Universal Quantum Computation and Leakage Reduction in the 3-Qubit Decoherence Free Subsystem

TL;DR

This paper presents new exchange-only pulse sequences for universal quantum computation and leakage reduction in the 3-qubit decoherence free subsystem, with exact solutions and optimized pulse counts.

Contribution

It introduces the first explicit leakage reduction sequence for the 3-qubit DFS and provides optimized, exact pulse sequences for CNOT and leakage reduction operations.

Findings

DFS CNOT sequence requires 22 pulses in 13 steps

Leakage reduction sequence requires 30 pulses in 20 steps

Solutions are exact with closed-form expressions

Abstract

We describe exchange-only universal quantum computation and leakage reduction in the 3-qubit decoherence free subsystem (DFS). We discuss the angular momentum structure of the DFS, the proper forms for the DFS CNOT and leakage reduction operators in the total angular momentum basis, and new exchange-only pulse sequences for the CNOT and leakage reduction operators. Our new DFS CNOT sequence requires 22 pulses in 13 time steps. The DFS leakage reduction sequence, the first explicit leakage reduction sequence of its kind, requires 30 pulses in 20 time steps. Although the search for sequences was performed numerically using a genetic algorithm, the solutions presented here are exact, with closed-form expressions.