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arXiv:1305.0749 · Physical Review B

Noise-protected gate for six-electron double-dot qubit

Sebastian Mehl, David Peter Divincenzo

Published Oct 28, 2013• 15 citations
arXivHTMLPDF

Abstract

Singlet-triplet spin qubits in six-electron double quantum dots, in moderate magnetic fields, can show superior immunity to charge noise. This immunity results from the symmetry of orbitals in the second energy shell of circular quantum dots: singlet and triplet states in this shell have identical charge distributions. Our phase-gate simulations, which include $1/f$ charge noise from fluctuating traps, show that this symmetry is most effectively exploited if the gate operation switches rapidly between sweet spots deep in the (3,3) and (4,2) charge stability regions; fidelities very close to 1 are predicted if subnanosecond switching can be performed.

DOI
10.1103/physrevb.88.161408

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Singlet-triplet spin qubits in six-electron double quantum dots, in moderate magnetic fields, can show superior immunity to charge noise. This immunity results from the symmetry of orbitals in the second energy shell of circular quantum dots: singlet and triplet states in this shell have identical charge distributions. Our phase-gate simulations, which include 1/f1/f1/f charge noise from fluctuating traps, show that this symmetry is most effectively exploited if the gate operation switches rapidly between sweet spots deep in the (3,3) and (4,2) charge stability regions; fidelities very close to 1 are predicted if subnanosecond switching can be performed.
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.
We propose an optimal set of quantum gates for a singlet-triplet qubit in a double quantum dot with two electrons utilizing the S-T− subspace. Qubit rotations are driven by the applied magnetic field and an orthogonal field gradient provided by a micromagnet. We optimize the fidelity of this qubit as a function of magnetic fields, taking advantage of “sweet spots” where the rotation frequencies are independent of the energy level detuning, providing protection against charge noise. We simulate gate operations and qubit rotations in the presence of quasistatic noise from charge and nuclear spins as well as leakage to nonqubit states, and predict that in silicon quantum dots gate fidelities greater than 99% can be achieved for two nearly-orthogonal rotation axes.
We propose an optimized set of quantum gates for a singlet-triplet qubit in a double quantum dot with two electrons utilizing the $S\text{\ensuremath{-}}{T}_{\ensuremath{-}}$ subspace. Qubit rotations are driven by the applied magnetic field and a field gradient provided by a micromagnet. We optimize the fidelity of this qubit as a function of the magnetic fields, taking advantage of ``sweet spots'' where the rotation frequencies are independent of the energy level detuning, providing protection against charge noise. We simulate gate operations and qubit rotations in the presence of quasistatic noise from charge and nuclear spins as well as leakage to nonqubit states. Our results show that, for silicon quantum dots, gate fidelities greater than 9999%99 should be realizable, for rotations about two nearly orthogonal axes.
Charge noise is the main hurdle preventing high-fidelity operation, in particular that of two-qubit gates, of semiconductor-quantum-dot-based spin qubits. While certain sweet spots where charge noise is substantially suppressed have been demonstrated in several types of spin qubits, the existence of one for coupled singlet-triplet qubits is unclear. We theoretically demonstrate, using full configuration-interaction calculations, that a range of nearly sweet spots appears in the coupled singlet-triplet qubit system when a strong enough magnetic field is applied externally. We further demonstrate that ramping to and from the judiciously chosen nearly sweet spot using sequences based on the shortcut to adiabaticity offers maximal gate fidelities under charge noise and phonon-induced decoherence. These results should facilitate realization of high-fidelity two-qubit gates in singlet-triplet qubit systems.
We theoretically study the influence of charge noise on a controlled phase gate, implemented using two proximal double quantum dots coupled electrostatically. Using the configuration interaction method, we present a full description of the conditional control scheme and quantitatively calculate the gate error arising from charge fluctuations. Our key finding is that the existence of noise-immune sweet spots depends on not only the energy detuning but also the device geometry. The conditions for sweet spots with minimal charge noise are predicted analytically and verified numerically. Going beyond the simple sweet-spot concept we demonstrate the existence of other optimal situations for fast and low-noise singlet-triplet two-qubit gates.