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arXiv:1806.07597 · Journal of Physics Communications

Gate fidelity comparison in semiconducting spin qubit implementations affected by control noises

Elena Ferraro, Marco Fanciulli, Marco De Michielis

Published Nov 13, 2018• 10 citations
arXivHTMLPDF

Abstract

A comparison of gate fidelities between different spin qubit types defined in quantum dots and a donor under different control errors is reported. We studied five qubit types, namely the quantum dot spin qubit, the double quantum dot singlet-triplet qubit, the double quantum dot hybrid qubit, the donor qubit and the quantum dot spin-donor qubit. For each one, we derived analytical time sequences that realize single qubit rotations along the principal axis of the Bloch sphere. We estimated the effects of control errors on the gate fidelity by using a Gaussian noise model. Then we compared the gate fidelities among qubit implementations due to pulse timing errors by using a realistic set of values for the error parameters of control amplitudes.

DOI
10.1088/2399-6528/aaf088

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A comparison of gate fidelities between different spin qubit types defined in quantum dots and a donor under different control errors is reported. We studied five qubit types, namely the quantum dot spin qubit, the double quantum dot singlet-triplet qubit, the double quantum dot hybrid qubit, the donor qubit and the quantum dot spin-donor qubit. For each one, we derived analytical time sequences that realize single qubit rotations along the principal axis of the Bloch sphere. We estimated the effects of control errors on the gate fidelity by using a Gaussian noise model. Then we compared the gate fidelities among qubit implementations due to pulse timing errors by using a realistic set of values for the error parameters of control amplitudes.
Spin qubits are very valuable and scalable candidates in the area of quantum computation and simulation applications. In the last decades, they have been deeply investigated from a theoretical point of view and realized on the scale of few devices in the laboratories. In semiconductors, spin qubits can be built confining the spin of electrons in electrostatically defined quantum dots. Through this approach, it is possible to create different implementations: single electron spin qubit, singlet–triplet spin qubit, or a three-electron architecture, e.g., the hybrid qubit. For each qubit type, we study the single qubit rotations along the principal axis of Bloch sphere including the mandatory non-idealities of the control signals that realize the gate operations. The realistic transient of the control signal pulses are obtained by adopting an appropriate low-pass filter function. In addition. the effect of disturbances on the input signals is taken into account by using a Gaussian noise model.
Several spin qubit architectures have been proposed, theoretically investigated and realized at least on the scale of single devices in view of quantum computation and simulation applications. We focus our study on five qubit types: quantum dot spin qubit, double quantum dot singlet-triplet qubit, double quantum dot hybrid qubit, donor qubit, quantum dot spin-donor qubit and for each one we derived a compact effective Hamiltonian. Single qubit gate fidelities when time interval error is included are compared. A realistic set of values for the error parameters of amplitude controls linked to the z and x contribution appearing in the Hamiltonian models has been used. This study provides a ranking of the gate fidelities for the different qubit architectures highlighting which one is the most robust with respect to the considered control noises.
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.
One of the main challenges in building a quantum processor is to characterize the environmental noise. Noise characterization can be achieved by exploiting different techniques, such as randomization where several sequences of random quantum gates are applied to the qubit under test to derive statistical characteristics about the affecting noises. A scalable and robust algorithm able to benchmark the full set of Clifford gates using randomization techniques is called randomized benchmarking. In this study, we simulated randomized benchmarking protocols in a semiconducting all-electrical three-electron double-quantum dot qubit, i.e. hybrid qubit, under different error models, that include quasi-static Gaussian and the more realistic 1/f noise model, for the input controls. The average error of specific quantum computational gates is extracted through interleaved randomized benchmarking obtained including Clifford gates between the gate of interest. It provides an estimate of the fidelity as well as theoretical bounds for the average error of the gate under test.
Implementing high-fidelity two-qubit gates in single-electron spin qubits in silicon double quantum dots is still a major challenge. In this work we employ analytical methods to design control pulses that generate high-fidelity entangling gates for quantum computers based on this platform. Using realistic parameters and initially assuming a noise-free environment, we present simple control pulses that generate cnot, cphase, and cz gates with average fidelities greater than 99.99% and gate times as short as 45 ns. Moreover, using the local invariants of the system's evolution operator, we show that a simple square pulse generates a cnot gate in less than 27 ns and with a fidelity greater than 99.99%. Last, we use the same analytical methods to generate two-qubit gates locally equivalent to CNOT\sqrt{\mathrm{CNOT}}CNOT​ and CZ\sqrt{\mathrm{CZ}}CZ​ that are used to implement simple two-piece pulse sequences that produce high-fidelity cnot and cz gates in the presence of low-frequency noise.
Charge noise has been one of the main issues in realizing high fidelity two-qubit quantum gates in semiconductor based qubits. Here, we study the influence of quasistatic noise in quantum dot detuning on the controlled phase gate for spin qubits that defined on a double quantum dot. Analytical expressions for the noise averaged Hamiltonian, exchange interaction, as well as the gate fidelity are derived for weak noise covering experimental relevant regime. We also perform interleaved two-qubit randomized benchmarking analysis for the controlled phase gate and show that an exponential decay of the sequential fidelity is still valid for the weak noise.