Reduction of circuit depth by mapping qubitbased quantum gates to a qudit basis
Abstract
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 multiplycontrolledZ 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 quditbasis to Grover's Algorithm and compare the circuit depth vs. system size to a qubitbased circuit. The results show that there is a dramatic reduction in circuit depth as the size of the system increases for the qudit circuit compared to qubit circuit. In particular, multiply controlled gates are the driving factor in the reduction of circuit complexity for quditbased system scales with D.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.09902
 Bibcode:
 2021arXiv210909902R
 Keywords:

 Quantum Physics
 EPrint:
 9 pages, 3 figures, 6 tables