Many-body strategies for multi-qubit gates - quantum control through Krawtchouk chain dynamics

TL;DR

This paper introduces a quantum control strategy for multi-qubit gates using Krawtchouk chain dynamics, involving state mapping, resonant driving, and reverse mapping, demonstrated for specific couplings and qubit numbers.

Contribution

It presents a novel multi-qubit gate engineering method based on eigengates and resonant driving tailored for Krawtchouk chains, expanding quantum control techniques.

Findings

Successfully implements iSWAP_N gate for N=4 and 6 qubits.

Demonstrates the effectiveness of the strategy through numerical simulations.

Provides a scalable approach for multi-qubit gate design in quantum systems.

Abstract

We propose a strategy for engineering multi-qubit quantum gates. As a first step, it employs an eigengate to map states in the computational basis to eigenstates of a suitable many-body Hamiltonian. The second step employs resonant driving to enforce a transition between a single pair of eigenstates, leaving all others unchanged. The procedure is completed by mapping back to the computational basis. We demonstrate the strategy for the case of a linear array with an even number N of qubits, with specific XX+YY couplings between nearest neighbors. For this so-called Krawtchouk chain, a 2-body driving term leads to the iSWAP$_N$ gate, which we numerically test for N = 4 and 6.