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arXiv:2411.06058 · Physical Review Letters

Proposed Five-Electron Charge Quadrupole Qubit

John H. Caporaletti, J. P. Kestner

Published Jul 21, 2025• 2 citations
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Abstract

A charge qubit couples to environmental electric field fluctuations through its dipole moment, resulting in fast decoherence. We propose the p-orbital (pO) qubit, formed by the single-electron, p-like valence states of a five-electron Si quantum dot, which couples to charge noise through the quadrupole moment. We demonstrate that the pO qubit offers distinct advantages in quality factor, gate speed, readout, and size. We use a phenomenological, dipole two-level-fluctuator charge noise model to estimate a T_{2}^{*}∼80 ns. In conjunction with Rabi frequencies of order 10 GHz, an order of magnitude improvement in qubit quality factor is expected relative to state-of-the-art semiconductor spin qubits. The pO qubit features all-electrical control via modulating the dot's eccentricity. We also show how to perform two-qubit gates via the 1/r^{5} quadrupole-quadrupole interaction. We find a universal gate set using gradient ascent-based control pulse optimization, subject to 10 GHz maximum allowable bandwidth and 1 ns pulse times.

DOI
10.1103/l1x2-n2w9

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A charge qubit couples to environmental electric field fluctuations through its dipole moment, resulting in fast decoherence. We propose the p-orbital (pO) qubit, formed by the single-electron, p-like valence states of a five-electron Si quantum dot, which couples to charge noise through the quadrupole moment. We demonstrate that the pO qubit offers distinct advantages in quality factor, gate speed, readout, and size. We use a phenomenological, dipole two-level-fluctuator charge noise model to estimate a T_{2}^{*}∼80 ns. In conjunction with Rabi frequencies of order 10 GHz, an order of magnitude improvement in qubit quality factor is expected relative to state-of-the-art semiconductor spin qubits. The pO qubit features all-electrical control via modulating the dot's eccentricity. We also show how to perform two-qubit gates via the 1/r^{5} quadrupole-quadrupole interaction. We find a universal gate set using gradient ascent-based control pulse optimization, subject to 10 GHz maximum allowable bandwidth and 1 ns pulse times.
Quantum computing promises significant speed-up for certain types of computational problems. However, robust implementations of semiconducting qubits must overcome the effects of charge noise that currently limit coherence during gate operations. Here we describe a scheme for protecting solid-state qubits from uniform electric field fluctuations by generalizing the concept of a decoherence-free subspace for spins, and we propose a specific physical implementation: a quadrupole charge qubit formed in a triple quantum dot. The unique design of the quadrupole qubit enables a particularly simple pulse sequence for suppressing the effects of noise during gate operations. Simulations yield gate fidelities 10-1,000 times better than traditional charge qubits, depending on the magnitude of the environmental noise. Our results suggest that any qubit scheme employing Coulomb interactions (for example, encoded spin qubits or two-qubit gates) could benefit from such a quadrupolar design.
We propose encoding a qubit in a two-level subspace spanned by the lowest ppp-orbital state in the excited valley of an anisotropic quantum dot and the excited ppp-orbital in the ground valley, which we dub the pOvpOvpOv qubit. There is an avoided crossing between these states due to valley-orbit coupling (VOC) induced by alloy disorder, enabling complete single-qubit control using baseband electrical control of the dot anisotropy. We find that `sweet spots' exist at specific dot orientations where the instantaneous eigenstates are first-order insensitive to charge noise. Using a phenomenological two-level fluctuator (TLF) dipole noise model, we estimate an average dephasing time of T2∗≈10 μsT_2^*\approx 10\,μ\text{s}T2∗​≈10μs and a quality factor of Q∼104Q\sim 10^4Q∼104. Alternatively, encoding in the ppp-orbital states in the ground valley near the isotropic dot point, we show that one can induce a similar sweet spot via an out-of-plane magnetic field. Finally, we find that two-qubit gates for the pOvpOvpOv qubit are mediated by the quadrupole-quadrupole Coulomb interaction and can be electrically tuned from zero to ∼1 GHz\sim 1~\text{GHz}∼1 GHz by adjusting the relative orientation of the anisotropic dots, providing a novel pathway towards scalable quantum computation.
