Southwest Quantum Information and Technology

Measurement-Based Quantum Computing as a Tangram Puzzle using Stabilizer formalism

Presenting Author: Ashlesha Patil, University of Arizona

Stabilizer formalism is an important tool to simulate Clifford operations & Pauli measurements. We have extended the stabilizer formalism by (1) incorporating multi-qubit stabilizer measurements (e.g. BSM), (2) providing an explicit procedure using Karnaugh maps from Boolean algebra for converting any stabilizer gate into stabilizer tableau operations (3) designing a new canonicalization algorithm for stabilizer tableaus that first minimizes the number of stabilizer generators with X or Y operators & then those with only Z operators. We use the extended stabilizer formalism to design a Tangram-like game to teach Measurement-Based Quantum Computing (MBQC). The player is given a quantum circuit which they have to map to MBQC using polyominos. Polyominos, consist of square tiles joined edge-to-edge to form different shapes. Each tile denotes one of the three Pauli measurements, differentiated by its color. Polyominos rest on a square-grid playing board, signifying a cluster state. Mapping a quantum circuit to MBQC is equivalent to arranging a set of polyominos, each corresponding to a quantum gate, on the playing board, subject to certain rules. We use the stabilizer formalism & the canonicalization algorithm to evaluate a solution. Higher-scoring correct solution fills up less space on the board, resulting in a lower-overhead embedding of the circuit in MBQC, a challenging research problem.

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