Characterizing gate operations near the sweet spot of an exchange-only qubit

Abstract

Optimal working points or "sweet spots" have arisen as an important tool for mitigating charge noise in quantum dot logical spin qubits. The exchange-only qubit provides an ideal system for studying this effect because Z rotations are performed directly at the sweet spot, while X rotations are not. Here for the first time we quantify the ability of the sweet spot to mitigate charge noise by treating X and Z rotations on an equal footing. Specifically, we optimize X rotations and determine an upper bound on their fidelity. We find that sweet spots offer a fidelity improvement factor of at least 20 for typical GaAs devices, and more for Si devices.

Charge-noise-insensitive gate operations for always-on, exchange-only qubits

“…We calculated the energy spectrum and the sweet spot for t l =t r (solid curves) corresponding to a rotation aroundẑ axis, and t l =( √ 6 + √ 2)t r /2 (dashed curves) corresponding to a rotation aroundn=−(x +ẑ)/ √ 2 axis which, in combination with the Pauli Z gate, can be used to implement Pauli X gate [22,28], X=Rn(π)ZRn(π) where Rn(π) is a π rotation aroundn and Z is Pauli Z gate which is a π rotation aroundẑ axis. Figure 2(a) shows the energy spectrum as a function of ε with fixed ε M =0.05U .…”

“…Unfortunately, a full sweet spot for an RX qubit (where the first derivative with respect to both detuning parameters goes to zero) is outside of the (111) singly occupied regime; there, higher order effects limit the coherence of the qubit [23]. A full sweet spot for a 3-spin qubit was found for a symmetric triple quantum dot (TQD) [22], but in that case one needs to move away from this sweet spot to perform a full set of single-qubit gate operations.In this work, we show that there exists a full sweet spot for an exchange-only qubit and we can implement full single-and two-qubit gate operations on this sweet spot with only DC voltage pulses to control the tunneling elements. We will call this qubit the "Always-on, Exchange-ONly qubit" (AEON), since both exchange interactions in an AEON qubit are kept on for logical gate operations while remaining on the sweet spot.…”

“…Unfortunately, a full sweet spot for an RX qubit (where the first derivative with respect to both detuning parameters goes to zero) is outside of the (111) singly occupied regime; there, higher order effects limit the coherence of the qubit [23]. A full sweet spot for a 3-spin qubit was found for a symmetric triple quantum dot (TQD) [22], but in that case one needs to move away from this sweet spot to perform a full set of single-qubit gate operations.…”

“…Sweet spots have been an effective tool to increase the coherence of superconducting qubits [18,19] and more recently have been applied to exchange-only qubits [20][21][22][23][24]. For example, in the "resonant exchange" (RX) qubit-an encoded qubit made out of 3 quantum dot qubits with "always-on" exchange interactions and a much higher chemical potential for the middle dot than the outer dots-a partial sweet spot is maintained while microwave control allows for single qubit operations [20,21] "resonant" with the gap of the 3-spin system.…”

High-fidelity two-qubit gates via dynamical decoupling of local1/fnoise at the optimal point

“…This concept has been generalized to more complex architectures and proved to be efficient in reducing defocussing due to 1/f noise also in two-qubit gates 9,10 . Optimal tuning is a passive (or error avoiding) stabilization strategy which, in combination with improved materials and environment engineering, has led to high-fidelity superconducting 6 and semiconducting quantum dot charge-11 and spin-qubits [12][13][14][15][16] . Dynamical decoupling (DD) is an active (or error correcting) scheme, based on the repeated application of control pulses designed to coherently average out unwanted interactions with the environment 17,18 .…”