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We show that it is theoretically possible to use higher energy levels forstoring and controlling two qubits within a superconducting transmon. This isdone by identifying energy levels as product states between multiple effecitvequbits. As a proof of concept we realise a complete set of gates necessary foruniversal computing by numerically optimising control pulses for single qubitgates on each of the qubits, entangling gates between the two qubits in onetransmon, and an entangling gate between two qubits from two coupled transmons.The optimisation considers parameters which could make it possible to validatethis experimentally. With these control pulses it is in principle possible todouble the number of available qubits without any overhead in hardware. Theadditional qubits could be used in algorithms which need many short-livingqubits such as syndrom qubits in error correction or by embedding effecitvehigher connectivity in qubit networks.

Two qubits in one transmon -- QEC without ancilla hardware