# Quantum gates by resonantly driving many-body eigenstates, with a focus on Polychronakos' model

## TL;DR

This paper proposes a protocol for implementing multi-qubit gates in strongly-coupled many-body quantum systems using resonant driving, with applications demonstrated on Polychronakos' spin chain model, highlighting efficient control and error scaling.

## Contribution

It introduces a resonant driving protocol for selective multi-qubit gates in many-body systems, utilizing an eigengate basis transformation, with numerical validation on Polychronakos' model.

## Key findings

- Error scales as t^{-2} with gate time
- Protocol is efficient for small to moderate qubit numbers
- Eigenstate exchange is achieved through resonant driving

## Abstract

Accurate, nontrivial quantum operations on many qubits are experimentally challenging. As opposed to the standard approach of compiling larger unitaries into sequences of 2-qubit gates, we propose a protocol on Hamiltonian control fields which implements highly selective multi-qubit gates in a strongly-coupled many-body quantum system. We exploit the selectiveness of resonant driving to exchange only 2 out of $2^N$ eigenstates of some background Hamiltonian, and discuss a basis transformation, the eigengate, that makes this operation relevant to the computational basis. The latter has a second use as a Hahn echo which undoes the dynamical phases due to the background Hamiltonian. We find that the error of such protocols scales favourably with the gate time as $t^{-2}$, but the protocol becomes inefficient with a growing number of qubits N. The framework is numerically tested in the context of a spin chain model first described by Polychronakos, for which we show that an earlier solution method naturally gives rise to an eigengate. Our techniques could be of independent interest for the theory of driven many-body systems.

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Source: https://tomesphere.com/paper/1901.06144