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arXiv:1602.08596 · Physical review. B./Physical review. B

Coherent transfer of singlet-triplet qubit states in an architecture of triple quantum dots

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

Published Jun 29, 2018• 7 citations
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Abstract

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 $94.3%<\mathcal{F}<99.5%$ at sub-ns gate times for the pulse-gated scheme and between $75.4%<\mathcal{F}<99.0%$ at tens of ns for the adiabatic scheme. Taking into account dephasing from charge noise, we obtain state transfer fidelities between $94.0%<\mathcal{F}<99.2%$ for the pulse-gated scheme and between $64.9%<\mathcal{F}<93.6%$ for the adiabatic scheme.

DOI
10.1103/physrevb.97.245428

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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.
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.
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.
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.
Semiconductor quantum-dot spin qubits are a promising platform for quantum computation, because they are scalable and possess long coherence times. In order to realize this full potential, however, high-fidelity information transfer mechanisms are required for quantum error correction and efficient algorithms. Here, we present evidence of adiabatic quantum-state transfer in a chain of semiconductor quantum-dot electron spins. By adiabatically modifying exchange couplings, we transfer single- and two-spin states between distant electrons in less than 127 ns. We also show that this method can be cascaded for spin-state transfer in long spin chains. Based on simulations, we estimate that the probability to correctly transfer single-spin eigenstates and two-spin singlet states can exceed 0.95 for the experimental parameters studied here. In the future, state and process tomography will be required to verify the transfer of arbitrary single qubit states with a fidelity exceeding the classical bound. Adiabatic quantum-state transfer is robust to noise and pulse-timing errors. This method will be useful for initialization, state distribution, and readout in large spin-qubit arrays for gate-based quantum computing. It also opens up the possibility of universal adiabatic quantum computing in semiconductor quantum-dot spin qubits.
We analyze a simple exchange-based two-qubit gate for singlet-triplet qubits in gate-defined semiconductor quantum dots that can be implemented in a single exchange pulse. Excitations from the logical subspace are suppressed by a magnetic field gradient that causes spin-flip transitions to be non-energy-conserving. We show that the use of adiabatic pulses greatly reduces leakage processes comapred to square pulses. We also characterize the effect of charge noise on the entanglement fidelity of the gate both analytically and in simulations; demonstrating high entanglement fidelities for physically realistic experimental parameters. Specifically we find that it is possible to achieve fidelities and gate times that are comparable to single-qubit states using realistic magnetic field gradients.
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.