Southwest Quantum Information and Technology

Optimizing n-to-1 stabilizer circuits for producing non-stabilizer qubits

Presenting Author: Raymond Wong, Department of Computer Science, University of California, Santa Barbara
Contributing Author(s): Wim van Dam

We look at the problem of optimally producing non-stabilizer states using resource qubits and stabilizer operations only. In particular, we look at n-to-1 stabilizer circuits on n qubits that use n-1 measurements to produce a single qubit and we investigate when and how we can rearrange such circuits to produce the same output with higher efficiency. We find that the efficiency can be improved if the circuit can be rewritten as a binary tree where each node represents a two qubit stabilizer subcircuit with one measurement, and the leaf nodes are the initial resource states. As a consequence of this tree form, circuits with a binary tree structure lead to a natural conversion protocol with a lower expected resource cost than their non-binary tree counterparts. Furthermore we also present an algorithm for finding a circuit in binary tree form given the original circuit, and show conditions for its existence. We apply our results to the construction of certain non-stabilizer states from [Phys. Rev. A 88, 042325 (2013)] to demonstrate where improvements are possible.

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