Multi-qubit compensation sequences

TL;DR

This paper explores the use of composite pulse techniques to correct systematic errors in multi-qubit quantum systems, enhancing control precision for quantum computing applications.

Contribution

It extends single-qubit composite pulse methods to multi-qubit systems, demonstrating how to achieve arbitrary error correction with specific control Hamiltonians.

Findings

Composite pulses can correct systematic errors in multi-qubit systems.

Error correction is effective with two non-commuting control Hamiltonians or an error-free Hamiltonian.

For XY interactions, single-qubit composite pulses improve accuracy; for Heisenberg interactions, they reduce single-qubit errors but may increase two-qubit errors.

Abstract

The Hamiltonian control of n qubits requires precision control of both the strength and timing of interactions. Compensation pulses relax the precision requirements by reducing unknown but systematic errors. Using composite pulse techniques designed for single qubits, we show that systematic errors for n qubit systems can be corrected to arbitrary accuracy given either two non-commuting control Hamiltonians with identical systematic errors or one error-free control Hamiltonian. We also examine composite pulses in the context of quantum computers controlled by two-qubit interactions. For quantum computers based on the XY interaction, single-qubit composite pulse sequences naturally correct systematic errors. For quantum computers based on the Heisenberg or exchange interaction, the composite pulse sequences reduce the logical single-qubit gate errors but increase the errors for logical two-qubit gates.