We study quantum coherence in a semiconductor charge qubit formed from a GaAs double quantum dot containing a single electron. Voltage pulses are applied to depletion gates to drive qubit rotations and noninvasive state readout is achieved using a quantum point contact charge detector. We measure a maximum coherence time of ∼7 ns at the charge degeneracy point, where the qubit level splitting is first-order insensitive to gate voltage fluctuations. We compare measurements of the coherence time as a function of detuning with numerical simulations and predictions from a 1/f noise model.
The spin of an electron confined in semiconductor quantum dots is currently a promising candidate for quantum bit (qubit) implementations. Taking advantage of the existing CMOS integration technologies, such devices can offer a platform for large scale quantum computation. However, a quantum mechanical framework bridging a device's physical design and operational parameters to the qubit's energy space is lacking. Furthermore, the spin to charge coupling introduced by intrinsic or induced spin-orbit interaction (SOI) exposes the qubits to charge noise compromising their coherence properties and inducing quantum gate errors. We present here a comodeling framework for double quantum dot (DQD) devices and their charge noise environments. We use a combination of an electrostatic potential solver, full configuration interaction quantum mechanical methods, and two-level-fluctuator models to study the quantum gate performance in realistic device designs and operation conditions. We utilize the developed models together alongside the single electron solutions of the quantum dots to simulate one- and two-qubit gates in the presence of charge noise. We find an inverse correlation between quantum gate errors and quantum dot confinement frequencies. We calculate X-gate fidelities >97>97%>97 in the simulated Si-MOS devices at a typical TLF density of ${10}^{11}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$. We also find that exchange driven two-qubit SWAP gates show higher sensitivity to charge noise with fidelities down to 9191%91 in the presence of the same density of TLFs. We further investigate the one- and two-qubit gate fidelities at different TLF densities. We find that given the small size of the quantum dots, sensitivity of a quantum gate to the distance between the noise sources and the quantum dot creates a strong variability in the quantum gate fidelities, which can compromise the device yields in scaled qubit technologies.
Semiconductor quantum dots in silicon are promising qubits because of long spin coherence times and their potential for scalability. However, such qubits with complete electrical control and fidelities above the threshold for quantum error correction have not yet been achieved. We show theoretically that the threshold fidelity can be achieved with ac gate operation of the quantum dot hybrid qubit. Formed by three electrons in a double dot, this qubit is electrically controlled, does not require magnetic fields, and runs at gigahertz (GHz) gate speeds. We analyze the decoherence caused by 1/f1/f1/f charge noise in this qubit, find parameters that minimize the charge noise dependence in the qubit frequency, and determine the optimal working points for ac gate operations that drive the detuning and tunnel coupling.
In this dissertation we discuss decoherence in charge qubits formed by multiple lateral quantum dots in the framework of the spin-boson model and the Born-Markov approximation. We consider the intrinsic decoherence caused by the coupling to bulk phonon modes and electromagnetic environmental fluctuations. In the case of decoherence caused by phonon coupling, two distinct quantum dot configurations are studied and proposed as setups that mitigate its nocive effects : (i) Three quantum dots in a ring geometry with one excess electron in total and (ii) arrays of quantum dots where the computational basis states form multipole charge configurations. For the three-dot qubit, we demonstrate the possibility of performing one- and two-qubit operations by solely tuning gate voltages. Compared to a previous proposal involving a linear three-dot spin qubit, the three-dot charge qubit allows for less overhead on two-qubit operations. For small interdot tunnel amplitudes, the three-dot qubits have Q factors much higher than those obtained for double-dot systems. The high-multipole dot configurations also show a substantial decrease in decoherence at low operation frequencies when compared to the double-dot qubit. We also discuss decoherence due to electromagnetic fluctuations in charge qubits formed by two lateral quantum dots. We use effective circuit models to evaluate correlations of voltage fluctuations in the qubit setup. These correlations allows us to estimate energy (T1) and phase (T2) relaxation times of the the qubit system. We also discuss the dependence the quality factor Q shows with respect to parameters of the setup, such as temperature and capacitive coupling between the electrodes.