Universal Control Induced by Noise

TL;DR

This paper demonstrates how strong noise and decoherence-free subspaces can enable universal quantum control and computation, transforming simple Hamiltonians into more complex, controllable operations.

Contribution

It generalizes the quantum Zeno effect to identify decoherence-free subspaces as a means to achieve full controllability under dissipation.

Findings

Full controllability within DFS's for certain quantum systems.

Transformation of Ising to Heisenberg Hamiltonian under strong decoherence.

Numerical analysis of process fidelity scaling with noise strength.

Abstract

On the basis of the quantum Zeno effect it has been recently shown [D. K. Burgarth et al., Nat. Commun. 5, 5173 (2014)] that a strong amplitude damping process applied locally on a part of a quantum system can have a beneficial effect on the dynamics of the remaining part of the system. Quantum operations that cannot be implemented without the dissipation become achievable by the action of the strong dissipative process. Here we generalize this idea by identifying decoherence-free subspaces (DFS's) as the subspaces in which the dynamics becomes more complex. Applying methods from quantum control theory we characterize the set of reachable operations within the DFS's. We provide three examples which become fully controllable within the DFS's while the control over the original Hilbert space in the absence of dissipation is trivial. In particular, we show that the (classical) Ising Hamiltonian is turned into a Heisenberg Hamiltonian by strong collective decoherence, which provides universal quantum computation within the DFS's. Moreover we perform numerical gate optimization to study how the process fidelity scales with the noise strength. As a byproduct a subsystem fidelity which can be applied in other optimization problems for open quantum systems is developed.