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We report on an optimal single-electron charge qubit for a solid-state doublequantum dot (DQD) system and analyse its dynamics under a time-dependent lineardetuning, using GPU accelerated numerical solutions to the time-dependentSchr\"odinger equation. The optimal qubit is found to have basis states definedas the symmetric and antisymmetric linear combinations of the lowest energybonding and anti-bonding states of the DQD at zero bias. In contrast to chargequbits defined by the two localised ground states of the uncoupled DQD, thischoice of the basis causes the resulting dynamics to have a maximal overlapwith an idealised two-state model. Our optimal qubit basis states are notlocalised to a single quantum dot and, as such, initialising the qubit requiresa particular sequence of gate pulses to take the system from an initialfiducial state of the DQD to the logical $0$ or $1$. We determine this sequenceusing pulses that incorporate the expected experimental finite rise times. Wealso show how to perform arbitrary single qubit operations on the Bloch sphereusing spin-echo type pulsing, allowing us to obtain any qubit state with atmost two single pulses. Measurement of the optimal qubits is achieved bydetermining the probability of finding the electron in one of the dots.

An optimal single-electron charge qubit for solid-state double quantum dots