Resetting uncontrolled quantum systems

TL;DR

This paper demonstrates that it is theoretically possible to reset an unknown quantum system to its past state with protocols that succeed with non-zero probability, even under unknown Hamiltonian dynamics, and discusses practical implementations for qubits.

Contribution

It introduces protocols within quantum physics that can reset an unknown system to a previous state with non-zero probability, regardless of the system's Hamiltonian or interactions, and proposes methods to enhance success rates.

Findings

Existence of protocols that reset unknown quantum systems with non-zero probability

Successful implementation for qubits with current quantum technology

Chaining protocols can significantly increase overall success probability

Abstract

We consider a scenario where we wish to bring a closed system of known Hilbert space dimension $d_S$ (the target), subject to an unknown Hamiltonian evolution, back to its quantum state at a past time $t_0$. The target is out of our control: this means that we ignore both its free Hamiltonian and how the system interacts with other quantum systems we may use to influence it. Under these conditions, we prove that there exist protocols within the framework of non-relativistic quantum physics which reset the target system to its exact quantum state at $t_0$. Each "resetting protocol" is successful with non-zero probability for all possible free Hamiltonians and interaction unitaries, save a subset of zero measure. When the target is a qubit and the interaction is sampled from the Haar measure, the simplest resetting circuits have a significant average probability of success and their implementation is within reach of current quantum technologies. Finally, we find that, in case the resetting protocol fails, it is possible to run a further protocol that, if successful, undoes both the natural evolution of the target and the effects of the failed protocol over the latter. By chaining in this fashion several such protocols, one can substantially increase the overall probability of a successful resetting.