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Coherent transfer of singlet-triplet qubit states in a scalable architecture of linear quantum dots

Chang Jian Kwong, Teck Seng Koh, L. C. Kwek

Published Feb 27, 2016• 0 citations
OpenAlex

Abstract

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.

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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.
We propose two schemes to coherently transfer arbitrary quantum states of the two-electron singlet-triplet qubit across a chain of three quantum dots. The schemes are based on electrical control over the detuning energy of the quantum dots. The first is a pulse-gated scheme, requiring dc pulses and engineering of inter- and intradot Coulomb energies. The second scheme is based on the adiabatic theorem, requiring time-dependent control of the detuning energy through avoided crossings at a rate that the system remains in the ground state. We simulate the transfer fidelity using typical experimental parameters for silicon quantum dots. Our results give state transfer fidelities between 94.394.3%<\mathcal{F}<99.5%94.3 at sub-ns gate times for the pulse-gated scheme and between 75.475.4%<\mathcal{F}<99.0%75.4 at tens of ns for the adiabatic scheme. Taking into account dephasing from charge noise, we obtain state transfer fidelities between 94.094.0%<\mathcal{F}<99.2%94.0 for the pulse-gated scheme and between 64.964.9%<\mathcal{F}<93.6%64.9 for the adiabatic scheme.
Several logical qubits and quantum gates have been proposed for semiconductor quantum dots controlled by voltages applied to top gates. The different schemes can be difficult to compare meaningfully. Here we develop a theoretical framework to evaluate disparate qubit-gating schemes on an equal footing. We apply the procedure to two types of double-dot qubits: the singlet-triplet and the semiconducting quantum dot hybrid qubit. We investigate three quantum gates that flip the qubit state: a DC pulsed gate, an AC gate based on logical qubit resonance, and a gate-like process known as stimulated Raman adiabatic passage. These gates are all mediated by an exchange interaction that is controlled experimentally using the interdot tunnel coupling g and the detuning [Symbol: see text], which sets the energy difference between the dots. Our procedure has two steps. First, we optimize the gate fidelity (f) for fixed g as a function of the other control parameters; this yields an f(opt)(g) that is universal for different types of gates. Next, we identify physical constraints on the control parameters; this yields an upper bound f(max) that is specific to the qubit-gate combination. We show that similar gate fidelities (~99:5%) should be attainable for singlet-triplet qubits in isotopically purified Si, and for hybrid qubits in natural Si. Considerably lower fidelities are obtained for GaAs devices, due to the fluctuating magnetic fields ΔB produced by nuclear spins.
Abstract Long-distance fast and precise transfer of charge in semiconductor nanostructures is one of the goals for scalable electronic devices. We study theoretically the control of shuttling of an electron along a linear chain of semiconductor electrostatically defined quantum dots by an electric field pulse with nonlinear time-dependent profile. We show that this essential nonlinearity along with shortcuts to adiabaticity techniques speed up the electron transfer with high fidelity, while still holding great robustness under spin-flip interactions and inhomogeneities in the couplings of the chain. A given fidelity can be set experimentally by controlling the maximum sweep energy and duration of the control pulse.
In double quantum dot singlet–triplet qubits, the exchange interaction is used in both quantum gate operation and the measurement of the state of the qubit. The exchange can be controlled electronically by applying gate voltage pulses. We simulate the exchange induced charge state transitions in one and two singlet–triplet qubit systems using the exact diagonalization method. We find that fast detuning pulses may result in leakage between different singlet charge states. The leakage could cause measurement errors and hinder quantum gate operation for example in the case of the two-qubit Coulomb gate.
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 analyze the optically driven dynamics of a qubit implemented on a singlet-triplet subspace of two-electron states in a self-assembled quantum dot molecule. We study two possible control schemes based on the coupling to an excited (four-particle) state either by two spectrally separated laser pulses or by a single spectrally broad pulse. We quantitatively characterize the imperfections of the qubit operation resulting from nonadiabatic evolution and from limited spectral selectivity in a real system, as compared to the ideal adiabatic Raman transfer of occupation in the $\mathrm{\ensuremath{\Lambda}}$ system. Next, we study the effects of decoherence induced by the coupling to the phonons of the surrounding crystal lattice and by radiative recombination. As a result, we are able to identify the optimization trade-offs between different sources of errors and indicate the most favorable conditions for quantum control of the singlet-triplet qubit in the two optical control schemes.