  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.
