Figure 1
Exchange-coupled quantum-dot hybrid qubits. (a) Schematic of the two-qubit system, comprising four dots in a linear array; the left () and right () double dots define the left and right qubits. The full system contains six electrons, with three electrons per qubit. For each qubit, we assume the two lowest-energy states have the same (1,2) charge occupation, but different spin configurations. We also assume that each double dot has one low-energy charge excitation, corresponding to a (2,1) leakage state. The tunnel couplings between these different charge configurations are designated and , where , and refer to the single-electron ground and excited energy levels. The qubit detuning parameters are designated . We also assume a tunable tunnel coupling between the second and third dots, which mediates an exchange interaction via the four-dot charge configuration (1,1,2,2). The corresponding tunnel couplings are designated and , and the detuning parameter between the second and third dots is . (b) Tunnel coupling control pulse for a cz gate: The tunnel coupling is ramped linearly from zero to its peak value, ( or ), held constant for a waiting period, then ramped back down to zero. (c) Typical energy levels for the four logical states (blue) and 24 leakage states (red) considered here. Many of the leakage levels are degenerate or nearly degenerate, with degeneracy factors indicated on the right. The most dangerous leakage states occur in the low-energy manifold, and have the same (1,2,1,2) charge configuration as the logical states. However, not all these states couple to the logical states via second-order tunneling processes, as discussed in Appendix pp1-s3; the number of tunnel-coupled leakage states are indicated in parentheses. The system parameters used for this calculation are , as consistent with recent experiments [10, 36]; we also take . Note that we choose to suppress single-qubit dephasing in the far-detuned regime [27, 35, 37].
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