Reduction of circuit depth by mapping qubit-based quantum gates to a qudit basis

Understand

We present a scalable set of universal gates and multiply controlled gates in a qudit basis through a bijective mapping from N qubits to qudits with D = 2^N levels via rotations in U(2).

• For each of the universal gates (H, CNOT, and T), as well as the NOT gate and multiply-controlled-Z gates, we describe a systematic approach to identifying the set of U(2) rotations required to implement each gate for any qudit of size N and with minimal use of an ancilla level.
• The qudit gates are analyzed in terms of the total rotation count and gate depth as the system scales with D.
• We apply the qudit-basis to Grover's Algorithm and compare the circuit depth vs.