A scheduled talk at the ACMD Seminar on “Advances in Number-Theoretic Methods for Characterizing and Optimizing Fault-Tolerant Quantum Circuits” by Andrew Glaudell from Booz Allen Hamilton was cancelled. The talk aimed to present two key findings:
1. Establishing that unitaries over specific rings (ℤ[1/2], ℤ[1/√2], ℤ[1/√-2], and ℤ[1/2,i]) are in exact correspondence to universal gate sets, demonstrating a deeper understanding of Clifford+T circuits and their applications in quantum compiling.
2. Developing an efficient exact synthesis algorithm for two-qubit circuits over ℤ[1/2,i], corresponding to the Clifford+CS gate set, using the Spin(6) ~ SU(4) isomorphism to show optimality in CS-count.
Andrew Glaudell, a Booz Allen Hamilton Quantum Information fellow, earned his Ph.D. from the University of Maryland-College Park in December 2019, focusing on number-theoretic methods for characterizing and optimizing quantum circuits for fault-tolerant gate sets in the Clifford hierarchy for both qubits and qudits.
Keywords: Quantum, Circuits, Synthesis, Algorithms, Fault-tolerant
