Southwest Quantum Information and Technology

Quantum circuits synthesis using lattices over number fields

Presenting Author: Vadym Kliuchnikov, Microsoft Research
Contributing Author(s): Sebastian Schoennenbeck

We present new algorithms for multiple qubit exact synthesis and exact state preparation. The algorithms work for the unitaries related to Clifford+T, Real Clifford+Controlled-H, and other similar gate sets. The algorithms run-time is polynomial in the bit-size of the input when the number of qubits is fixed. We prove the correctness of the algorithms for two qubits. For three and more qubits our algorithms either solve the problem in polynomial time or report that the solution was not found. We conjecture that the second outcome never happens based on empirical results. Experiments show that our algorithms produce circuits with a smaller number of T-gates than the algorithms for state preparation and exact synthesis by Giles and Selinger [10.1103/PhysRevA.87.032332].

(Session 5 : Thursday from 5:00pm - 7:00pm)