Resetting Uncontrolled Quantum Systems

• Published in: Physical review. X Vol. 8; no. 3; p. 031008
• Main Author: Navascués, Miguel
• Format: Journal Article
• Language: English
• Published: College Park American Physical Society 01.07.2018
• Subjects: Evolution; Hilbert space; Protocol; Quantum theory; Qubits (quantum computing); Relativity
• ISSN: 2160-3308; 2160-3308
• DOI: 10.1103/PhysRevX.8.031008

We consider a scenario where we wish to bring a closed system of known Hilbert space dimensiondS(the target), subject to an unknown Hamiltonian evolution, back to its quantum state at a past timet0. 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 nonrelativistic quantum physics that reset the target system to its exact quantum state att0. Each “resetting protocol” is successful with nonzero 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.