Indirect Adaptive Control of Quantum Systems

Robert L. Kosut, HERSCHEL A. RABITZ

In this paper we promote the use of adaptive control for deducing the external control fields required to make a quantum computer behave as desired in an uncertain environment. Adaptive systems can be classified as indirect or direct. In an indirect adaptive control system, data is used to first. determine parameters in a system model. Then the model is used to determine the control parameters in order to achieve a desired goal.

Arijit Das, Masaki Owari

The indirect-control paradigm offers a scalable approach to quantum computation by restricting external operations to a small subset of qubits, whereas the entire system evolves under its intrinsic many-body Hamiltonian. This framework reduces hardware complexity and limits the noise introduced through control channels. Recently, Anan et al. proposed an implementation of the variational quantum eigensolver (VQE) within this indirect-control architecture. However, the impact and integration of quantum error mitigation techniques in such a setting remain largely unexplored. In particular, zero-noise extrapolation (ZNE), a widely used error mitigation strategy, has not yet been systematically adapted to indirect-control VQE. A key requirement of ZNE is the controlled amplification of noise, which is commonly achieved through circuit-level techniques such as unitary folding. In the indirect-control framework, however, quantum operations are largely governed by continuous time-evolution under the system Hamiltonian, making the construction of physically realizable inverse operations non-trivial. In this study, we investigate the feasibility of implementing ZNE within the indirect-controlVQEframework.We address the challenges associated with unitary folding in the presence of time-evolution operators and, with a minimal relaxation of the indirect-control constraint, we propose a ZNE-based error-mitigation strategy that exploits the symmetry of the one-dimensional XY spin chain.

M. R. James

J. W. Clark, Dennis G. Lucarelli, Tzyh‐Jong Tarn

Domenico D’Alessandro, Raffaele Romano

In many experiments, a target quantum mechanical system is controlled and-or measured indirectly using an auxiliary quantum system. In the case of control, this means that the control action only affects the auxiliary system while the evolution of the target system is affected indirectly through the interaction with the auxiliary system. In the case of measurement, only the state of the auxiliary system can be measured, providing information on the initial state of the target system. Indirect controllability is the property of the target system of being driven between two arbitrary states while indirect observability refers to the possibility of extracting all the information on the state of the target system by measuring the auxiliary system. This paper has three main goals. First, we summarize recent notions and results introduced by us on the study of indirect controllability. Then, we present some new technical results on indirect controllability. In particular, we present a counterexample to the converse of a criterion for indirect controllability, which shows that the Lie algebraic condition introduced in this criterion is necessary but not sufficient for indirect controllability. This gives an open problem which is how to strengthen this condition to obtain a necessary and sufficient condition for indirect controllability. Lastly, we present a parallel treatment of indirect observability, give the relevant notions and definitions and relate the properties of indirect controllability and observability. Our final result says that strong notions of indirect controllability and observability are equivalent properties to complete controllability of the system. We discuss examples of physical systems which are controlled and-or measured indirectly. The research is motivated by experimental schemes of current interest

P. Zoller, J. I. Cirac, S. M. Girvin +1 more