We propose two schemes to coherently transfer arbitrary quantum states of the two electron singlet-triplet qubit across an empty chain of quantum dots. The schemes are based on electrical control over the detuning energy of the quantum dots. The first scheme is a pulse-gating scheme, requiring dc pulses and engineering of inter- and intra-dot Coulomb energies. The second scheme is based on the adiabatic theorem, requiring time-dependent linear control of the detuning energy through avoided crossings at a rate that the system remains in the ground state. We simulate the transfer fidelity for 3 dots using typical experimental parameters for silicon quantum dots, then generalize our results to arbitrary number of dots. Our results give state transfer fidelities in excess of 98.7% and 99.3%, and at sub-nanosecond and tens of nanosecond timescales, for the pulse-gated and adiabatic schemes, respectively.
Abstract We present a protocol based on shortcuts to adiabaticity for the manipulation of an electron in a linear quantum dot array of arbitrary size on an InSb heterostructure. We propose a model where the couplings between neighboring dots have a particular form, related to a spin operator that depends on the size of the chain. The system is driven by an electric field with a modified Landau–Zener time-dependence. We find that the transmission of the electron from the first site to the last one can be achieved with any desired fidelity (99.9% or even more) by choosing the appropriate evolution time of the system according to the length of the chain. Then, we consider Rashba spin–orbit (SO) interaction effects and possible chain defects and find that transmission probabilities are larger than 90% for moderate intensity of SO interactions. However, we can increase even more the fidelity by increasing the static magnetic field, since it would diminish the effect of the SO mechanism in the dynamics.
Long-distance transfer of quantum information in architectures based on quantum dot spin qubits will be necessary for their scalability. One way of achieving this goal is to simply move the electron between two quantum registers. Precise control over the process of shuttling such a single electron through a chain of tunnel-coupled quantum dots is possible when interdot energy detunings are changed adiabatically. The deterministic character of shuttling is, however, endangered by the open nature of the system, as the transferred electron is coupled to thermal reservoirs: sources of fluctuations of electric fields and lattice vibrations. We present a comprehensive analysis showing how the electron transfer between two voltage-controlled quantum dots is affected by electron-phonon scattering and interaction with sources of
1/f and Johnson charge noise in both detuning and tunnel coupling. The electron-phonon scattering turns out to be irrelevant in Si quantum dots, with charge noise dominating the dynamics of the system at slow detuning sweep, when the electron spends more time delocalized between the dots (i.e., near the anticrossing of the tunnel-coupled states). Competition between the effects of charge noise and the Landau-Zener effect leads to an existence of an optimal detuning sweep rate, leading to minimal probability of leaving the electron behind. In GaAs quantum dots, on the other hand, piezoelectric coupling to phonons is strong enough to make the processes of interdot transfer assisted by phonon emission and absorption dominate over transitions caused by charge noise. The probability of leaving the electron behind then depends monotonically on detuning the sweep rate over a broad range of rates, and values much smaller than in silicon can be obtained for slow sweeps. However, after taking into account limitations on transfer time imposed by the need for preservation of a shuttled electron's spin coherence, the minimal probabilities of leaving the electron behind in both GaAs- and Si-based double quantum dots turn out to be of the same order of magnitude. Bringing them down below ${10}^{\ensuremath{-}3}$ requires temperatures $\ensuremath{\le}100$ mK and tunnel couplings above $20\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{eV}$.
Charge, spin and quantum states transfer in solid state devices is an important issue in quantum information. Adiabatic protocols, such as coherent transfer by adiabatic passage have been proposed for direct charge transfer, also denoted as long-range transfer, between the outer dots in a QD array without occupying the intermediate ones. However adiabatic protocols are prone to decoherence. With the aim of achieving direct charge transfer between the outer dots of a QD array with high fidelity, we propose a protocol to speed up the adiabatic transfer, in order to increase the fidelity of the process. Based on adiabaticity shortcuts, by properly engineering the pulses, fast adiabatic-like direct charge transfer between the outer dots can be obtained. We also discuss the impact of transfer fidelity on the operation time in the presence of dephasing. The proposed protocols for accelerating long-range charge and state transfer in a QD array offer a robust mechanism for quantum information transfer, by minimizing the decoherence and relaxation processes.
Controlled adiabatic transfer of a single electron through a chain of quantum dots has been recently achieved in GaAs and Si/SiGe based quantum dots, opening prospects for turning stationary spin qubits into mobile ones and solving in this way the problem of long-distance communication between quantum registers in a scalable quantum computing architecture based on quantum dots. We consider theoretically the process of such an electron transfer between two tunnel-coupled quantum dots, focusing on control by slowly varying the detuning of energy levels in the dots. We take into account the fluctuations in detuning caused by
1/f-type noise that is ubiquitous in semiconductor nanostructures and analyze their influence on probability of successful transfer of an electron in a spin eigenstate. With numerical and analytical calculations we show that probability of electron not being transferred due to $1/{f}^{\ensuremath{\beta}}$ noise in detuning is $\ensuremath{\propto}\phantom{\rule{0.16em}{0ex}}{\ensuremath{\sigma}}^{2}{t}^{\ensuremath{\beta}\ensuremath{-}1}/v$, where $\ensuremath{\sigma}$ characterizes the noise amplitude,
t is the interdot tunnel coupling, and
v is the detuning sweep rate. Interestingly, this means that the noise-induced errors in charge transfer are independent of
t for
1/f noise. For realistic parameters taken from experiments on silicon-based quantum dots, we obtain the minimal probability of charge transfer failure between a pair of dots is limited by
1/f noise in detuning to be the on the order of 0.01. This means that in order to reliably transfer charges across many quantum dots, charge noise in the devices should be further suppressed, or tunnel couplings should be increased, in order to allow for faster transfer (and less exposure to noise), while not triggering the deterministic Landau-Zener excitation.
In semiconductor spin qubits which typically interact through short-range exchange coupling, shuttling of spin is a practical way to generate quantum operations between distant qubits. Although the exchange is often tunable through voltages applied to gate electrodes, its minimal value can be significantly large, which hinders the applicability of existing shuttling protocols to such devices, requiring a different approach. In this work, we extend our previous results for double- and triple-dot systems, and describe a method for implementing spin state transfer in long chains of singly occupied quantum dots in a non-adiabatic manner. We make use of Cartan decomposition to break down the interacting problem into simpler problems in a systematic way, and use dynamical invariants to design smooth non-adiabatic pulses that can be implemented in devices with modest control bandwidth. Finally, we discuss the extensibility of our results to directed shuttling of spin states on two-dimensional lattices of quantum dots with fixed coupling. This article is part of the theme issue 'Shortcuts to adiabaticity: theoretical, experimental and interdisciplinary perspectives'.