive to electrical noise. In this paper, we propose singlet-triplet qubits based on two quantum dots of different sizes. Such asymmetric double quantum dot systems allow the implementation of exchange gates with controllable exchange splitting JJJ operated in the doubly occupied charge region of the larger dot, where the qubit has high resilience to charge noise. In the larger dot, JJJ can be quenched to a value smaller than the intradot tunneling using magnetic fields, while the smaller dot and its larger splitting can be used in the projective readout of the qubit.