Significant Depth Reduction of Qudit Quantum Circuits via Dynamic Circuits

Dynamic circuits, i.e. quantum circuits with mid-circuit measurements and feed forward conditional operations, prove to be an extremely important concept from fault-tolerant quantum computation to quantum compilation and depth reduction. There exists many cases such that a quantum circuit with Poly(n) depth can be performed with a dynamic circuit with O(1) constant depth, which spans applications such as generating matrix product states, long range qubit entanglement and certain qubit logical and Clifford operations. Here, we present a universal method to obtain such circuits for any d-dimensional qudit circuits. Our results indicated that 1) any qudit Clifford circuit can be performed in constant depth with an ancilla count depending on the structure of the entangling gates, 2) T-depth of any fault-tolerant qudit circuit can be reduced by a factor of 2 with the usage of at most 2n ancillas, and 3) any generic fan-out circuit can be implemented within O(1) depth. This paves the way for more efficient implementation of qudit quantum circuits across the Clifford hierarchy by utilizing mid-circuit measurement.