2021/09/21 by Pamela B. Rambow, Rambow, Pamela, Mingzhen Tian +1 · 1 citation
Computer Science · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum-Dot Cellular Automata
paper · pdf · doi:10.48550/arxiv.2109.09902
openalex publication_date 2021/09/21 · openalex created_date 2021/09/27 · openalex updated_date 2026/07/28
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 = 2N 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. system size to a qubit-based 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 qudit-based system scales with D.