Figure 2: The multi-output duality quantum computing circuit in a quantum computer.
From: Duality quantum algorithm efficiently simulates open quantum systems
|Ψ〉 denotes the initial state of work qubit, and |0〉 is the initial state of the controlling auxiliary qudit. The circles represent the state of the controlling qudit and the squares represent unitary operations. Unitary operations U0, U1 
, Ud−1 are activated only when the qudit holds the respective values indicated in circles18. The “readout” part marked by yellow rectangle means that: When the auxiliary qudit in the |j〉 state, where j ∈ {0, 1 
, d}, the corresponding output (final state) of the work qubit will be redout by corresponding detector.
